Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1004 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1004 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. #26031190 | C2 | semidirect |
| 3. #26019330 | C2 | semidirect |
| 4. #26019311 | C2 | semidirect |
| 5. #26018914 | C2 | semidirect |
| 6. #26018673 | C2 | semidirect |
| 7. C89×#3550 | C2 | semidirect |
| 19. #19151347 | C22 | semidirect |
| 20. #19151342 | C22 | semidirect |
| 21. Q8⋊#10623494 | C22 | semidirect |
| 23. #559×C89 | C22 | semidirect |
| 24. Q82×C89 | C22 | semidirect |
| 168. #3550 | D89 | semidirect |
| 175. C89 | #18718 | semidirect |
| 178. #559 | C2×D89 | semidirect |
| 179. Q82 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031190 | 2 |
| #26030705 | 2 |
| #26019330 | 2 |
| #26019311 | 2 |
| #26018914 | 2 |
| #26018673 | 2 |
| C89×#3550 | 2 |
| #18718 | 89 |