Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups.
The subgroup lattice has 362 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 |
| 186. C89 | #7715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020232 | 2 |
| #26018078 | 2 |
| #26018075 | 2 |
| C89×#2855 | 2 |
| #7715 | 89 |