Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
468 conjugacy classes of subgroups.
The subgroup lattice has 386 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×C4×#88324 | C4 | semidirect |
| 9. #16811489 | C4 | semidirect |
| 35. #13133124 | C8 | semidirect |
| 39. #95×C53 | C8 | semidirect |
| 207. C53 | #7024 | semidirect |
| 232. #95 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290569 | 2 |
| C4×C22⋊#88324 | 2 |
| #20272940 | 2 |
| #7024 | 53 |