Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
242 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 104 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. #21460842 | C2 | semidirect |
| 4. #21460841 | C2 | semidirect |
| 112. C61 | #11997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462152 | 2 |
| D61⋊(C4⋊C16) | 2 |
| #21460842 | 2 |
| #21460841 | 2 |
| #21444104 | 2 |
| #11997 | 61 |