Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 156. C89 | #9861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030762 | 2 |
| #26020423 | 2 |
| #26018708 | 2 |
| #26018707 | 2 |
| #26018706 | 2 |
| C2×#19151320 | 2 |
| C89×#1493 | 2 |
| #9861 | 89 |