Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1258 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 259 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 |
|---|---|---|
| 3. #26021094 | C2 | semidirect |
| 120. C2×Dic89 | #101 | semidirect |
| 151. C89 | #21799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668010 | 2 |
| #26028881 | 2 |
| #26021094 | 2 |
| #26020176 | 2 |
| #26020175 | 2 |
| C89×#1784 | 2 |
| #21799 | 89 |