Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
766 conjugacy classes of subgroups.
The subgroup lattice has 602 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20272843 | C2 | direct (N × H) |
| 6. C22×#11719917 | C4 | semidirect |
| 7. C23×#88322 | C4 | semidirect |
| 10. #16810607 | C4 | semidirect |
| 12. C2×#13133136 | C4 | semidirect |
| 16. #16810590 | C4 | semidirect |
| 37. C2×#11719917 | C2×C4 | semidirect |
| 44. C22×#88322 | C2×C4 | semidirect |
| 46. #13133136 | C2×C4 | semidirect |
| 303. C2×C53 | #1395 | semidirect |
| 328. C53 | C2×#1395 | semidirect |
| 599. C2 | #20272843 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810607 | 2 |
| C2×#16810590 | 2 |
| #20272843 | 2 |
| C2×C53×#410 | 2 |
| C2×#1395 | 53 |