Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #26022025 | C2 | semidirect |
| 4. #26021043 | C2 | semidirect |
| 5. #26018366 | C2 | semidirect |
| 6. #26018339 | C2 | semidirect |
| 23. #361×C89 | C4 | semidirect |
| 52. M32×C89 | C2×C4 | semidirect |
| 55. #108×C89 | C2×C4 | semidirect |
| 145. C89 | #12953 | semidirect |
| 160. #361 | Dic89 | semidirect |
| 181. M32 | C2×Dic89 | semidirect |
| 188. #108 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029104 | 2 |
| #26022025 | 2 |
| C2×#19151411 | 2 |
| #26021043 | 2 |
| #26018366 | 2 |
| #26018339 | 2 |
| C2×#361×C89 | 2 |
| #12953 | 89 |