Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 9. #19152002 | C4 | semidirect |
| 10. #19151976 | C4 | semidirect |
| 14. Q16×Dic89 | C4 | semidirect |
| 15. #19151692 | C4 | semidirect |
| 164. C89 | #11857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030833 | 2 |
| #26022048 | 2 |
| #26020378 | 2 |
| #26018265 | 2 |
| #26018264 | 2 |
| #26018263 | 2 |
| C89×#1348 | 2 |
| #11857 | 89 |