Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups.
The subgroup lattice has 320 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #16810349 | C4 | semidirect |
| 22. C2×C4⋊C4×C53 | C8 | semidirect |
| 29. C2×C42×C53 | C8 | semidirect |
| 169. C53 | #7189 | semidirect |
| 180. C2×C4⋊C4 | #88322 | semidirect |
| 187. C2×C42 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810349 | 2 |
| C53×C4⋊#95 | 2 |
| #7189 | 53 |