Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
444 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 58. Q32×C89 | Q8 | semidirect |
| 134. C89 | #33957 | semidirect |
| 172. Q32 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033143 | 2 |
| #26022536 | 2 |
| #26022531 | 2 |
| #26022418 | 2 |
| #26022416 | 2 |
| #26022402 | 2 |
| #26022160 | 2 |
| #26022123 | 2 |
| C4×Q32×C89 | 2 |
| #33957 | 89 |