Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
374 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 2. #21462156 | C2 | semidirect |
| 3. #21462154 | C2 | semidirect |
| 5. #21460870 | C2 | semidirect |
| 6. #21460869 | C2 | semidirect |
| 166. C61 | #12915 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462788 | 2 |
| #21462156 | 2 |
| #21462154 | 2 |
| #21462051 | 2 |
| #21460870 | 2 |
| #21460869 | 2 |
| #21445618 | 2 |
| #12915 | 61 |