Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
566 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 1. C22×Dic712 | C2 | semidirect |
| 3. C2×#19151403 | C2 | semidirect |
| 4. #26018344 | C2 | semidirect |
| 84. C23×C89 | Q32 | semidirect |
| 137. C89 | #13306 | semidirect |
| 216. C23 | Dic712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic712 | 2 |
| C2×#19151839 | 2 |
| C2×#19151403 | 2 |
| #26018344 | 2 |
| C2×C22⋊C16×C89 | 2 |
| #13306 | 89 |