Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2110 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19151356 | C2 | direct (N × H) |
| 11. #19151356 | C22 | direct (N × H) |
| 146. C22×C89 | #338 | semidirect |
| 163. C2×C89 | C2×#338 | semidirect |
| 168. C89 | C22×#338 | semidirect |
| 311. C22 | #19151356 | direct (N × H) |
| 327. C2 | C2×#19151356 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13083558 | 2 |
| C2×#19151356 | 2 |
| C23×M16×C89 | 2 |
| C22×#338 | 89 |