Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1630 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1630 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. #26030626 | C2 | semidirect |
| 2. #26030351 | C2 | semidirect |
| 3. #26019431 | C2 | semidirect |
| 4. #26018966 | C2 | semidirect |
| 5. #26018695 | C2 | semidirect |
| 7. #19152155 | C22 | semidirect |
| 9. #19151944 | C22 | semidirect |
| 11. #19151878 | C22 | semidirect |
| 12. #19151803 | C22 | semidirect |
| 15. #19151655 | C22 | semidirect |
| 17. C4×#13083558 | C22 | semidirect |
| 18. #19151342 | C22 | semidirect |
| 19. D4⋊#10623494 | C22 | semidirect |
| 30. #15668012 | C23 | semidirect |
| 36. C4⋊#10623494 | C23 | semidirect |
| 43. C4×#10623494 | C23 | semidirect |
| 173. C89 | #18529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030626 | 2 |
| #26030351 | 2 |
| #26019431 | 2 |
| #26018966 | 2 |
| #26018695 | 2 |
| C2×D42×C89 | 2 |
| #18529 | 89 |