Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
314 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 10. #16840691 | C4 | semidirect |
| 11. #16840690 | C4 | semidirect |
| 17. #16839592 | C4 | semidirect |
| 18. #16839591 | C4 | semidirect |
| 19. C61×#368 | C4 | semidirect |
| 93. #6923 | #368 | direct (N × H) |
| 117. #368 | #6923 | direct (N × H) |
| 121. C61 | C4×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#368 | 2 |
| C2×C16×#6923 | 2 |
| #108×#6923 | 2 |
| #21460878 | 2 |
| #368×D61 | 2 |
| C4×#368 | 61 |