Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
724 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#16839918 | C2 | semidirect |
| 3. #21445743 | C2 | semidirect |
| 4. #21444182 | C2 | semidirect |
| 6. #21443707 | C2 | semidirect |
| 246. C61 | #9989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456625 | 2 |
| C2×#16839918 | 2 |
| #21445743 | 2 |
| #21444182 | 2 |
| #21444179 | 2 |
| #21443707 | 2 |
| C2×C61×#448 | 2 |
| #9989 | 61 |