Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1654 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1654 conjugacy classes of subgroups — too many to draw. Only its 167 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. C2×#19152160 | C2 | semidirect |
| 2. #26029504 | C2 | semidirect |
| 3. #26019203 | C2 | semidirect |
| 4. #26019169 | C2 | semidirect |
| 5. #26018780 | C2 | semidirect |
| 6. #26018579 | C2 | semidirect |
| 7. C89×#2404 | C2 | semidirect |
| 18. #19151737 | C22 | semidirect |
| 19. #19151732 | C22 | semidirect |
| 21. #19151562 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151322 | C22 | semidirect |
| 24. C22×#41×C89 | C22 | semidirect |
| 27. #393×C89 | C22 | semidirect |
| 28. #392×C89 | C22 | semidirect |
| 31. #381×C89 | C22 | semidirect |
| 34. C22×D356 | D4 | semidirect |
| 51. #15667986 | D4 | semidirect |
| 56. C2×C4⋊Dic89 | D4 | semidirect |
| 62. C22⋊#10623494 | C23 | semidirect |
| 67. C22×Q8×C89 | C23 | semidirect |
| 70. C22×D4×C89 | C23 | semidirect |
| 84. #95×C89 | C23 | semidirect |
| 179. C23×C89 | AGL(1,ℤ/8) | semidirect |
| 269. #2404 | D89 | semidirect |
| 274. C89 | #18132 | semidirect |
| 275. C22×#41 | C2×D89 | semidirect |
| 292. #393 | C2×D89 | semidirect |
| 293. #392 | C2×D89 | semidirect |
| 296. #381 | C2×D89 | semidirect |
| 304. C22×Q8 | C22×D89 | semidirect |
| 314. C22×D4 | C22×D89 | semidirect |
| 351. #95 | C22×D89 | semidirect |
| 454. C23 | #15668037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152160 | 2 |
| #26029504 | 2 |
| #26019203 | 2 |
| #26019169 | 2 |
| #26018780 | 2 |
| #26018579 | 2 |
| C89×#2404 | 2 |
| #18132 | 89 |