Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
316 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 34. #15667952 | Q8 | semidirect |
| 50. M32×C89 | Q8 | semidirect |
| 133. C89 | #13270 | semidirect |
| 167. M32 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029184 | 2 |
| #26022017 | 2 |
| #26021856 | 2 |
| #26018338 | 2 |
| #26018333 | 2 |
| C89×#1378 | 2 |
| #13270 | 89 |