Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
350 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 8. #16840655 | C4 | semidirect |
| 9. #16840654 | C4 | semidirect |
| 10. #16840653 | C4 | semidirect |
| 11. #16840652 | C4 | semidirect |
| 12. #16840649 | C4 | semidirect |
| 13. C16×#6923 | C4 | semidirect |
| 20. #16839538 | C4 | semidirect |
| 21. #16839537 | C4 | semidirect |
| 22. C16×Dic61 | C4 | semidirect |
| 23. C4×C16×C61 | C4 | semidirect |
| 117. C4×C16 | #6923 | semidirect |
| 121. C61 | #12542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462041 | 2 |
| #21462038 | 2 |
| #21462027 | 2 |
| #21461540 | 2 |
| #21447414 | 2 |
| #12542 | 61 |