Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
814 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 1. #26030991 | C2 | semidirect |
| 2. #26030989 | C2 | semidirect |
| 3. #26030706 | C2 | semidirect |
| 4. #26030647 | C2 | semidirect |
| 5. #26019916 | C2 | semidirect |
| 6. #26019909 | C2 | semidirect |
| 7. #26019888 | C2 | semidirect |
| 8. #26019886 | C2 | semidirect |
| 9. #26019858 | C2 | semidirect |
| 10. #26018554 | C2 | semidirect |
| 11. C89×#1708 | C2 | semidirect |
| 195. #1708 | D89 | semidirect |
| 197. C89 | #19750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030991 | 2 |
| #26030989 | 2 |
| #26030706 | 2 |
| #26030647 | 2 |
| #26019916 | 2 |
| #26019909 | 2 |
| #26019888 | 2 |
| #26019886 | 2 |
| #26019858 | 2 |
| #26018554 | 2 |
| C89×#1708 | 2 |
| #19750 | 89 |