Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
894 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 1. #21462057 | C2 | semidirect |
| 2. #21462055 | C2 | semidirect |
| 3. #21462051 | C2 | semidirect |
| 4. #21462049 | C2 | semidirect |
| 6. C2×#14519851 | C22 | semidirect |
| 7. C2×#14519851 | C22 | semidirect |
| 8. C22×#11758187 | C22 | semidirect |
| 186. C61 | #12684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462057 | 2 |
| #21462055 | 2 |
| #21462051 | 2 |
| #21462049 | 2 |
| #21460532 | 2 |
| #12684 | 61 |