Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
238 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 90 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. #21460849 | C2 | semidirect |
| 4. #21460848 | C2 | semidirect |
| 5. #21460842 | C2 | semidirect |
| 6. #21460841 | C2 | semidirect |
| 124. C61 | #12016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462183 | 2 |
| D61⋊(C4⋊C16) | 2 |
| #21460849 | 2 |
| #21460848 | 2 |
| #21460842 | 2 |
| #21460841 | 2 |
| #21444098 | 2 |
| #12016 | 61 |