Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2238 conjugacy classes of subgroups.
The subgroup lattice has 318 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#16810387 | C2 | direct (N × H) |
| 15. #16810387 | C22 | direct (N × H) |
| 140. C22×C53 | #341 | semidirect |
| 160. C2×C53 | C2×#341 | semidirect |
| 180. C53 | C22×#341 | semidirect |
| 298. C22 | #16810387 | direct (N × H) |
| 314. C2 | C2×#16810387 | 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 |
| C24×#88322 | 2 |
| C2×#16810387 | 2 |
| C23×M16×C53 | 2 |
| C22×#341 | 53 |