Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26021917 | C2 | semidirect |
| 2. #26018417 | C2 | semidirect |
| 3. #26018415 | C2 | semidirect |
| 9. #532×C89 | C4 | semidirect |
| 12. #494×C89 | C4 | semidirect |
| 14. #492×C89 | C4 | semidirect |
| 16. C2×C4×C8×C89 | C4 | semidirect |
| 129. C89 | #13583 | semidirect |
| 131. #532 | Dic89 | semidirect |
| 134. #494 | Dic89 | semidirect |
| 136. #492 | Dic89 | semidirect |
| 139. C2×C4×C8 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021917 | 2 |
| #26018417 | 2 |
| #26018415 | 2 |
| C89×#3147 | 2 |
| #13583 | 89 |