Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 16. #391×C89 | C4 | semidirect |
| 17. #382×C89 | C4 | semidirect |
| 147. C89 | #9460 | semidirect |
| 152. #391 | Dic89 | semidirect |
| 154. #382 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022855 | 2 |
| #26020332 | 2 |
| #26018785 | 2 |
| #26018105 | 2 |
| C89×#2503 | 2 |
| #9460 | 89 |