Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
318 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 105 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. #15667948 | Q8 | semidirect |
| 51. M32×C89 | Q8 | semidirect |
| 55. C2×C16×C89 | Q8 | semidirect |
| 141. C89 | #13455 | semidirect |
| 172. M32 | Dic178 | semidirect |
| 176. C2×C16 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030791 | 2 |
| #26022040 | 2 |
| C2×#19151424 | 2 |
| #26021037 | 2 |
| #26018361 | 2 |
| #26018348 | 2 |
| C89×#1379 | 2 |
| #13455 | 89 |