Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
616 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 11. C23×Q8×C89 | C4 | semidirect |
| 18. #385×C89 | C4 | semidirect |
| 19. #380×C89 | C4 | semidirect |
| 27. #15667927 | Q8 | semidirect |
| 180. C89 | #13296 | semidirect |
| 181. C23×Q8 | Dic89 | semidirect |
| 191. #385 | Dic89 | semidirect |
| 192. #380 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020244 | 2 |
| C4×#15667927 | 2 |
| #26018370 | 2 |
| C89×#2409 | 2 |
| #13296 | 89 |