Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
260 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 3. #21460734 | C2 | semidirect |
| 4. #21460732 | C2 | semidirect |
| 5. #21460731 | C2 | semidirect |
| 6. C8×#11758187 | C2 | semidirect |
| 120. C61 | #11412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462178 | 2 |
| #21460734 | 2 |
| #21460732 | 2 |
| #21460731 | 2 |
| C8×#11758187 | 2 |
| #21444104 | 2 |
| #11412 | 61 |