Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
680 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26018274 | C2 | semidirect |
| 5. C23×Dic178 | C4 | semidirect |
| 9. #19151510 | C4 | semidirect |
| 13. C2×#15667919 | C4 | semidirect |
| 196. C89 | #11808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151510 | 2 |
| #26020326 | 2 |
| #26018274 | 2 |
| C89×#1462 | 2 |
| #11808 | 89 |