Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
874 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 874 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 |
|---|---|---|
| 1. D61⋊#362 | C2 | semidirect |
| 2. #21462134 | C2 | semidirect |
| 3. #21462056 | C2 | semidirect |
| 4. #21461703 | C2 | semidirect |
| 250. C61 | #12744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#362 | 2 |
| #21462134 | 2 |
| #21462056 | 2 |
| #21461703 | 2 |
| C2×#16840576 | 2 |
| #12744 | 61 |