Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26033385 | C2 | semidirect |
| 2. #26022565 | C2 | semidirect |
| 3. #26022352 | C2 | semidirect |
| 4. #26018440 | C2 | semidirect |
| 5. #26018439 | C2 | semidirect |
| 6. #26018391 | C2 | semidirect |
| 7. C89×#2263 | C2 | semidirect |
| 19. #19151432 | C22 | semidirect |
| 20. #19151426 | C22 | semidirect |
| 23. C2×D16×C89 | C22 | semidirect |
| 26. M64×C89 | C22 | semidirect |
| 38. Dic712 | D4 | semidirect |
| 43. D1424 | D4 | semidirect |
| 53. Q32×C89 | D4 | semidirect |
| 57. D16×C89 | D4 | semidirect |
| 147. #2263 | D89 | semidirect |
| 152. C89 | #13667 | semidirect |
| 161. C2×D16 | C2×D89 | semidirect |
| 169. M64 | C2×D89 | semidirect |
| 187. Q32 | C22⋊D89 | semidirect |
| 196. D16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033385 | 2 |
| #26022565 | 2 |
| #26022352 | 2 |
| #26018440 | 2 |
| #26018439 | 2 |
| #26018391 | 2 |
| C89×#2263 | 2 |
| #13667 | 89 |