Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
566 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16840205 | C2 | semidirect |
| 3. C2×#16840146 | C2 | semidirect |
| 4. C2×#16839579 | C2 | semidirect |
| 5. C2×#16839576 | C2 | semidirect |
| 6. #21446707 | C2 | semidirect |
| 7. C61×#1376 | C2 | semidirect |
| 199. #1376 | D61 | semidirect |
| 229. C61 | #13332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840205 | 2 |
| C2×#16840200 | 2 |
| C2×#16840146 | 2 |
| C2×#16839579 | 2 |
| C2×#16839576 | 2 |
| #21446707 | 2 |
| C61×#1376 | 2 |
| #13332 | 61 |