Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#19151421 | C2 | semidirect |
| 3. C2×#19151415 | C2 | semidirect |
| 6. #26021123 | C2 | semidirect |
| 7. C2×#347×C89 | C2 | semidirect |
| 12. C2×Dic712 | C4 | semidirect |
| 13. C2×#15667957 | C4 | semidirect |
| 169. C2×#347 | D89 | semidirect |
| 172. C89 | #13250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152041 | 2 |
| C2×#19151421 | 2 |
| C2×#19151415 | 2 |
| C2×#19151409 | 2 |
| #26021145 | 2 |
| #26021123 | 2 |
| C2×#347×C89 | 2 |
| #13250 | 89 |