Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
538 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 11. #19151456 | C4 | semidirect |
| 15. C22⋊C4×Dic89 | C4 | semidirect |
| 210. C89 | #8750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022848 | 2 |
| #26020324 | 2 |
| #26018156 | 2 |
| C89×#1304 | 2 |
| #8750 | 89 |