Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
498 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26021917 | C2 | semidirect |
| 2. #26018844 | C2 | semidirect |
| 3. #26018403 | C2 | semidirect |
| 7. #19151393 | C22 | semidirect |
| 10. #19151338 | C22 | semidirect |
| 11. #585×C89 | C4 | semidirect |
| 14. #456×C89 | C4 | semidirect |
| 19. #413×C89 | C4 | semidirect |
| 179. C89 | #13568 | semidirect |
| 180. #585 | Dic89 | semidirect |
| 183. #456 | Dic89 | semidirect |
| 188. #413 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021917 | 2 |
| #26018844 | 2 |
| #26018403 | 2 |
| C89×#3018 | 2 |
| #13568 | 89 |