Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
310 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 35. #15667952 | Q8 | semidirect |
| 37. C2×#13083549 | Q8 | semidirect |
| 54. #108×C89 | Q8 | semidirect |
| 133. C89 | #13460 | semidirect |
| 173. #108 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030783 | 2 |
| #26022026 | 2 |
| C2×#19151422 | 2 |
| #26018366 | 2 |
| #26018352 | 2 |
| #26018338 | 2 |
| C89×#1953 | 2 |
| #13460 | 89 |