Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups.
The subgroup lattice has 354 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20272538 | C2 | semidirect |
| 4. #20272538 | C2 | semidirect |
| 199. C53 | #7691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274477 | 2 |
| C2×#16810378 | 2 |
| #20272538 | 2 |
| C53×#2851 | 2 |
| #7691 | 53 |