Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
726 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #26018772 | C2 | semidirect |
| 4. #26018138 | C2 | semidirect |
| 15. #397×C89 | C4 | semidirect |
| 16. #393×C89 | C4 | semidirect |
| 33. C22×Q8×C89 | C2×C4 | semidirect |
| 39. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 51. #95×C89 | C2×C4 | semidirect |
| 174. C89 | #9407 | semidirect |
| 179. #397 | Dic89 | semidirect |
| 180. #393 | Dic89 | semidirect |
| 191. C22×Q8 | C2×Dic89 | semidirect |
| 199. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 220. #95 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022605 | 2 |
| #26018772 | 2 |
| #26018579 | 2 |
| #26018138 | 2 |
| C89×#2561 | 2 |
| #9407 | 89 |