Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups.
The subgroup lattice has 370 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #26018078 | C2 | semidirect |
| 4. #26018075 | C2 | semidirect |
| 190. C89 | #7681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019946 | 2 |
| C2×#19151353 | 2 |
| #26018078 | 2 |
| #26018075 | 2 |
| C89×#2855 | 2 |
| #7681 | 89 |