Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
736 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 736 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. #26030993 | C2 | semidirect |
| 4. #26019915 | C2 | semidirect |
| 5. #26019910 | C2 | semidirect |
| 6. #26019909 | C2 | semidirect |
| 7. #26019865 | C2 | semidirect |
| 8. #26018555 | C2 | semidirect |
| 9. C89×#3185 | C2 | semidirect |
| 12. #19151994 | C22 | semidirect |
| 13. #19151977 | C22 | semidirect |
| 16. #19151950 | C22 | semidirect |
| 17. #19151948 | C22 | semidirect |
| 29. #19151320 | C22 | semidirect |
| 30. #19151319 | C22 | semidirect |
| 31. C8×#10623494 | C22 | semidirect |
| 33. #498×C89 | C22 | semidirect |
| 34. #494×C89 | C22 | semidirect |
| 35. #487×C89 | C22 | semidirect |
| 161. #3185 | D89 | semidirect |
| 169. C89 | #19753 | semidirect |
| 174. #498 | C2×D89 | semidirect |
| 176. #494 | C2×D89 | semidirect |
| 181. #487 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030993 | 2 |
| #26030628 | 2 |
| #26030627 | 2 |
| #26019915 | 2 |
| #26019910 | 2 |
| #26019909 | 2 |
| #26019865 | 2 |
| #26018555 | 2 |
| C89×#3185 | 2 |
| #19753 | 89 |