Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 79 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. C2×#19151393 | C2 | semidirect |
| 2. #26018876 | C2 | semidirect |
| 3. #26018403 | C2 | semidirect |
| 8. #19151393 | C22 | semidirect |
| 10. #19151338 | C22 | semidirect |
| 11. C2×2−1+4×C89 | C4 | semidirect |
| 16. #454×C89 | C4 | semidirect |
| 19. C2×#101×C89 | C4 | semidirect |
| 29. 2−1+4×C89 | C2×C4 | semidirect |
| 52. #101×C89 | C2×C4 | semidirect |
| 181. C89 | #13569 | semidirect |
| 182. C2×2−1+4 | Dic89 | semidirect |
| 187. #454 | Dic89 | semidirect |
| 191. C2×#101 | Dic89 | semidirect |
| 200. 2−1+4 | C2×Dic89 | semidirect |
| 225. #101 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151393 | 2 |
| #26018876 | 2 |
| #26018403 | 2 |
| C2×#454×C89 | 2 |
| #13569 | 89 |