Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
482 conjugacy classes of subgroups.
The subgroup lattice has 334 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #26018133 | C2 | semidirect |
| 4. #26018133 | C2 | semidirect |
| 172. C89 | #8720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020014 | 2 |
| #26018133 | 2 |
| C89×#2283 | 2 |
| #8720 | 89 |