Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26029289 | C2 | semidirect |
| 3. #26020080 | C2 | semidirect |
| 4. #26018864 | C2 | semidirect |
| 5. #26018746 | C2 | semidirect |
| 6. #26018150 | C2 | semidirect |
| 7. C89×#1285 | C2 | semidirect |
| 11. #19151889 | C4 | semidirect |
| 12. #19151889 | C4 | semidirect |
| 13. #19151794 | C4 | semidirect |
| 14. #19151794 | C4 | semidirect |
| 227. #1285 | D89 | semidirect |
| 228. C89 | #9163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030344 | 2 |
| #26029289 | 2 |
| #26020080 | 2 |
| #26018864 | 2 |
| #26018746 | 2 |
| #26018150 | 2 |
| C89×#1285 | 2 |
| #9163 | 89 |