Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
486 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 486 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 |
|---|---|---|
| 1. #21462788 | C2 | semidirect |
| 2. D61⋊#361 | C2 | semidirect |
| 3. #21461704 | C2 | semidirect |
| 4. #21460901 | C2 | semidirect |
| 27. #14519852 | D4 | semidirect |
| 208. C61 | #13079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462788 | 2 |
| D61⋊#361 | 2 |
| #21461704 | 2 |
| #21460901 | 2 |
| #21455465 | 2 |
| #13079 | 61 |