Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1716 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 195 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. #26030702 | C2 | semidirect |
| 2. #26030343 | C2 | semidirect |
| 3. #26019368 | C2 | semidirect |
| 4. #26019306 | C2 | semidirect |
| 5. #26018966 | C2 | semidirect |
| 6. #26018695 | C2 | semidirect |
| 7. C2×D42×C89 | C2 | semidirect |
| 9. #19152148 | C22 | semidirect |
| 11. #19151974 | C22 | semidirect |
| 12. #19151970 | C22 | semidirect |
| 14. #19151888 | C22 | semidirect |
| 15. #19151793 | C22 | semidirect |
| 18. #19151655 | C22 | semidirect |
| 19. C4×#13083558 | C22 | semidirect |
| 20. #19151342 | C22 | semidirect |
| 21. D4⋊#10623494 | C22 | semidirect |
| 36. #15668012 | C23 | semidirect |
| 37. #15668009 | C23 | semidirect |
| 42. C4⋊#10623494 | C23 | semidirect |
| 48. C4×#10623494 | C23 | semidirect |
| 139. D4×C89 | AGL(1,ℤ/8) | semidirect |
| 184. C2×D42 | D89 | semidirect |
| 191. C89 | #18524 | semidirect |
| 327. D4 | #15668038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030702 | 2 |
| #26030343 | 2 |
| #26019368 | 2 |
| #26019306 | 2 |
| #26018966 | 2 |
| #26018695 | 2 |
| C2×D42×C89 | 2 |
| #18524 | 89 |