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. #26030832 | C2 | semidirect |
| 2. #26030830 | C2 | semidirect |
| 3. #26030681 | C2 | semidirect |
| 4. #26030675 | C2 | semidirect |
| 5. #26019924 | C2 | semidirect |
| 6. #26019922 | C2 | semidirect |
| 7. #26019920 | C2 | semidirect |
| 8. #26019918 | C2 | semidirect |
| 9. #26019916 | C2 | semidirect |
| 10. #322×D89 | C2 | semidirect |
| 11. C89×#1722 | C2 | semidirect |
| 116. C8×D89 | D8 | semidirect |
| 199. #1722 | 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 |
|---|---|
| #26030832 | 2 |
| #26030830 | 2 |
| #26030681 | 2 |
| #26030675 | 2 |
| #26019924 | 2 |
| #26019922 | 2 |
| #26019920 | 2 |
| #26019918 | 2 |
| #26019916 | 2 |
| #322×D89 | 2 |
| C89×#1722 | 2 |
| #19616 | 89 |