Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
718 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 718 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. #26020329 | C2 | semidirect |
| 2. #26020323 | C2 | semidirect |
| 3. #26018808 | C2 | semidirect |
| 4. #26018808 | C2 | semidirect |
| 19. #544×C89 | C4 | semidirect |
| 21. #537×C89 | C4 | semidirect |
| 24. #520×C89 | C4 | semidirect |
| 183. C89 | #8463 | semidirect |
| 188. #544 | Dic89 | semidirect |
| 190. #537 | Dic89 | semidirect |
| 193. #520 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020329 | 2 |
| #26020323 | 2 |
| #26018808 | 2 |
| C89×#3493 | 2 |
| #8463 | 89 |