Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. #21461292 | C2 | semidirect |
| 4. #21461143 | C2 | semidirect |
| 5. #21460712 | C2 | semidirect |
| 6. #21460685 | C2 | semidirect |
| 225. C61 | #9312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462390 | 2 |
| #21461292 | 2 |
| #21461151 | 2 |
| #21461143 | 2 |
| #21460712 | 2 |
| #21460685 | 2 |
| #21455978 | 2 |
| #9312 | 61 |