Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups.
The subgroup lattice has 392 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×#13133284 | C4 | semidirect |
| 9. #16811489 | C4 | semidirect |
| 210. C53 | #7039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290571 | 2 |
| #20272943 | 2 |
| #7039 | 53 |