Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
3246 conjugacy classes of subgroups.
The subgroup lattice has 540 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #21444072 | C2 | direct (N × H) |
| 23. C22×C4⋊C4×C61 | C4 | semidirect |
| 71. C2×C4⋊C4×C61 | C2×C4 | semidirect |
| 110. C22×C4×C61 | C4⋊C4 | semidirect |
| 201. C2×C4×C61 | C2×C4⋊C4 | semidirect |
| 264. C2×C61 | #1441 | semidirect |
| 286. C22×C4⋊C4 | Dic61 | semidirect |
| 294. C61 | C2×#1441 | semidirect |
| 338. C2×C4⋊C4 | C2×Dic61 | semidirect |
| 407. C22×C4 | C4⋊Dic61 | semidirect |
| 487. C2×C4 | C2×C4⋊Dic61 | semidirect |
| 527. C2 | #21444072 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Dic61 | 2 |
| C22×#14519684 | 2 |
| #21444072 | 2 |
| C23×C4⋊C4×C61 | 2 |
| C2×#1441 | 61 |