Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 94. Dic178 | Q32 | semidirect |
| 121. C89 | #33962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033256 | 2 |
| #26022503 | 2 |
| #26022300 | 2 |
| #26022299 | 2 |
| C16×Dic178 | 2 |
| C4×Dic712 | 2 |
| Q32×Dic89 | 2 |
| C89×#2247 | 2 |
| #33962 | 89 |