Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1122 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 183 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. #26035026 | C2 | semidirect |
| 2. C2×#19152034 | C2 | semidirect |
| 3. #26022197 | C2 | semidirect |
| 4. #26021987 | C2 | semidirect |
| 5. #26021873 | C2 | semidirect |
| 6. C89×#3058 | C2 | semidirect |
| 12. #19152398 | C22 | semidirect |
| 16. #19152034 | C22 | semidirect |
| 19. C2×#15667952 | C22 | semidirect |
| 20. #19151407 | C22 | semidirect |
| 21. #19151380 | C22 | semidirect |
| 22. C22×D8×C89 | C22 | semidirect |
| 25. #469×C89 | C22 | semidirect |
| 27. #427×C89 | C22 | semidirect |
| 46. #15668034 | D4 | semidirect |
| 49. C2×Dic356 | D4 | semidirect |
| 53. C2×D712 | D4 | semidirect |
| 205. #3058 | D89 | semidirect |
| 209. C89 | #33531 | semidirect |
| 218. C22×D8 | C2×D89 | semidirect |
| 226. #469 | C2×D89 | semidirect |
| 228. #427 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26035026 | 2 |
| C2×#19152034 | 2 |
| #26022197 | 2 |
| #26021987 | 2 |
| #26021873 | 2 |
| C89×#3058 | 2 |
| #33531 | 89 |