Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2238 conjugacy classes of subgroups.
The subgroup lattice has 510 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×#16840637 | C2 | direct (N × H) |
| 19. #16840637 | C22 | direct (N × H) |
| 222. C22×C61 | #341 | semidirect |
| 233. C2×D61 | #341 | semidirect |
| 253. C2×C61 | C2×#341 | semidirect |
| 257. D61 | C2×#341 | semidirect |
| 283. C61 | C22×#341 | semidirect |
| 489. C22 | #16840637 | direct (N × H) |
| 507. C2 | C2×#16840637 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D61⋊M16 | 2 |
| C23×D61⋊C8 | 2 |
| C2×#16840637 | 2 |
| C22×M16×D61 | 2 |
| C22×#341 | 61 |