Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 70. Q8×C89 | Q32 | semidirect |
| 106. C89 | #33930 | semidirect |
| 174. Q8 | Dic712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033258 | 2 |
| Q8×Dic356 | 2 |
| #26022480 | 2 |
| #26022405 | 2 |
| #26022303 | 2 |
| C4×Dic712 | 2 |
| Q8×C16×C89 | 2 |
| #33930 | 89 |