Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
448 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 45. Q32×C89 | Q8 | semidirect |
| 113. C89 | #33950 | semidirect |
| 142. Q32 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033141 | 2 |
| #26022529 | 2 |
| #26022527 | 2 |
| #26022418 | 2 |
| #26022394 | 2 |
| C16×Dic178 | 2 |
| Q32×Dic89 | 2 |
| C4×Q32×C89 | 2 |
| #33950 | 89 |