Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
682 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 155 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. #26030765 | C2 | semidirect |
| 3. #26022495 | C2 | semidirect |
| 4. #26022494 | C2 | semidirect |
| 5. #26022493 | C2 | semidirect |
| 6. #26022474 | C2 | semidirect |
| 7. #26021966 | C2 | semidirect |
| 8. #26021845 | C2 | semidirect |
| 9. C89×#2244 | C2 | semidirect |
| 15. #19152002 | C22 | semidirect |
| 16. #19152000 | C22 | semidirect |
| 26. #19151400 | C22 | semidirect |
| 27. #19151399 | C22 | semidirect |
| 28. #19151398 | C22 | semidirect |
| 29. #19151374 | C22 | semidirect |
| 30. C16×Dic89 | C22 | semidirect |
| 31. #499×C89 | C22 | semidirect |
| 33. #357×C89 | C22 | semidirect |
| 34. #346×C89 | C22 | semidirect |
| 161. #2244 | D89 | semidirect |
| 165. C89 | #33704 | semidirect |
| 174. #499 | C2×D89 | semidirect |
| 187. #357 | C2×D89 | semidirect |
| 189. #346 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030765 | 2 |
| #493×D89 | 2 |
| #26022495 | 2 |
| #26022494 | 2 |
| #26022493 | 2 |
| #26022474 | 2 |
| #26021966 | 2 |
| #26021845 | 2 |
| C89×#2244 | 2 |
| #33704 | 89 |