Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
776 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 776 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. #26018273 | C2 | direct (N × H) |
| 11. C23×Q8×C89 | C4 | semidirect |
| 16. #393×C89 | C4 | semidirect |
| 19. C2×#95×C89 | C4 | semidirect |
| 33. C22×Q8×C89 | C2×C4 | semidirect |
| 50. #95×C89 | C2×C4 | semidirect |
| 203. C2×C89 | #1351 | semidirect |
| 211. C89 | C2×#1351 | semidirect |
| 212. C23×Q8 | Dic89 | semidirect |
| 219. #393 | Dic89 | semidirect |
| 222. C2×#95 | Dic89 | semidirect |
| 232. C22×Q8 | C2×Dic89 | semidirect |
| 257. #95 | C2×Dic89 | semidirect |
| 409. C2 | #26018273 | 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 |
| #26018273 | 2 |
| C2×#393×C89 | 2 |
| C2×#1351 | 89 |