Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
526 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#16840131 | C2 | semidirect |
| 4. #21446791 | C2 | semidirect |
| 5. C2×#16839503 | C2 | semidirect |
| 7. C61×#1295 | C2 | semidirect |
| 189. #1295 | D61 | semidirect |
| 219. C61 | #10083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840131 | 2 |
| C2×#16840122 | 2 |
| #21453871 | 2 |
| #21446791 | 2 |
| C2×#16839503 | 2 |
| C2×#16839501 | 2 |
| C61×#1295 | 2 |
| #10083 | 61 |