Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
676 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26029302 | C2 | semidirect |
| 3. #26020195 | C2 | semidirect |
| 4. #26020163 | C2 | semidirect |
| 5. #26018744 | C2 | semidirect |
| 6. #26018098 | C2 | semidirect |
| 7. C89×#1298 | C2 | semidirect |
| 12. #19151756 | C4 | semidirect |
| 13. #19151751 | C4 | semidirect |
| 15. #19151739 | C4 | semidirect |
| 16. #19151734 | C4 | semidirect |
| 295. #1298 | D89 | semidirect |
| 297. C89 | #9037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029474 | 2 |
| #26029302 | 2 |
| #26020195 | 2 |
| #26020163 | 2 |
| #26018744 | 2 |
| #26018098 | 2 |
| C89×#1298 | 2 |
| #9037 | 89 |