Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #26018764 | C2 | semidirect |
| 5. #26018113 | C2 | semidirect |
| 6. #26018080 | C2 | semidirect |
| 7. C89×#1497 | C2 | semidirect |
| 9. #19152001 | C4 | semidirect |
| 10. #19151994 | C4 | semidirect |
| 11. #19151946 | C4 | semidirect |
| 12. #19151946 | C4 | semidirect |
| 173. #1497 | D89 | semidirect |
| 176. C89 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031388 | 2 |
| #26029327 | 2 |
| #26018764 | 2 |
| #26018761 | 2 |
| #26018113 | 2 |
| #26018080 | 2 |
| C89×#1497 | 2 |
| #9279 | 89 |