Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1170 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 312 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. #21461561 | C2 | semidirect |
| 3. #21461549 | C2 | semidirect |
| 6. #16840732 | C4 | semidirect |
| 9. C2×#14519832 | C22 | semidirect |
| 10. C2×C4×#92420 | C22 | semidirect |
| 11. #16840628 | C22 | semidirect |
| 139. C61 | #20529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840732 | 2 |
| #21461561 | 2 |
| #21461549 | 2 |
| #21448197 | 2 |
| #20529 | 61 |