Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
782 conjugacy classes of subgroups.
The subgroup lattice has 606 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20272835 | C2 | direct (N × H) |
| 5. C22×#11719917 | C4 | semidirect |
| 6. C23×#88322 | C4 | semidirect |
| 10. #16810597 | C4 | semidirect |
| 13. C2×#13133132 | C4 | semidirect |
| 16. #16810590 | C4 | semidirect |
| 24. C53×#410 | C4 | semidirect |
| 27. C2×#99×C53 | C4 | semidirect |
| 31. C2×#11719917 | C2×C4 | semidirect |
| 37. C22×#88322 | C2×C4 | semidirect |
| 48. #13133132 | C2×C4 | semidirect |
| 82. #99×C53 | C2×C4 | semidirect |
| 305. C2×C53 | #1391 | semidirect |
| 318. #410 | Dic53 | semidirect |
| 323. C2×#99 | Dic53 | semidirect |
| 330. C53 | C2×#1391 | semidirect |
| 381. #99 | C2×Dic53 | semidirect |
| 603. C2 | #20272835 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810597 | 2 |
| C2×#16810590 | 2 |
| #20272835 | 2 |
| C2×C53×#410 | 2 |
| C2×#1391 | 53 |