Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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×#19152038 | C2 | semidirect |
| 2. C22×#15667957 | C2 | semidirect |
| 4. #26029119 | C2 | semidirect |
| 5. #26022317 | C2 | semidirect |
| 6. #26022291 | C2 | semidirect |
| 7. #26022010 | C2 | semidirect |
| 8. #26021967 | C2 | semidirect |
| 9. C89×#2138 | C2 | semidirect |
| 16. C2×#15667958 | C22 | semidirect |
| 19. C2×#15667956 | C22 | semidirect |
| 25. #19151692 | C22 | semidirect |
| 28. #19151416 | C22 | semidirect |
| 33. #358×C89 | C22 | semidirect |
| 34. #357×C89 | C22 | semidirect |
| 40. C2×Dic356 | D4 | semidirect |
| 185. #2138 | D89 | semidirect |
| 186. C89 | #33587 | semidirect |
| 209. #358 | C2×D89 | semidirect |
| 211. #357 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152038 | 2 |
| C22×#15667957 | 2 |
| #26030739 | 2 |
| #26029119 | 2 |
| #26022317 | 2 |
| #26022291 | 2 |
| #26022010 | 2 |
| #26021967 | 2 |
| C89×#2138 | 2 |
| #33587 | 89 |