Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
450 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #21444414 | C2 | semidirect |
| 5. #21443712 | C2 | semidirect |
| 6. #21443692 | C2 | semidirect |
| 7. C61×#1506 | C2 | semidirect |
| 10. #16840054 | C4 | semidirect |
| 11. #16840049 | C4 | semidirect |
| 12. #16839969 | C4 | semidirect |
| 13. #16839964 | C4 | semidirect |
| 194. #1506 | D61 | semidirect |
| 227. C61 | #9160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455975 | 2 |
| #21454836 | 2 |
| #21445630 | 2 |
| #21444414 | 2 |
| #21443712 | 2 |
| #21443692 | 2 |
| C61×#1506 | 2 |
| #9160 | 61 |