Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
668 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26023342 | C2 | semidirect |
| 2. C2×#19151397 | C2 | semidirect |
| 4. #26018378 | C2 | semidirect |
| 19. #456×C89 | C4 | semidirect |
| 189. C89 | #13058 | semidirect |
| 194. #456 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023342 | 2 |
| C2×#19151397 | 2 |
| #26020211 | 2 |
| #26018378 | 2 |
| C2×#456×C89 | 2 |
| #13058 | 89 |