Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
736 conjugacy classes of subgroups.
The subgroup lattice has 598 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20272837 | C2 | semidirect |
| 326. C53 | #12579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810607 | 2 |
| #20283160 | 2 |
| #20272837 | 2 |
| C2×C53×#413 | 2 |
| #12579 | 53 |