Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2350 conjugacy classes of subgroups.
The subgroup lattice has 594 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #21445551 | C2 | direct (N × H) |
| 14. C2×#14519736 | C4 | semidirect |
| 15. C2×#14519736 | C4 | semidirect |
| 19. C22×C4⋊Dic61 | C4 | semidirect |
| 23. C22×C4×Dic61 | C4 | semidirect |
| 28. C2×#117×C61 | C4 | semidirect |
| 45. #14519736 | C2×C4 | semidirect |
| 51. C2×C4⋊Dic61 | C2×C4 | semidirect |
| 67. C2×C4×Dic61 | C2×C4 | semidirect |
| 86. #117×C61 | C2×C4 | semidirect |
| 299. C2×C61 | #1740 | semidirect |
| 317. C2×#117 | Dic61 | semidirect |
| 329. C61 | C2×#1740 | semidirect |
| 361. #117 | C2×Dic61 | semidirect |
| 590. C2 | #21445551 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519736 | 2 |
| #21445551 | 2 |
| C2×#16839528 | 2 |
| C22×#117×C61 | 2 |
| C2×#1740 | 61 |