Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
804 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 8. #19152328 | C4 | semidirect |
| 123. Dic178 | #103 | semidirect |
| 152. C89 | #8451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152328 | 2 |
| #26021055 | 2 |
| #26020258 | 2 |
| C2×#19151328 | 2 |
| C2×#333×C89 | 2 |
| #8451 | 89 |