Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
668 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 668 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 |
|---|---|---|
| 3. #26018252 | C2 | direct (N × H) |
| 11. C22×C4⋊C4×C89 | C4 | semidirect |
| 16. #397×C89 | C4 | semidirect |
| 19. C2×#95×C89 | C4 | semidirect |
| 36. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 50. #95×C89 | C2×C4 | semidirect |
| 196. C2×C89 | #1344 | semidirect |
| 204. C89 | C2×#1344 | semidirect |
| 205. C22×C4⋊C4 | Dic89 | semidirect |
| 212. #397 | Dic89 | semidirect |
| 215. C2×#95 | Dic89 | semidirect |
| 230. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 250. #95 | C2×Dic89 | semidirect |
| 395. C2 | #26018252 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151365 | 2 |
| C2×#19151322 | 2 |
| #26018252 | 2 |
| C2×#397×C89 | 2 |
| C2×#1344 | 89 |