Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1222 conjugacy classes of subgroups.
The subgroup lattice has 318 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C61⋊#401 | C4 | direct (N × H) |
| 147. C4×C61 | #401 | semidirect |
| 180. C61 | C4×#401 | semidirect |
| 309. C4 | C61⋊#401 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C61⋊#401 | 2 |
| #21444081 | 2 |
| #21444080 | 2 |
| #21444079 | 2 |
| C4×#14519684 | 2 |
| C4×#95×C61 | 2 |
| C4×#401 | 61 |