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. #20272845 | C2 | direct (N × H) |
| 5. C22×#11719917 | C4 | semidirect |
| 6. C23×#88322 | C4 | semidirect |
| 16. #16810590 | C4 | semidirect |
| 24. C53×#413 | C4 | semidirect |
| 26. C2×#101×C53 | C4 | semidirect |
| 31. C2×#11719917 | C2×C4 | semidirect |
| 37. C22×#88322 | C2×C4 | semidirect |
| 80. #101×C53 | C2×C4 | semidirect |
| 303. C2×C53 | #1395 | semidirect |
| 312. #413 | Dic53 | semidirect |
| 314. C2×#101 | Dic53 | semidirect |
| 328. C53 | C2×#1395 | semidirect |
| 373. #101 | C2×Dic53 | semidirect |
| 599. C2 | #20272845 | 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 |
| #20272845 | 2 |
| C2×C53×#413 | 2 |
| C2×#1395 | 53 |