Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
3246 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #21444046 | C2 | direct (N × H) |
| 9. C2×#14519684 | C4 | semidirect |
| 17. C22×C42×C61 | C4 | semidirect |
| 29. #14519684 | C2×C4 | semidirect |
| 49. C2×C42×C61 | C2×C4 | semidirect |
| 187. C2×C61 | #1434 | semidirect |
| 202. C22×C42 | Dic61 | semidirect |
| 210. C61 | C2×#1434 | semidirect |
| 238. C2×C42 | C2×Dic61 | semidirect |
| 373. C2 | #21444046 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519684 | 2 |
| #21444046 | 2 |
| C23×C42×C61 | 2 |
| C2×#1434 | 61 |