Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1014 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1014 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 |
|---|---|---|
| 1. #26020170 | C2 | semidirect |
| 2. #26020164 | C2 | semidirect |
| 3. #26018808 | C2 | semidirect |
| 7. C2×C22⋊#10623494 | C22 | semidirect |
| 8. #19151461 | C22 | semidirect |
| 11. C2×H(5,𝔽2)×C89 | C4 | semidirect |
| 15. #536×C89 | C4 | semidirect |
| 19. #518×C89 | C4 | semidirect |
| 167. C89 | #8462 | semidirect |
| 168. C2×H(5,𝔽2) | Dic89 | semidirect |
| 172. #536 | Dic89 | semidirect |
| 176. #518 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020170 | 2 |
| #26020164 | 2 |
| #26018808 | 2 |
| C89×#3485 | 2 |
| #8462 | 89 |