Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 120 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. #21462786 | C2 | semidirect |
| 2. #21462061 | C2 | semidirect |
| 3. #21462055 | C2 | semidirect |
| 4. #21460863 | C2 | semidirect |
| 25. #14519851 | D4 | semidirect |
| 163. C61 | #12982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462786 | 2 |
| #21462061 | 2 |
| #21462055 | 2 |
| #21460863 | 2 |
| #21454531 | 2 |
| #12982 | 61 |