Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
410 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×ΓL(1,𝔽16) | C2 | semidirect |
| 2. C2×D3×ΓL(1,𝔽16) | C2 | semidirect |
| 4. #10624098 | C2 | semidirect |
| 5. Dic3⋊ΓL(1,𝔽16) | C2 | semidirect |
| 6. (C2×D3)⋊ΓL(1,𝔽16) | C2 | semidirect |
| 7. Dic3×ΓL(1,𝔽16) | C2 | semidirect |
| 18. C3×#1220 | C4 | semidirect |
| 19. C3×C5×#67 | C4 | semidirect |
| 20. C3×#1202 | C4 | semidirect |
| 21. C3×#1201 | C4 | semidirect |
| 25. C22×ΓL(1,𝔽16) | D3 | semidirect |
| 39. C22×C32×C5 | C2×C4 | semidirect |
| 40. C2×C3×D15 | C2×C4 | semidirect |
| 41. C2×C3×C5×D3 | C2×C4 | semidirect |
| 44. C2×C32×D5 | C2×C4 | semidirect |
| 51. C3×ΓL(1,𝔽16) | D4 | semidirect |
| 52. C3×Dic15 | C2×C4 | semidirect |
| 53. C3×C5×Dic3 | C2×C4 | semidirect |
| 82. #1220 | Dic3 | semidirect |
| 83. C5×#67 | Dic3 | semidirect |
| 88. #1202 | Dic3 | semidirect |
| 89. #1201 | Dic3 | semidirect |
| 114. C3×#67 | AGL(1,𝔽5) | semidirect |
| 122. C22×C3×C5 | C4×D3 | semidirect |
| 123. C22×C3×C5 | C2×Dic3 | semidirect |
| 124. C2×D15 | C2×Dic3 | semidirect |
| 125. C2×C5×D3 | C2×Dic3 | semidirect |
| 137. C2×C3×D5 | C4×D3 | semidirect |
| 138. C2×C3×D5 | C2×Dic3 | semidirect |
| 150. ΓL(1,𝔽16) | #67 | direct (N × H) |
| 154. Dic15 | C2×Dic3 | semidirect |
| 156. C5×Dic3 | C2×Dic3 | semidirect |
| 172. C32×C5 | C4×D4 | semidirect |
| 190. C22×C32 | C2×AGL(1,𝔽5) | semidirect |
| 194. C2×C3×D3 | C2×AGL(1,𝔽5) | semidirect |
| 200. C3×Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 237. #67 | ΓL(1,𝔽16) | direct (N × H) |
| 251. C22×C5 | D3×Dic3 | semidirect |
| 257. C2×D5 | D3×Dic3 | semidirect |
| 280. C3×C5 | C4×#67 | semidirect |
| 281. C3×C5 | D4×Dic3 | semidirect |
| 299. C22×C3 | D3×AGL(1,𝔽5) | semidirect |
| 300. C22×C3 | C2×ΓL(1,𝔽16) | semidirect |
| 304. C2×D3 | C2×ΓL(1,𝔽16) | semidirect |
| 318. Dic3 | C2×ΓL(1,𝔽16) | semidirect |
| 326. C32 | D4×AGL(1,𝔽5) | semidirect |
| 359. C5 | Dic3×#67 | semidirect |
| 368. C22 | D3×ΓL(1,𝔽16) | semidirect |
| 376. C3 | AGL(1,𝔽5)×#67 | semidirect |
| 377. C3 | D4×ΓL(1,𝔽16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×ΓL(1,𝔽16) | 2 |
| C2×D3×ΓL(1,𝔽16) | 2 |
| C3×D5×#67 | 2 |
| #10624098 | 2 |
| Dic3⋊ΓL(1,𝔽16) | 2 |
| (C2×D3)⋊ΓL(1,𝔽16) | 2 |
| Dic3×ΓL(1,𝔽16) | 2 |
| D4×ΓL(1,𝔽16) | 3 |
| AGL(1,𝔽5)×#67 | 3 |
| Dic3×#67 | 5 |