Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
388 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 20. #19151414 | C4 | semidirect |
| 158. C89 | #12941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029120 | 2 |
| #26022038 | 2 |
| C2×#19151414 | 2 |
| #26021035 | 2 |
| #26018348 | 2 |
| #26018340 | 2 |
| C2×#358×C89 | 2 |
| #12941 | 89 |