Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
318 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 33. #15667952 | Q8 | semidirect |
| 37. C2×#13083549 | Q8 | semidirect |
| 51. #108×C89 | Q8 | semidirect |
| 141. C89 | #13455 | semidirect |
| 178. #108 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030791 | 2 |
| #26022038 | 2 |
| C2×#19151423 | 2 |
| #26018362 | 2 |
| #26018349 | 2 |
| #26018341 | 2 |
| C89×#1952 | 2 |
| #13455 | 89 |