Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
470 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 86 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×#16840657 | C2 | semidirect |
| 2. #21461696 | C2 | semidirect |
| 3. #21460806 | C2 | semidirect |
| 4. #21460805 | C2 | semidirect |
| 10. #16840657 | C22 | semidirect |
| 11. #16840636 | C22 | semidirect |
| 12. C2×D8×D61 | C4 | semidirect |
| 16. #16839998 | C4 | semidirect |
| 20. #107×D61 | C4 | semidirect |
| 22. C61×#466 | C4 | semidirect |
| 203. #466 | #6923 | semidirect |
| 211. C61 | #11886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840657 | 2 |
| #21461696 | 2 |
| #21460806 | 2 |
| #21460805 | 2 |
| #466×D61 | 2 |
| #11886 | 61 |