Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 179 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. #26030830 | C2 | semidirect |
| 2. #26030829 | C2 | semidirect |
| 3. #26030679 | C2 | semidirect |
| 4. #26030675 | C2 | semidirect |
| 5. #26019925 | C2 | semidirect |
| 6. #26019923 | C2 | semidirect |
| 7. #26019921 | C2 | semidirect |
| 8. #26019919 | C2 | semidirect |
| 9. #26019917 | C2 | semidirect |
| 10. #322×D89 | C2 | semidirect |
| 11. C89×#1721 | C2 | semidirect |
| 113. C8×D89 | D8 | semidirect |
| 202. #1721 | D89 | semidirect |
| 204. C89 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030830 | 2 |
| #26030829 | 2 |
| #26030679 | 2 |
| #26030675 | 2 |
| #26019925 | 2 |
| #26019923 | 2 |
| #26019921 | 2 |
| #26019919 | 2 |
| #26019917 | 2 |
| #322×D89 | 2 |
| C89×#1721 | 2 |
| #19616 | 89 |