Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
468 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 3. #26020349 | C2 | semidirect |
| 4. #26020321 | C2 | semidirect |
| 6. #26018098 | C2 | semidirect |
| 7. C89×#1298 | C2 | semidirect |
| 11. #19151934 | C4 | semidirect |
| 12. #19151929 | C4 | semidirect |
| 14. #19151917 | C4 | semidirect |
| 15. #19151912 | C4 | semidirect |
| 235. #1298 | D89 | semidirect |
| 237. C89 | #9038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030167 | 2 |
| #26029302 | 2 |
| #26020349 | 2 |
| #26020321 | 2 |
| #26018744 | 2 |
| #26018098 | 2 |
| C89×#1298 | 2 |
| #9038 | 89 |