Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
930 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 159 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. #26021988 | C2 | semidirect |
| 2. #26021968 | C2 | semidirect |
| 3. #26021873 | C2 | semidirect |
| 4. #26020298 | C2 | semidirect |
| 6. C2×#15667952 | C22 | semidirect |
| 7. #19151636 | C22 | semidirect |
| 18. C2×#135×C89 | C4 | semidirect |
| 20. C22×D8×C89 | C4 | semidirect |
| 180. C89 | #12741 | semidirect |
| 186. C2×#135 | Dic89 | semidirect |
| 188. C22×D8 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021988 | 2 |
| #26021968 | 2 |
| #26021873 | 2 |
| #26020298 | 2 |
| C2×#576×C89 | 2 |
| #12741 | 89 |