Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
394 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #26021971 | C2 | semidirect |
| 4. #26021856 | C2 | semidirect |
| 5. #26021165 | C2 | semidirect |
| 7. C89×#2155 | C2 | semidirect |
| 12. C2×Dic712 | C4 | semidirect |
| 13. C2×#15667957 | C4 | semidirect |
| 164. #2155 | D89 | semidirect |
| 170. C89 | #13248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152041 | 2 |
| #26021979 | 2 |
| #26021971 | 2 |
| #26021856 | 2 |
| #26021165 | 2 |
| #26021148 | 2 |
| C89×#2155 | 2 |
| #13248 | 89 |