Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
978 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 978 conjugacy classes of subgroups — too many to draw. Only its 323 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 |
|---|---|---|
| 2. #26021246 | C2 | semidirect |
| 111. C89 | #21830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028885 | 2 |
| #26021246 | 2 |
| #26020332 | 2 |
| C22×#125×C89 | 2 |
| #21830 | 89 |