Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
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×#16810381 | C2 | direct (N × H) |
| 11. #16810381 | C22 | direct (N × H) |
| 147. C22×C53 | #338 | semidirect |
| 166. C2×C53 | C2×#338 | semidirect |
| 182. C53 | C22×#338 | semidirect |
| 311. C22 | #16810381 | direct (N × H) |
| 327. C2 | C2×#16810381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719917 | 2 |
| C2×#16810381 | 2 |
| C23×M16×C53 | 2 |
| C22×#338 | 53 |