Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 432 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 |
|---|---|---|
| 6. C22×Dic356 | C4 | semidirect |
| 13. #19151636 | C4 | semidirect |
| 14. #19151608 | C4 | semidirect |
| 165. C89 | #13233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029907 | 2 |
| #26021946 | 2 |
| #26021905 | 2 |
| #26020302 | 2 |
| C89×#1757 | 2 |
| #13233 | 89 |