Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 10. #16840689 | C4 | semidirect |
| 11. #16840688 | C4 | semidirect |
| 12. C16×#6923 | C4 | semidirect |
| 13. C16×#6923 | C4 | semidirect |
| 17. #16839592 | C4 | semidirect |
| 18. #16839591 | C4 | semidirect |
| 19. C61×#368 | C4 | semidirect |
| 115. #368 | #6923 | semidirect |
| 121. C61 | #12670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462170 | 2 |
| C2×C16×#6923 | 2 |
| #21461624 | 2 |
| #21460882 | 2 |
| #368×D61 | 2 |
| #12670 | 61 |