Order 768.
8078 conjugacy classes of subgroups.
The subgroup lattice has 1864 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C3 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#3558 | C2 | semidirect |
| 2. C3×#3549 | C2 | semidirect |
| 3. C3×#3546 | C2 | semidirect |
| 4. C3×#3546 | C2 | semidirect |
| 5. C3×#3543 | C2 | semidirect |
| 6. C3×#3543 | C2 | semidirect |
| 7. C3×#3542 | C2 | semidirect |
| 8. C3×#3542 | C2 | semidirect |
| 9. C3×#3537 | C2 | semidirect |
| 10. C3×#3532 | C2 | semidirect |
| 11. C3×#3519 | C2 | semidirect |
| 12. C3×#3514 | C2 | semidirect |
| 13. C3×#3508 | C2 | semidirect |
| 14. C3×#3506 | C2 | semidirect |
| 15. C3×#3498 | C2 | semidirect |
| 16. C3×#3498 | C2 | semidirect |
| 17. C3×#3496 | C2 | semidirect |
| 18. C3×#3494 | C2 | semidirect |
| 19. C3×#3488 | C2 | semidirect |
| 20. C3×#3484 | C2 | semidirect |
| 21. C3×#3484 | C2 | semidirect |
| 22. C3×#3475 | C2 | semidirect |
| 23. C3×D4×#41 | C2 | semidirect |
| 24. C2×C3×D42 | C2 | semidirect |
| 25. C3×#3460 | C2 | semidirect |
| 26. C2×C3×#535 | C2 | semidirect |
| 27. #62912 | C3 | direct (N × H) |
| 28. C2×C3×H(5,𝔽2) | C22 | semidirect |
| 29. C2×C3×H(5,𝔽2) | C22 | semidirect |
| 30. C22×C3×#41 | C22 | semidirect |
| 31. C23×C3×D4 | C22 | semidirect |
| 32. C23×C3×D4 | C22 | semidirect |
| 33. C3×#562 | C22 | semidirect |
| 34. C3×H(3,𝔽4) | C22 | semidirect |
| 35. C3×#560 | C22 | semidirect |
| 36. C3×#560 | C22 | semidirect |
| 37. C3×#560 | C22 | semidirect |
| 38. C3×#560 | C22 | semidirect |
| 39. C3×#559 | C22 | semidirect |
| 40. C3×#559 | C22 | semidirect |
| 41. C3×#559 | C22 | semidirect |
| 42. C3×#556 | C22 | semidirect |
| 43. C3×#556 | C22 | semidirect |
| 44. C3×#555 | C22 | semidirect |
| 45. C3×#555 | C22 | semidirect |
| 46. C3×#555 | C22 | semidirect |
| 47. C3×#555 | C22 | semidirect |
| 48. C3×#554 | C22 | semidirect |
| 49. C3×#553 | C22 | semidirect |
| 50. C3×#553 | C22 | semidirect |
| 51. C3×#553 | C22 | semidirect |
| 52. C3×#553 | C22 | semidirect |
| 53. C3×#553 | C22 | semidirect |
| 54. C3×#552 | C22 | semidirect |
| 55. C3×#552 | C22 | semidirect |
| 56. C3×#551 | C22 | semidirect |
| 57. C3×#551 | C22 | semidirect |
| 58. C3×#551 | C22 | semidirect |
| 59. C3×#550 | C22 | semidirect |
| 60. C3×#550 | C22 | semidirect |
| 61. C3×#550 | C22 | semidirect |
| 62. C3×#550 | C22 | semidirect |
| 63. C3×#550 | C22 | semidirect |
| 64. C3×#550 | C22 | semidirect |
| 65. C3×#550 | C22 | semidirect |
| 66. C3×#550 | C22 | semidirect |
| 67. C3×D4×Q8 | C22 | semidirect |
| 68. C3×#548 | C22 | semidirect |
| 69. C3×#548 | C22 | semidirect |
| 70. C3×#547 | C22 | semidirect |
| 71. C3×#547 | C22 | semidirect |
| 72. C3×#547 | C22 | semidirect |
| 73. C3×#547 | C22 | semidirect |
| 74. C3×#547 | C22 | semidirect |
| 75. C3×#546 | C22 | semidirect |
| 76. C3×#546 | C22 | semidirect |
| 77. C3×#546 | C22 | semidirect |
| 78. C3×#546 | C22 | semidirect |
| 79. C3×#546 | C22 | semidirect |
| 80. C3×#546 | C22 | semidirect |
| 81. C3×#546 | C22 | semidirect |
| 82. C3×#546 | C22 | semidirect |
| 83. C3×#546 | C22 | semidirect |
| 84. C3×#546 | C22 | semidirect |
| 85. C3×#546 | C22 | semidirect |
| 86. C3×#546 | C22 | semidirect |
| 87. C3×#546 | C22 | semidirect |
| 88. C3×#546 | C22 | semidirect |
| 89. C3×#546 | C22 | semidirect |
| 90. C3×#546 | C22 | semidirect |
| 91. C3×#546 | C22 | semidirect |
| 92. C3×#546 | C22 | semidirect |
| 93. C3×D42 | C22 | semidirect |
| 94. C3×D42 | C22 | semidirect |
| 95. C3×D42 | C22 | semidirect |
| 96. C3×D42 | C22 | semidirect |
| 97. C3×D42 | C22 | semidirect |
| 98. C3×D42 | C22 | semidirect |
| 99. C3×D42 | C22 | semidirect |
| 100. C3×D42 | C22 | semidirect |
| 101. C3×D42 | C22 | semidirect |
| 102. C3×D42 | C22 | semidirect |
| 103. C3×D42 | C22 | semidirect |
| 104. C3×D42 | C22 | semidirect |
| 105. C3×D42 | C22 | semidirect |
| 106. C3×D42 | C22 | semidirect |
| 107. C3×D42 | C22 | semidirect |
| 108. C3×D42 | C22 | semidirect |
| 109. C3×D42 | C22 | semidirect |
| 110. C3×D42 | C22 | semidirect |
| 111. C3×D42 | C22 | semidirect |
| 112. C3×D42 | C22 | semidirect |
| 113. C3×D42 | C22 | semidirect |
| 114. C3×D42 | C22 | semidirect |
| 115. C3×#544 | C22 | semidirect |
| 116. C3×#542 | C22 | semidirect |
| 117. C3×#542 | C22 | semidirect |
| 118. C3×#542 | C22 | semidirect |
| 119. C3×#542 | C22 | semidirect |
| 120. C3×#540 | C22 | semidirect |
| 121. C3×#540 | C22 | semidirect |
| 122. C3×#540 | C22 | semidirect |
| 123. C3×#540 | C22 | semidirect |
| 124. C3×#540 | C22 | semidirect |
| 125. C3×#540 | C22 | semidirect |
| 126. C3×#538 | C22 | semidirect |
| 127. C3×#538 | C22 | semidirect |
| 128. C3×#538 | C22 | semidirect |
| 129. C3×#538 | C22 | semidirect |
| 130. C3×#538 | C22 | semidirect |
| 131. C3×#538 | C22 | semidirect |
| 132. C3×#538 | C22 | semidirect |
| 133. C3×#537 | C22 | semidirect |
| 134. C3×#537 | C22 | semidirect |
| 135. C3×#537 | C22 | semidirect |
| 136. C3×#535 | C22 | semidirect |
| 137. C3×#535 | C22 | semidirect |
| 138. C3×#535 | C22 | semidirect |
| 139. C3×#535 | C22 | semidirect |
| 140. C3×#535 | C22 | semidirect |
| 141. C3×#535 | C22 | semidirect |
| 142. C3×#535 | C22 | semidirect |
| 143. C3×#535 | C22 | semidirect |
| 144. C3×#535 | C22 | semidirect |
| 145. C3×#535 | C22 | semidirect |
| 146. C3×#535 | C22 | semidirect |
| 147. C3×#535 | C22 | semidirect |
| 148. C3×#535 | C22 | semidirect |
| 149. C3×#535 | C22 | semidirect |
| 150. C3×#535 | C22 | semidirect |
| 151. C3×#535 | C22 | semidirect |
| 152. C3×#535 | C22 | semidirect |
| 153. C3×#534 | C22 | semidirect |
| 154. C3×#534 | C22 | semidirect |
| 155. C3×#534 | C22 | semidirect |
| 156. C3×#534 | C22 | semidirect |
| 157. C3×#534 | C22 | semidirect |
| 158. C3×#533 | C22 | semidirect |
| 159. C3×#532 | C22 | semidirect |
| 160. C3×#532 | C22 | semidirect |
| 161. C3×#532 | C22 | semidirect |
| 162. C3×#532 | C22 | semidirect |
| 163. C3×#532 | C22 | semidirect |
| 164. C3×#532 | C22 | semidirect |
| 165. C3×#532 | C22 | semidirect |
| 166. C3×#532 | C22 | semidirect |
| 167. C2×C3×#127 | C22 | semidirect |
| 168. C2×C3×#127 | C22 | semidirect |
| 169. C2×C3×#127 | C22 | semidirect |
| 170. C3×#529 | C22 | semidirect |
| 171. C3×#529 | C22 | semidirect |
| 172. C3×#529 | C22 | semidirect |
| 173. C3×#529 | C22 | semidirect |
| 174. C3×#529 | C22 | semidirect |
| 175. C2×C3×#124 | C22 | semidirect |
| 176. C3×#525 | C22 | semidirect |
| 177. C3×#525 | C22 | semidirect |
| 178. C3×#525 | C22 | semidirect |
| 179. C3×#525 | C22 | semidirect |
| 180. C3×#525 | C22 | semidirect |
| 181. C3×#525 | C22 | semidirect |
| 182. C2×C3×#121 | C22 | semidirect |
| 183. C2×C3×#121 | C22 | semidirect |
| 184. C2×C3×#121 | C22 | semidirect |
| 185. C2×C3×#121 | C22 | semidirect |
| 186. C2×C3×#121 | C22 | semidirect |
| 187. C2×C3×#120 | C22 | semidirect |
| 188. C2×C3×#120 | C22 | semidirect |
| 189. C2×C3×#120 | C22 | semidirect |
| 190. C3×#520 | C22 | semidirect |
| 191. C3×#518 | C22 | semidirect |
| 192. C3×#518 | C22 | semidirect |
| 193. C3×C4×#41 | C22 | semidirect |
| 194. C3×C4×#41 | C22 | semidirect |
| 195. C3×C4×#41 | C22 | semidirect |
| 196. C2×C3×C4×D4 | C22 | semidirect |
| 197. C2×C3×C4×D4 | C22 | semidirect |
| 198. C2×C3×C4×D4 | C22 | semidirect |
| 199. C2×C3×#117 | C22 | semidirect |
| 200. #3558 | C2×C3 | semidirect |
| 201. #3549 | C2×C3 | semidirect |
| 202. #3546 | C2×C3 | semidirect |
| 203. #3546 | C2×C3 | semidirect |
| 204. #3543 | C2×C3 | semidirect |
| 205. #3543 | C2×C3 | semidirect |
| 206. #3542 | C2×C3 | semidirect |
| 207. #3542 | C2×C3 | semidirect |
| 208. #3537 | C2×C3 | semidirect |
| 209. #3532 | C2×C3 | semidirect |
| 210. #3519 | C2×C3 | semidirect |
| 211. #3514 | C2×C3 | semidirect |
| 212. #3508 | C2×C3 | semidirect |
| 213. #3506 | C2×C3 | semidirect |
| 214. #3498 | C2×C3 | semidirect |
| 215. #3498 | C2×C3 | semidirect |
| 216. #3496 | C2×C3 | semidirect |
| 217. #3494 | C2×C3 | semidirect |
| 218. #3488 | C2×C3 | semidirect |
| 219. #3484 | C2×C3 | semidirect |
| 220. #3484 | C2×C3 | semidirect |
| 221. #3475 | C2×C3 | semidirect |
| 222. D4×#41 | C2×C3 | semidirect |
| 223. C2×D42 | C2×C3 | semidirect |
| 224. #3460 | C2×C3 | semidirect |
| 225. C2×#535 | C2×C3 | semidirect |
| 235. C2×C3×#41 | C23 | semidirect |
| 236. C2×C3×#41 | C23 | semidirect |
| 237. C2×C3×#41 | C23 | semidirect |
| 238. C2×C3×#41 | C23 | semidirect |
| 239. C2×C3×#41 | C23 | semidirect |
| 240. C2×C3×#41 | C23 | semidirect |
| 241. C2×C3×#41 | C23 | semidirect |
| 242. C2×C3×#41 | C23 | semidirect |
| 243. C2×C3×#41 | C23 | semidirect |
| 244. C2×C3×#41 | C23 | semidirect |
| 245. C22×C3×Q8 | C23 | semidirect |
| 265. C22×C3×D4 | C23 | semidirect |
| 266. C22×C3×D4 | C23 | semidirect |
| 267. C22×C3×D4 | C23 | semidirect |
| 268. C22×C3×D4 | C23 | semidirect |
| 269. C22×C3×D4 | C23 | semidirect |
| 270. C22×C3×D4 | C23 | semidirect |
| 271. C22×C3×D4 | C23 | semidirect |
| 272. C22×C3×D4 | C23 | semidirect |
| 273. C22×C3×D4 | C23 | semidirect |
| 274. C22×C3×D4 | C23 | semidirect |
| 277. C23×C3×C4 | C23 | semidirect |
| 278. C3×C4⋊Q8 | C23 | semidirect |
| 279. C3×C4⋊Q8 | C23 | semidirect |
| 280. C3×C4⋊Q8 | C23 | semidirect |
| 281. C3×C4⋊Q8 | C23 | semidirect |
| 282. C3×C4⋊Q8 | C23 | semidirect |
| 283. C3×C4⋊Q8 | C23 | semidirect |
| 292. C3×#127 | C23 | semidirect |
| 293. C3×#127 | C23 | semidirect |
| 294. C3×#127 | C23 | semidirect |
| 295. C3×#127 | C23 | semidirect |
| 296. C3×#127 | C23 | semidirect |
| 297. C3×#127 | C23 | semidirect |
| 298. C3×#127 | C23 | semidirect |
| 299. C3×#127 | C23 | semidirect |
| 300. C3×#126 | C23 | semidirect |
| 301. C3×#126 | C23 | semidirect |
| 302. C3×#126 | C23 | semidirect |
| 303. C3×#126 | C23 | semidirect |
| 304. C3×#126 | C23 | semidirect |
| 305. C3×#126 | C23 | semidirect |
| 306. C3×#126 | C23 | semidirect |
| 307. C3×#126 | C23 | semidirect |
| 308. C3×#125 | C23 | semidirect |
| 309. C3×#125 | C23 | semidirect |
| 310. C3×#125 | C23 | semidirect |
| 311. C3×#125 | C23 | semidirect |
| 312. C3×#125 | C23 | semidirect |
| 317. C3×#124 | C23 | semidirect |
| 318. C3×#124 | C23 | semidirect |
| 319. C3×#124 | C23 | semidirect |
| 320. C3×#124 | C23 | semidirect |
| 321. C3×#124 | C23 | semidirect |
| 322. C3×#124 | C23 | semidirect |
| 323. C3×#124 | C23 | semidirect |
| 324. C3×#124 | C23 | semidirect |
| 325. C3×#124 | C23 | semidirect |
| 326. C3×#124 | C23 | semidirect |
| 327. C3×#124 | C23 | semidirect |
| 328. C3×#124 | C23 | semidirect |
| 329. C3×#124 | C23 | semidirect |
| 330. C3×#124 | C23 | semidirect |
| 331. C3×#124 | C23 | semidirect |
| 335. C3×#123 | C23 | semidirect |
| 336. C3×#123 | C23 | semidirect |
| 337. C3×#123 | C23 | semidirect |
| 338. C3×#123 | C23 | semidirect |
| 339. C3×#123 | C23 | semidirect |
| 340. C3×#123 | C23 | semidirect |
| 341. C3×#123 | C23 | semidirect |
| 342. C3×#123 | C23 | semidirect |
| 343. C3×#123 | C23 | semidirect |
| 344. C3×#123 | C23 | semidirect |
| 345. C3×#123 | C23 | semidirect |
| 346. C3×#123 | C23 | semidirect |
| 347. C3×#123 | C23 | semidirect |
| 348. C3×#123 | C23 | semidirect |
| 349. C3×#123 | C23 | semidirect |
| 350. C3×#123 | C23 | semidirect |
| 351. C3×#123 | C23 | semidirect |
| 352. C3×#123 | C23 | semidirect |
| 353. C3×#123 | C23 | semidirect |
| 357. C3×C22⋊Q8 | C23 | semidirect |
| 358. C3×C22⋊Q8 | C23 | semidirect |
| 359. C3×C22⋊Q8 | C23 | semidirect |
| 360. C3×C22⋊Q8 | C23 | semidirect |
| 361. C3×C22⋊Q8 | C23 | semidirect |
| 362. C3×C22⋊Q8 | C23 | semidirect |
| 363. C3×C22⋊Q8 | C23 | semidirect |
| 364. C3×C22⋊Q8 | C23 | semidirect |
| 365. C3×C22⋊Q8 | C23 | semidirect |
| 366. C3×C22⋊Q8 | C23 | semidirect |
| 367. C3×C22⋊Q8 | C23 | semidirect |
| 368. C3×C22⋊Q8 | C23 | semidirect |
| 369. C3×C22⋊Q8 | C23 | semidirect |
| 370. C3×C22⋊Q8 | C23 | semidirect |
| 391. C3×#121 | C23 | semidirect |
| 392. C3×#121 | C23 | semidirect |
| 393. C3×#121 | C23 | semidirect |
| 394. C3×#121 | C23 | semidirect |
| 395. C3×#121 | C23 | semidirect |
| 396. C3×#121 | C23 | semidirect |
| 397. C3×#121 | C23 | semidirect |
| 398. C3×#121 | C23 | semidirect |
| 399. C3×#121 | C23 | semidirect |
| 400. C3×#121 | C23 | semidirect |
| 401. C3×#121 | C23 | semidirect |
| 402. C3×#121 | C23 | semidirect |
| 403. C3×#121 | C23 | semidirect |
| 404. C3×#121 | C23 | semidirect |
| 405. C3×#121 | C23 | semidirect |
| 406. C3×#121 | C23 | semidirect |
| 407. C3×#121 | C23 | semidirect |
| 408. C3×#121 | C23 | semidirect |
| 409. C3×#121 | C23 | semidirect |
| 410. C3×#121 | C23 | semidirect |
| 411. C3×#121 | C23 | semidirect |
| 412. C3×#121 | C23 | semidirect |
| 413. C3×#121 | C23 | semidirect |
| 414. C3×#121 | C23 | semidirect |
| 415. C3×#121 | C23 | semidirect |
| 416. C3×#121 | C23 | semidirect |
| 417. C3×#121 | C23 | semidirect |
| 418. C3×#121 | C23 | semidirect |
| 419. C3×#121 | C23 | semidirect |
| 420. C3×#121 | C23 | semidirect |
| 421. C3×#121 | C23 | semidirect |
| 422. C3×#121 | C23 | semidirect |
| 423. C3×#121 | C23 | semidirect |
| 424. C3×#121 | C23 | semidirect |
| 425. C3×#121 | C23 | semidirect |
| 426. C3×#121 | C23 | semidirect |
| 427. C3×#121 | C23 | semidirect |
| 428. C3×#121 | C23 | semidirect |
| 429. C3×#121 | C23 | semidirect |
| 430. C3×#121 | C23 | semidirect |
| 431. C3×#121 | C23 | semidirect |
| 432. C3×#121 | C23 | semidirect |
| 445. C3×#120 | C23 | semidirect |
| 446. C3×#120 | C23 | semidirect |
| 447. C3×#120 | C23 | semidirect |
| 448. C3×#120 | C23 | semidirect |
| 449. C3×#120 | C23 | semidirect |
| 450. C3×#120 | C23 | semidirect |
| 451. C3×#120 | C23 | semidirect |
| 452. C3×#120 | C23 | semidirect |
| 453. C3×#120 | C23 | semidirect |
| 454. C3×#120 | C23 | semidirect |
| 455. C3×#120 | C23 | semidirect |
| 456. C3×#120 | C23 | semidirect |
| 457. C3×#120 | C23 | semidirect |
| 458. C3×#120 | C23 | semidirect |
| 459. C3×#120 | C23 | semidirect |
| 460. C3×#120 | C23 | semidirect |
| 461. C3×C4×Q8 | C23 | semidirect |
| 462. C3×C4×Q8 | C23 | semidirect |
| 463. C3×C4×Q8 | C23 | semidirect |
| 464. C3×C4×Q8 | C23 | semidirect |
| 465. C3×C4×Q8 | C23 | semidirect |
| 466. C3×C4×Q8 | C23 | semidirect |
| 467. C3×C4×Q8 | C23 | semidirect |
| 468. C3×C4×Q8 | C23 | semidirect |
| 486. C3×C4×D4 | C23 | semidirect |
| 487. C3×C4×D4 | C23 | semidirect |
| 488. C3×C4×D4 | C23 | semidirect |
| 489. C3×C4×D4 | C23 | semidirect |
| 490. C3×C4×D4 | C23 | semidirect |
| 491. C3×C4×D4 | C23 | semidirect |
| 492. C3×C4×D4 | C23 | semidirect |
| 493. C3×C4×D4 | C23 | semidirect |
| 494. C3×C4×D4 | C23 | semidirect |
| 495. C3×C4×D4 | C23 | semidirect |
| 496. C3×C4×D4 | C23 | semidirect |
| 497. C3×C4×D4 | C23 | semidirect |
| 498. C3×C4×D4 | C23 | semidirect |
| 499. C3×C4×D4 | C23 | semidirect |
| 500. C3×C4×D4 | C23 | semidirect |
| 501. C3×C4×D4 | C23 | semidirect |
| 502. C3×C4×D4 | C23 | semidirect |
| 503. C3×C4×D4 | C23 | semidirect |
| 504. C3×C4×D4 | C23 | semidirect |
| 505. C3×C4×D4 | C23 | semidirect |
| 506. C3×C4×D4 | C23 | semidirect |
| 507. C3×C4×D4 | C23 | semidirect |
| 508. C3×C4×D4 | C23 | semidirect |
| 509. C3×C4×D4 | C23 | semidirect |
| 510. C3×C4×D4 | C23 | semidirect |
| 511. C3×C4×D4 | C23 | semidirect |
| 512. C3×C4×D4 | C23 | semidirect |
| 513. C3×C4×D4 | C23 | semidirect |
| 514. C3×C4×D4 | C23 | semidirect |
| 519. C3×#117 | C23 | semidirect |
| 520. C3×#117 | C23 | semidirect |
| 521. C3×#117 | C23 | semidirect |
| 522. C3×#117 | C23 | semidirect |
| 523. C3×#117 | C23 | semidirect |
| 524. C3×#117 | C23 | semidirect |
| 525. C3×#117 | C23 | semidirect |
| 526. C3×#117 | C23 | semidirect |
| 527. C3×#117 | C23 | semidirect |
| 528. C3×#117 | C23 | semidirect |
| 529. C3×#117 | C23 | semidirect |
| 532. C2×C3×C4⋊C4 | C23 | semidirect |
| 533. C2×C3×C4⋊C4 | C23 | semidirect |
| 534. C2×C3×C4⋊C4 | C23 | semidirect |
| 535. C2×C3×C4⋊C4 | C23 | semidirect |
| 541. C2×C3×C22⋊C4 | C23 | semidirect |
| 542. C2×C3×C22⋊C4 | C23 | semidirect |
| 543. C2×C3×C22⋊C4 | C23 | semidirect |
| 544. C2×C3×C22⋊C4 | C23 | semidirect |
| 545. C2×C3×C22⋊C4 | C23 | semidirect |
| 546. C2×C3×C22⋊C4 | C23 | semidirect |
| 548. C2×C3×C42 | C23 | semidirect |
| 549. C2×C3×C42 | C23 | semidirect |
| 550. C2×C3×C42 | C23 | semidirect |
| 551. C2×H(5,𝔽2) | C22×C3 | semidirect |
| 552. C2×H(5,𝔽2) | C22×C3 | semidirect |
| 553. C22×#41 | C22×C3 | semidirect |
| 554. C23×D4 | C22×C3 | semidirect |
| 555. C23×D4 | C22×C3 | semidirect |
| 556. #562 | C22×C3 | semidirect |
| 557. H(3,𝔽4) | C22×C3 | semidirect |
| 558. #560 | C22×C3 | semidirect |
| 559. #560 | C22×C3 | semidirect |
| 560. #560 | C22×C3 | semidirect |
| 561. #560 | C22×C3 | semidirect |
| 562. #559 | C22×C3 | semidirect |
| 563. #559 | C22×C3 | semidirect |
| 564. #559 | C22×C3 | semidirect |
| 565. #556 | C22×C3 | semidirect |
| 566. #556 | C22×C3 | semidirect |
| 567. #555 | C22×C3 | semidirect |
| 568. #555 | C22×C3 | semidirect |
| 569. #555 | C22×C3 | semidirect |
| 570. #555 | C22×C3 | semidirect |
| 571. #554 | C22×C3 | semidirect |
| 572. #553 | C22×C3 | semidirect |
| 573. #553 | C22×C3 | semidirect |
| 574. #553 | C22×C3 | semidirect |
| 575. #553 | C22×C3 | semidirect |
| 576. #553 | C22×C3 | semidirect |
| 577. #552 | C22×C3 | semidirect |
| 578. #552 | C22×C3 | semidirect |
| 579. #551 | C22×C3 | semidirect |
| 580. #551 | C22×C3 | semidirect |
| 581. #551 | C22×C3 | semidirect |
| 582. #550 | C22×C3 | semidirect |
| 583. #550 | C22×C3 | semidirect |
| 584. #550 | C22×C3 | semidirect |
| 585. #550 | C22×C3 | semidirect |
| 586. #550 | C22×C3 | semidirect |
| 587. #550 | C22×C3 | semidirect |
| 588. #550 | C22×C3 | semidirect |
| 589. #550 | C22×C3 | semidirect |
| 590. D4×Q8 | C22×C3 | semidirect |
| 591. #548 | C22×C3 | semidirect |
| 592. #548 | C22×C3 | semidirect |
| 593. #547 | C22×C3 | semidirect |
| 594. #547 | C22×C3 | semidirect |
| 595. #547 | C22×C3 | semidirect |
| 596. #547 | C22×C3 | semidirect |
| 597. #547 | C22×C3 | semidirect |
| 598. #546 | C22×C3 | semidirect |
| 599. #546 | C22×C3 | semidirect |
| 600. #546 | C22×C3 | semidirect |
| 601. #546 | C22×C3 | semidirect |
| 602. #546 | C22×C3 | semidirect |
| 603. #546 | C22×C3 | semidirect |
| 604. #546 | C22×C3 | semidirect |
| 605. #546 | C22×C3 | semidirect |
| 606. #546 | C22×C3 | semidirect |
| 607. #546 | C22×C3 | semidirect |
| 608. #546 | C22×C3 | semidirect |
| 609. #546 | C22×C3 | semidirect |
| 610. #546 | C22×C3 | semidirect |
| 611. #546 | C22×C3 | semidirect |
| 612. #546 | C22×C3 | semidirect |
| 613. #546 | C22×C3 | semidirect |
| 614. #546 | C22×C3 | semidirect |
| 615. #546 | C22×C3 | semidirect |
| 616. D42 | C22×C3 | semidirect |
| 617. D42 | C22×C3 | semidirect |
| 618. D42 | C22×C3 | semidirect |
| 619. D42 | C22×C3 | semidirect |
| 620. D42 | C22×C3 | semidirect |
| 621. D42 | C22×C3 | semidirect |
| 622. D42 | C22×C3 | semidirect |
| 623. D42 | C22×C3 | semidirect |
| 624. D42 | C22×C3 | semidirect |
| 625. D42 | C22×C3 | semidirect |
| 626. D42 | C22×C3 | semidirect |
| 627. D42 | C22×C3 | semidirect |
| 628. D42 | C22×C3 | semidirect |
| 629. D42 | C22×C3 | semidirect |
| 630. D42 | C22×C3 | semidirect |
| 631. D42 | C22×C3 | semidirect |
| 632. D42 | C22×C3 | semidirect |
| 633. D42 | C22×C3 | semidirect |
| 634. D42 | C22×C3 | semidirect |
| 635. D42 | C22×C3 | semidirect |
| 636. D42 | C22×C3 | semidirect |
| 637. D42 | C22×C3 | semidirect |
| 638. #544 | C22×C3 | semidirect |
| 639. #542 | C22×C3 | semidirect |
| 640. #542 | C22×C3 | semidirect |
| 641. #542 | C22×C3 | semidirect |
| 642. #542 | C22×C3 | semidirect |
| 643. #540 | C22×C3 | semidirect |
| 644. #540 | C22×C3 | semidirect |
| 645. #540 | C22×C3 | semidirect |
| 646. #540 | C22×C3 | semidirect |
| 647. #540 | C22×C3 | semidirect |
| 648. #540 | C22×C3 | semidirect |
| 649. #538 | C22×C3 | semidirect |
| 650. #538 | C22×C3 | semidirect |
| 651. #538 | C22×C3 | semidirect |
| 652. #538 | C22×C3 | semidirect |
| 653. #538 | C22×C3 | semidirect |
| 654. #538 | C22×C3 | semidirect |
| 655. #538 | C22×C3 | semidirect |
| 656. #537 | C22×C3 | semidirect |
| 657. #537 | C22×C3 | semidirect |
| 658. #537 | C22×C3 | semidirect |
| 659. #535 | C22×C3 | semidirect |
| 660. #535 | C22×C3 | semidirect |
| 661. #535 | C22×C3 | semidirect |
| 662. #535 | C22×C3 | semidirect |
| 663. #535 | C22×C3 | semidirect |
| 664. #535 | C22×C3 | semidirect |
| 665. #535 | C22×C3 | semidirect |
| 666. #535 | C22×C3 | semidirect |
| 667. #535 | C22×C3 | semidirect |
| 668. #535 | C22×C3 | semidirect |
| 669. #535 | C22×C3 | semidirect |
| 670. #535 | C22×C3 | semidirect |
| 671. #535 | C22×C3 | semidirect |
| 672. #535 | C22×C3 | semidirect |
| 673. #535 | C22×C3 | semidirect |
| 674. #535 | C22×C3 | semidirect |
| 675. #535 | C22×C3 | semidirect |
| 676. #534 | C22×C3 | semidirect |
| 677. #534 | C22×C3 | semidirect |
| 678. #534 | C22×C3 | semidirect |
| 679. #534 | C22×C3 | semidirect |
| 680. #534 | C22×C3 | semidirect |
| 681. #533 | C22×C3 | semidirect |
| 682. #532 | C22×C3 | semidirect |
| 683. #532 | C22×C3 | semidirect |
| 684. #532 | C22×C3 | semidirect |
| 685. #532 | C22×C3 | semidirect |
| 686. #532 | C22×C3 | semidirect |
| 687. #532 | C22×C3 | semidirect |
| 688. #532 | C22×C3 | semidirect |
| 689. #532 | C22×C3 | semidirect |
| 690. C2×#127 | C22×C3 | semidirect |
| 691. C2×#127 | C22×C3 | semidirect |
| 692. C2×#127 | C22×C3 | semidirect |
| 693. #529 | C22×C3 | semidirect |
| 694. #529 | C22×C3 | semidirect |
| 695. #529 | C22×C3 | semidirect |
| 696. #529 | C22×C3 | semidirect |
| 697. #529 | C22×C3 | semidirect |
| 698. C2×#124 | C22×C3 | semidirect |
| 699. #525 | C22×C3 | semidirect |
| 700. #525 | C22×C3 | semidirect |
| 701. #525 | C22×C3 | semidirect |
| 702. #525 | C22×C3 | semidirect |
| 703. #525 | C22×C3 | semidirect |
| 704. #525 | C22×C3 | semidirect |
| 705. C2×#121 | C22×C3 | semidirect |
| 706. C2×#121 | C22×C3 | semidirect |
| 707. C2×#121 | C22×C3 | semidirect |
| 708. C2×#121 | C22×C3 | semidirect |
| 709. C2×#121 | C22×C3 | semidirect |
| 710. C2×#120 | C22×C3 | semidirect |
| 711. C2×#120 | C22×C3 | semidirect |
| 712. C2×#120 | C22×C3 | semidirect |
| 713. #520 | C22×C3 | semidirect |
| 714. #518 | C22×C3 | semidirect |
| 715. #518 | C22×C3 | semidirect |
| 716. C4×#41 | C22×C3 | semidirect |
| 717. C4×#41 | C22×C3 | semidirect |
| 718. C4×#41 | C22×C3 | semidirect |
| 719. C2×C4×D4 | C22×C3 | semidirect |
| 720. C2×C4×D4 | C22×C3 | semidirect |
| 721. C2×C4×D4 | C22×C3 | semidirect |
| 722. C2×#117 | C22×C3 | semidirect |
| 953. C2×#41 | C23×C3 | semidirect |
| 954. C2×#41 | C23×C3 | semidirect |
| 955. C2×#41 | C23×C3 | semidirect |
| 956. C2×#41 | C23×C3 | semidirect |
| 957. C2×#41 | C23×C3 | semidirect |
| 958. C2×#41 | C23×C3 | semidirect |
| 959. C2×#41 | C23×C3 | semidirect |
| 960. C2×#41 | C23×C3 | semidirect |
| 961. C2×#41 | C23×C3 | semidirect |
| 962. C2×#41 | C23×C3 | semidirect |
| 963. C22×Q8 | C23×C3 | semidirect |
| 983. C22×D4 | C23×C3 | semidirect |
| 984. C22×D4 | C23×C3 | semidirect |
| 985. C22×D4 | C23×C3 | semidirect |
| 986. C22×D4 | C23×C3 | semidirect |
| 987. C22×D4 | C23×C3 | semidirect |
| 988. C22×D4 | C23×C3 | semidirect |
| 989. C22×D4 | C23×C3 | semidirect |
| 990. C22×D4 | C23×C3 | semidirect |
| 991. C22×D4 | C23×C3 | semidirect |
| 992. C22×D4 | C23×C3 | semidirect |
| 995. C23×C4 | C23×C3 | semidirect |
| 996. C4⋊Q8 | C23×C3 | semidirect |
| 997. C4⋊Q8 | C23×C3 | semidirect |
| 998. C4⋊Q8 | C23×C3 | semidirect |
| 999. C4⋊Q8 | C23×C3 | semidirect |
| 1000. C4⋊Q8 | C23×C3 | semidirect |
| 1001. C4⋊Q8 | C23×C3 | semidirect |
| 1010. #127 | C23×C3 | semidirect |
| 1011. #127 | C23×C3 | semidirect |
| 1012. #127 | C23×C3 | semidirect |
| 1013. #127 | C23×C3 | semidirect |
| 1014. #127 | C23×C3 | semidirect |
| 1015. #127 | C23×C3 | semidirect |
| 1016. #127 | C23×C3 | semidirect |
| 1017. #127 | C23×C3 | semidirect |
| 1018. #126 | C23×C3 | semidirect |
| 1019. #126 | C23×C3 | semidirect |
| 1020. #126 | C23×C3 | semidirect |
| 1021. #126 | C23×C3 | semidirect |
| 1022. #126 | C23×C3 | semidirect |
| 1023. #126 | C23×C3 | semidirect |
| 1024. #126 | C23×C3 | semidirect |
| 1025. #126 | C23×C3 | semidirect |
| 1026. #125 | C23×C3 | semidirect |
| 1027. #125 | C23×C3 | semidirect |
| 1028. #125 | C23×C3 | semidirect |
| 1029. #125 | C23×C3 | semidirect |
| 1030. #125 | C23×C3 | semidirect |
| 1035. #124 | C23×C3 | semidirect |
| 1036. #124 | C23×C3 | semidirect |
| 1037. #124 | C23×C3 | semidirect |
| 1038. #124 | C23×C3 | semidirect |
| 1039. #124 | C23×C3 | semidirect |
| 1040. #124 | C23×C3 | semidirect |
| 1041. #124 | C23×C3 | semidirect |
| 1042. #124 | C23×C3 | semidirect |
| 1043. #124 | C23×C3 | semidirect |
| 1044. #124 | C23×C3 | semidirect |
| 1045. #124 | C23×C3 | semidirect |
| 1046. #124 | C23×C3 | semidirect |
| 1047. #124 | C23×C3 | semidirect |
| 1048. #124 | C23×C3 | semidirect |
| 1049. #124 | C23×C3 | semidirect |
| 1053. #123 | C23×C3 | semidirect |
| 1054. #123 | C23×C3 | semidirect |
| 1055. #123 | C23×C3 | semidirect |
| 1056. #123 | C23×C3 | semidirect |
| 1057. #123 | C23×C3 | semidirect |
| 1058. #123 | C23×C3 | semidirect |
| 1059. #123 | C23×C3 | semidirect |
| 1060. #123 | C23×C3 | semidirect |
| 1061. #123 | C23×C3 | semidirect |
| 1062. #123 | C23×C3 | semidirect |
| 1063. #123 | C23×C3 | semidirect |
| 1064. #123 | C23×C3 | semidirect |
| 1065. #123 | C23×C3 | semidirect |
| 1066. #123 | C23×C3 | semidirect |
| 1067. #123 | C23×C3 | semidirect |
| 1068. #123 | C23×C3 | semidirect |
| 1069. #123 | C23×C3 | semidirect |
| 1070. #123 | C23×C3 | semidirect |
| 1071. #123 | C23×C3 | semidirect |
| 1075. C22⋊Q8 | C23×C3 | semidirect |
| 1076. C22⋊Q8 | C23×C3 | semidirect |
| 1077. C22⋊Q8 | C23×C3 | semidirect |
| 1078. C22⋊Q8 | C23×C3 | semidirect |
| 1079. C22⋊Q8 | C23×C3 | semidirect |
| 1080. C22⋊Q8 | C23×C3 | semidirect |
| 1081. C22⋊Q8 | C23×C3 | semidirect |
| 1082. C22⋊Q8 | C23×C3 | semidirect |
| 1083. C22⋊Q8 | C23×C3 | semidirect |
| 1084. C22⋊Q8 | C23×C3 | semidirect |
| 1085. C22⋊Q8 | C23×C3 | semidirect |
| 1086. C22⋊Q8 | C23×C3 | semidirect |
| 1087. C22⋊Q8 | C23×C3 | semidirect |
| 1088. C22⋊Q8 | C23×C3 | semidirect |
| 1109. #121 | C23×C3 | semidirect |
| 1110. #121 | C23×C3 | semidirect |
| 1111. #121 | C23×C3 | semidirect |
| 1112. #121 | C23×C3 | semidirect |
| 1113. #121 | C23×C3 | semidirect |
| 1114. #121 | C23×C3 | semidirect |
| 1115. #121 | C23×C3 | semidirect |
| 1116. #121 | C23×C3 | semidirect |
| 1117. #121 | C23×C3 | semidirect |
| 1118. #121 | C23×C3 | semidirect |
| 1119. #121 | C23×C3 | semidirect |
| 1120. #121 | C23×C3 | semidirect |
| 1121. #121 | C23×C3 | semidirect |
| 1122. #121 | C23×C3 | semidirect |
| 1123. #121 | C23×C3 | semidirect |
| 1124. #121 | C23×C3 | semidirect |
| 1125. #121 | C23×C3 | semidirect |
| 1126. #121 | C23×C3 | semidirect |
| 1127. #121 | C23×C3 | semidirect |
| 1128. #121 | C23×C3 | semidirect |
| 1129. #121 | C23×C3 | semidirect |
| 1130. #121 | C23×C3 | semidirect |
| 1131. #121 | C23×C3 | semidirect |
| 1132. #121 | C23×C3 | semidirect |
| 1133. #121 | C23×C3 | semidirect |
| 1134. #121 | C23×C3 | semidirect |
| 1135. #121 | C23×C3 | semidirect |
| 1136. #121 | C23×C3 | semidirect |
| 1137. #121 | C23×C3 | semidirect |
| 1138. #121 | C23×C3 | semidirect |
| 1139. #121 | C23×C3 | semidirect |
| 1140. #121 | C23×C3 | semidirect |
| 1141. #121 | C23×C3 | semidirect |
| 1142. #121 | C23×C3 | semidirect |
| 1143. #121 | C23×C3 | semidirect |
| 1144. #121 | C23×C3 | semidirect |
| 1145. #121 | C23×C3 | semidirect |
| 1146. #121 | C23×C3 | semidirect |
| 1147. #121 | C23×C3 | semidirect |
| 1148. #121 | C23×C3 | semidirect |
| 1149. #121 | C23×C3 | semidirect |
| 1150. #121 | C23×C3 | semidirect |
| 1163. #120 | C23×C3 | semidirect |
| 1164. #120 | C23×C3 | semidirect |
| 1165. #120 | C23×C3 | semidirect |
| 1166. #120 | C23×C3 | semidirect |
| 1167. #120 | C23×C3 | semidirect |
| 1168. #120 | C23×C3 | semidirect |
| 1169. #120 | C23×C3 | semidirect |
| 1170. #120 | C23×C3 | semidirect |
| 1171. #120 | C23×C3 | semidirect |
| 1172. #120 | C23×C3 | semidirect |
| 1173. #120 | C23×C3 | semidirect |
| 1174. #120 | C23×C3 | semidirect |
| 1175. #120 | C23×C3 | semidirect |
| 1176. #120 | C23×C3 | semidirect |
| 1177. #120 | C23×C3 | semidirect |
| 1178. #120 | C23×C3 | semidirect |
| 1179. C4×Q8 | C23×C3 | semidirect |
| 1180. C4×Q8 | C23×C3 | semidirect |
| 1181. C4×Q8 | C23×C3 | semidirect |
| 1182. C4×Q8 | C23×C3 | semidirect |
| 1183. C4×Q8 | C23×C3 | semidirect |
| 1184. C4×Q8 | C23×C3 | semidirect |
| 1185. C4×Q8 | C23×C3 | semidirect |
| 1186. C4×Q8 | C23×C3 | semidirect |
| 1204. C4×D4 | C23×C3 | semidirect |
| 1205. C4×D4 | C23×C3 | semidirect |
| 1206. C4×D4 | C23×C3 | semidirect |
| 1207. C4×D4 | C23×C3 | semidirect |
| 1208. C4×D4 | C23×C3 | semidirect |
| 1209. C4×D4 | C23×C3 | semidirect |
| 1210. C4×D4 | C23×C3 | semidirect |
| 1211. C4×D4 | C23×C3 | semidirect |
| 1212. C4×D4 | C23×C3 | semidirect |
| 1213. C4×D4 | C23×C3 | semidirect |
| 1214. C4×D4 | C23×C3 | semidirect |
| 1215. C4×D4 | C23×C3 | semidirect |
| 1216. C4×D4 | C23×C3 | semidirect |
| 1217. C4×D4 | C23×C3 | semidirect |
| 1218. C4×D4 | C23×C3 | semidirect |
| 1219. C4×D4 | C23×C3 | semidirect |
| 1220. C4×D4 | C23×C3 | semidirect |
| 1221. C4×D4 | C23×C3 | semidirect |
| 1222. C4×D4 | C23×C3 | semidirect |
| 1223. C4×D4 | C23×C3 | semidirect |
| 1224. C4×D4 | C23×C3 | semidirect |
| 1225. C4×D4 | C23×C3 | semidirect |
| 1226. C4×D4 | C23×C3 | semidirect |
| 1227. C4×D4 | C23×C3 | semidirect |
| 1228. C4×D4 | C23×C3 | semidirect |
| 1229. C4×D4 | C23×C3 | semidirect |
| 1230. C4×D4 | C23×C3 | semidirect |
| 1231. C4×D4 | C23×C3 | semidirect |
| 1232. C4×D4 | C23×C3 | semidirect |
| 1237. #117 | C23×C3 | semidirect |
| 1238. #117 | C23×C3 | semidirect |
| 1239. #117 | C23×C3 | semidirect |
| 1240. #117 | C23×C3 | semidirect |
| 1241. #117 | C23×C3 | semidirect |
| 1242. #117 | C23×C3 | semidirect |
| 1243. #117 | C23×C3 | semidirect |
| 1244. #117 | C23×C3 | semidirect |
| 1245. #117 | C23×C3 | semidirect |
| 1246. #117 | C23×C3 | semidirect |
| 1247. #117 | C23×C3 | semidirect |
| 1250. C2×C4⋊C4 | C23×C3 | semidirect |
| 1251. C2×C4⋊C4 | C23×C3 | semidirect |
| 1252. C2×C4⋊C4 | C23×C3 | semidirect |
| 1253. C2×C4⋊C4 | C23×C3 | semidirect |
| 1259. C2×C22⋊C4 | C23×C3 | semidirect |
| 1260. C2×C22⋊C4 | C23×C3 | semidirect |
| 1261. C2×C22⋊C4 | C23×C3 | semidirect |
| 1262. C2×C22⋊C4 | C23×C3 | semidirect |
| 1263. C2×C22⋊C4 | C23×C3 | semidirect |
| 1264. C2×C22⋊C4 | C23×C3 | semidirect |
| 1266. C2×C42 | C23×C3 | semidirect |
| 1267. C2×C42 | C23×C3 | semidirect |
| 1268. C2×C42 | C23×C3 | semidirect |
| 1348. C3×D4 | H(5,𝔽2) | semidirect |
| 1375. C2×C3×C4 | H(5,𝔽2) | semidirect |
| 1744. D4 | C3×H(5,𝔽2) | semidirect |
| 1771. C2×C4 | C3×H(5,𝔽2) | semidirect |
| 1851. C3 | #62912 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.