Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
380 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 85 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. #19151994 | C4 | semidirect |
| 10. #19151977 | C4 | semidirect |
| 11. #19151950 | C4 | semidirect |
| 12. #19151948 | C4 | semidirect |
| 155. C89 | #9416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030993 | 2 |
| #26029357 | 2 |
| #26018804 | 2 |
| #26018803 | 2 |
| #26018123 | 2 |
| #26018118 | 2 |
| C89×#1537 | 2 |
| #9416 | 89 |