Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2718 conjugacy classes of subgroups.
The subgroup lattice has 324 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#16839810 | C2 | direct (N × H) |
| 4. C22×#14519712 | C2 | semidirect |
| 16. #16839810 | C22 | direct (N × H) |
| 17. C2×#14519712 | C22 | semidirect |
| 38. #14519712 | C23 | semidirect |
| 144. C22×C61 | #430 | semidirect |
| 165. C2×C61 | C2×#430 | semidirect |
| 185. C61 | C22×#430 | semidirect |
| 305. C22 | #16839810 | direct (N × H) |
| 321. C2 | C2×#16839810 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11758194 | 2 |
| C2×#16839810 | 2 |
| C22×#14519712 | 2 |
| C23×M16×C61 | 2 |
| C22×#430 | 61 |