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 |
|---|---|---|
| 10. #19152001 | C4 | semidirect |
| 11. #19151994 | C4 | semidirect |
| 150. C89 | #9427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030799 | 2 |
| #26023432 | 2 |
| #26018970 | 2 |
| #26018803 | 2 |
| #26018118 | 2 |
| #26018116 | 2 |
| C89×#1515 | 2 |
| #9427 | 89 |