Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1398 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1398 conjugacy classes of subgroups — too many to draw. Only its 183 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. #26030188 | C2 | semidirect |
| 2. #26024526 | C2 | semidirect |
| 3. #26019272 | C2 | semidirect |
| 4. #26019238 | C2 | semidirect |
| 5. #26018781 | C2 | semidirect |
| 6. #26018579 | C2 | semidirect |
| 8. C2×#15667971 | C22 | semidirect |
| 10. #19151914 | C22 | semidirect |
| 11. #19151909 | C22 | semidirect |
| 14. #19151562 | C22 | semidirect |
| 15. #19151534 | C22 | semidirect |
| 16. #19151523 | C22 | semidirect |
| 19. #19151461 | C22 | semidirect |
| 21. #19151332 | C22 | semidirect |
| 22. #19151322 | C22 | semidirect |
| 35. C2×C4⋊Dic89 | C23 | semidirect |
| 36. C2×C4⋊Dic89 | C23 | semidirect |
| 48. C22⋊#10623494 | C23 | semidirect |
| 51. #15667919 | C23 | semidirect |
| 240. C89 | #18137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030188 | 2 |
| #26024526 | 2 |
| #26019272 | 2 |
| #26019238 | 2 |
| #26018781 | 2 |
| #26018579 | 2 |
| C2×#534×C89 | 2 |
| #18137 | 89 |