Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
782 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26020248 | C2 | semidirect |
| 3. #26018936 | C2 | semidirect |
| 5. C89×#1461 | C2 | semidirect |
| 130. D356 | #101 | semidirect |
| 167. #1461 | D89 | semidirect |
| 168. C89 | #8398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152308 | 2 |
| #26020248 | 2 |
| #26018936 | 2 |
| #26018678 | 2 |
| C89×#1461 | 2 |
| #8398 | 89 |