Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
612 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 612 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 |
| 24. #15667929 | Q8 | semidirect |
| 182. C89 | #13293 | semidirect |
| 183. C23×Q8 | Dic89 | semidirect |
| 193. #385 | Dic89 | semidirect |
| 195. #380 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020240 | 2 |
| C4×#15667929 | 2 |
| #26018370 | 2 |
| C89×#2409 | 2 |
| #13293 | 89 |