Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26029156 | C2 | semidirect |
| 2. #26022464 | C2 | semidirect |
| 3. #26022425 | C2 | semidirect |
| 4. #26022325 | C2 | semidirect |
| 5. #26022197 | C2 | semidirect |
| 6. #26022148 | C2 | semidirect |
| 7. #26022068 | C2 | semidirect |
| 8. C89×#3176 | C2 | semidirect |
| 18. #19151420 | C22 | semidirect |
| 19. #19151419 | C22 | semidirect |
| 20. #19151411 | C22 | semidirect |
| 23. #19151376 | C22 | semidirect |
| 25. #499×C89 | C22 | semidirect |
| 26. #493×C89 | C22 | semidirect |
| 30. #442×C89 | C22 | semidirect |
| 167. #3176 | D89 | semidirect |
| 175. C89 | #33692 | semidirect |
| 180. #499 | C2×D89 | semidirect |
| 181. #493 | C2×D89 | semidirect |
| 189. #442 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029156 | 2 |
| #26022464 | 2 |
| #26022425 | 2 |
| #26022325 | 2 |
| #26022197 | 2 |
| #26022148 | 2 |
| #26022068 | 2 |
| C89×#3176 | 2 |
| #33692 | 89 |