Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
692 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26021073 | C2 | semidirect |
| 2. #26018978 | C2 | semidirect |
| 3. #26018872 | C2 | semidirect |
| 4. #26018790 | C2 | semidirect |
| 16. Q82×C89 | C4 | semidirect |
| 17. #555×C89 | C4 | semidirect |
| 18. #554×C89 | C4 | semidirect |
| 179. C89 | #8498 | semidirect |
| 181. Q82 | Dic89 | semidirect |
| 182. #555 | Dic89 | semidirect |
| 183. #554 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021073 | 2 |
| #26018978 | 2 |
| #26018872 | 2 |
| #26018790 | 2 |
| C89×#3544 | 2 |
| #8498 | 89 |