Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
334 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 96 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. #21460837 | C2 | semidirect |
| 133. C61 | #11940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462152 | 2 |
| #21461367 | 2 |
| #21460837 | 2 |
| #500×D61 | 2 |
| #11940 | 61 |