Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
434 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 434 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. #19152004 | C4 | semidirect |
| 10. #19152004 | C4 | semidirect |
| 187. C89 | #9440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030805 | 2 |
| #26023357 | 2 |
| #26018878 | 2 |
| #26018764 | 2 |
| #26018145 | 2 |
| #26018144 | 2 |
| C89×#1506 | 2 |
| #9440 | 89 |