Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
976 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #26018785 | C2 | semidirect |
| 13. C23×Q8×C89 | C4 | semidirect |
| 19. C2×C22⋊Q8×C89 | C4 | semidirect |
| 21. C2×#117×C89 | C4 | semidirect |
| 197. C89 | #8520 | semidirect |
| 199. C23×Q8 | Dic89 | semidirect |
| 205. C2×C22⋊Q8 | Dic89 | semidirect |
| 207. C2×#117 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020180 | 2 |
| #26020170 | 2 |
| #26018785 | 2 |
| C2×#536×C89 | 2 |
| #8520 | 89 |