Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
656 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26018370 | C2 | semidirect |
| 12. C2×#117×C89 | C4 | semidirect |
| 13. C22×C42×C89 | C4 | semidirect |
| 16. #386×C89 | C4 | semidirect |
| 174. C89 | #12853 | semidirect |
| 176. C2×#117 | Dic89 | semidirect |
| 177. C22×C42 | Dic89 | semidirect |
| 185. #386 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020180 | 2 |
| #26020170 | 2 |
| #26018370 | 2 |
| C89×#2297 | 2 |
| #12853 | 89 |