Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
318 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#13083549 | Q8 | semidirect |
| 48. C2×C16×C89 | Q8 | semidirect |
| 52. #106×C89 | Q8 | semidirect |
| 127. C89 | #13459 | semidirect |
| 159. C2×C16 | Dic178 | semidirect |
| 168. #106 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030775 | 2 |
| #26022025 | 2 |
| #26022024 | 2 |
| #26021006 | 2 |
| #26018353 | 2 |
| #26018331 | 2 |
| C89×#1384 | 2 |
| #13459 | 89 |