Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
382 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #21462042 | C2 | semidirect |
| 4. #21462040 | C2 | semidirect |
| 5. #21460874 | C2 | semidirect |
| 6. #21460873 | C2 | semidirect |
| 10. C2×#14519852 | C4 | semidirect |
| 14. C2×D61⋊C16 | C4 | semidirect |
| 16. #16840659 | C4 | semidirect |
| 170. C61 | #12617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840821 | 2 |
| #21462057 | 2 |
| #21462042 | 2 |
| #21462040 | 2 |
| #21460874 | 2 |
| #21460873 | 2 |
| #21445618 | 2 |
| #12617 | 61 |