Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1132 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 179 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. #26031167 | C2 | semidirect |
| 2. #26030705 | C2 | semidirect |
| 3. #26019335 | C2 | semidirect |
| 4. #26019306 | C2 | semidirect |
| 5. #26018914 | C2 | semidirect |
| 6. #26018669 | C2 | semidirect |
| 7. C89×#3549 | C2 | semidirect |
| 9. C2×#15668009 | C22 | semidirect |
| 13. #19151972 | C22 | semidirect |
| 15. #19151793 | C22 | semidirect |
| 17. #19151651 | C22 | semidirect |
| 18. C4×#13083558 | C22 | semidirect |
| 19. #19151347 | C22 | semidirect |
| 20. #19151342 | C22 | semidirect |
| 21. D4⋊#10623494 | C22 | semidirect |
| 24. #555×C89 | C22 | semidirect |
| 26. D42×C89 | C22 | semidirect |
| 180. #3549 | D89 | semidirect |
| 187. C89 | #18714 | semidirect |
| 191. #555 | C2×D89 | semidirect |
| 193. D42 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031167 | 2 |
| #26030705 | 2 |
| #26019335 | 2 |
| #26019306 | 2 |
| #26018914 | 2 |
| #26018669 | 2 |
| C89×#3549 | 2 |
| #18714 | 89 |