Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
| 87. Dic178 | Q32 | direct (N × H) |
| 114. C89 | Q8×Q32 | semidirect |
| 143. Q32 | Dic178 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic178 | 2 |
| #26022527 | 2 |
| #26022526 | 2 |
| #26022404 | 2 |
| #26022402 | 2 |
| C16×Dic178 | 2 |
| Q32×Dic89 | 2 |
| C4×Q32×C89 | 2 |
| Q8×Q32 | 89 |