Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 9. #16840691 | C4 | semidirect |
| 10. #16840690 | C4 | semidirect |
| 11. #16840689 | C4 | semidirect |
| 12. #16840688 | C4 | semidirect |
| 17. C4×#11758185 | C4 | semidirect |
| 18. C16×Dic61 | C4 | semidirect |
| 19. C16×Dic61 | C4 | semidirect |
| 20. C4×C16×C61 | C4 | semidirect |
| 129. C4×C16 | #6923 | semidirect |
| 131. C61 | #12670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#368 | 2 |
| #21462170 | 2 |
| #21461621 | 2 |
| #21460881 | 2 |
| C4×C16×D61 | 2 |
| #12670 | 61 |