Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
822 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 159 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. #26030995 | C2 | semidirect |
| 2. #26030972 | C2 | semidirect |
| 4. #26030623 | C2 | semidirect |
| 5. #26019908 | C2 | semidirect |
| 6. #26019893 | C2 | semidirect |
| 7. #26019880 | C2 | semidirect |
| 8. #26019859 | C2 | semidirect |
| 9. #26019851 | C2 | semidirect |
| 10. #26018556 | C2 | semidirect |
| 11. C89×#1722 | C2 | semidirect |
| 16. #19151996 | C22 | semidirect |
| 21. #19151971 | C22 | semidirect |
| 23. #19151950 | C22 | semidirect |
| 24. #19151948 | C22 | semidirect |
| 26. #19151946 | C22 | semidirect |
| 36. #19151320 | C22 | semidirect |
| 37. C8×#10623494 | C22 | semidirect |
| 38. #500×C89 | C22 | semidirect |
| 39. #494×C89 | C22 | semidirect |
| 42. #322×C89 | C22 | semidirect |
| 192. #1722 | D89 | semidirect |
| 199. C89 | #19749 | semidirect |
| 204. #500 | C2×D89 | semidirect |
| 207. #494 | C2×D89 | semidirect |
| 229. #322 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030995 | 2 |
| #26030972 | 2 |
| #26030699 | 2 |
| #26030623 | 2 |
| #26019908 | 2 |
| #26019893 | 2 |
| #26019880 | 2 |
| #26019859 | 2 |
| #26019851 | 2 |
| #26018556 | 2 |
| C89×#1722 | 2 |
| #19749 | 89 |