Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 8. C22×#13083564 | C4 | semidirect |
| 16. #19151634 | C4 | semidirect |
| 17. #19151607 | C4 | semidirect |
| 18. #19151606 | C4 | semidirect |
| 211. C89 | #13233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029904 | 2 |
| #26021946 | 2 |
| #26021907 | 2 |
| #26021906 | 2 |
| #26020300 | 2 |
| #26020055 | 2 |
| C89×#2135 | 2 |
| #13233 | 89 |