Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2886 conjugacy classes of subgroups.
The subgroup lattice has 442 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×#13133124 | C4 | semidirect |
| 14. C22×C4⋊C4×C53 | C4 | semidirect |
| 104. C22×Dic53 | C4⋊C4 | semidirect |
| 156. C2×C4×C53 | #95 | semidirect |
| 229. C22×C4⋊C4 | Dic53 | semidirect |
| 235. C53 | #7557 | semidirect |
| 388. C2×C4 | #13133124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133124 | 2 |
| C23×C4⋊C4×C53 | 2 |
| #7557 | 53 |