Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26018862 | C2 | semidirect |
| 3. #26018813 | C2 | semidirect |
| 4. #26018790 | C2 | semidirect |
| 5. #26018152 | C2 | semidirect |
| 6. #26018134 | C2 | semidirect |
| 7. C89×#2968 | C2 | semidirect |
| 9. #19152008 | C4 | semidirect |
| 10. #19151988 | C4 | semidirect |
| 11. #19151964 | C4 | semidirect |
| 12. #19151957 | C4 | semidirect |
| 210. #2968 | D89 | semidirect |
| 216. C89 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030951 | 2 |
| #26018862 | 2 |
| #26018813 | 2 |
| #26018790 | 2 |
| #26018152 | 2 |
| #26018134 | 2 |
| C89×#2968 | 2 |
| #9432 | 89 |