Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26030906 | C2 | semidirect |
| 3. #26022471 | C2 | semidirect |
| 4. #26022427 | C2 | semidirect |
| 5. #26022332 | C2 | semidirect |
| 8. #26022146 | C2 | semidirect |
| 9. #26022142 | C2 | semidirect |
| 10. #26022065 | C2 | semidirect |
| 11. C89×#2239 | C2 | semidirect |
| 17. #19151998 | C22 | semidirect |
| 18. #19151976 | C22 | semidirect |
| 26. #19151705 | C22 | semidirect |
| 27. #19151704 | C22 | semidirect |
| 31. #19151422 | C22 | semidirect |
| 32. #19151418 | C22 | semidirect |
| 33. #19151413 | C22 | semidirect |
| 37. #19151375 | C22 | semidirect |
| 40. #365×C89 | C22 | semidirect |
| 41. #362×C89 | C22 | semidirect |
| 201. #2239 | D89 | semidirect |
| 209. C89 | #33693 | semidirect |
| 232. #365 | C2×D89 | semidirect |
| 235. #362 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030906 | 2 |
| #26029154 | 2 |
| #26022471 | 2 |
| #26022427 | 2 |
| #26022332 | 2 |
| #26022205 | 2 |
| #26022202 | 2 |
| #26022146 | 2 |
| #26022142 | 2 |
| #26022065 | 2 |
| C89×#2239 | 2 |
| #33693 | 89 |