Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 7. #19152003 | C4 | semidirect |
| 8. #19151978 | C4 | semidirect |
| 9. #19151949 | C4 | semidirect |
| 135. C89 | #9765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030838 | 2 |
| #26020003 | 2 |
| #26018868 | 2 |
| #26018765 | 2 |
| C89×#1568 | 2 |
| #9765 | 89 |