Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
468 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26020323 | C2 | semidirect |
| 5. #26018139 | C2 | semidirect |
| 6. #26018100 | C2 | semidirect |
| 7. C89×#1826 | C2 | semidirect |
| 10. #19151933 | C4 | semidirect |
| 11. #19151928 | C4 | semidirect |
| 13. #19151916 | C4 | semidirect |
| 14. #19151911 | C4 | semidirect |
| 232. #1826 | D89 | semidirect |
| 237. C89 | #9038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030165 | 2 |
| #26029302 | 2 |
| #26020323 | 2 |
| #26018741 | 2 |
| #26018139 | 2 |
| #26018100 | 2 |
| C89×#1826 | 2 |
| #9038 | 89 |