Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups.
The subgroup lattice has 372 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #26018077 | C2 | semidirect |
| 4. #26018076 | C2 | semidirect |
| 191. C89 | #7648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667991 | 2 |
| #26020232 | 2 |
| #26018077 | 2 |
| #26018076 | 2 |
| C89×#1817 | 2 |
| #7648 | 89 |