Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
308 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 112 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. #16840687 | C4 | semidirect |
| 10. #16840686 | C4 | semidirect |
| 15. #16839537 | C4 | semidirect |
| 16. #16839537 | C4 | semidirect |
| 17. C4×#11758185 | C4 | semidirect |
| 18. C4×C16×C61 | C4 | semidirect |
| 110. C4×C16 | #6923 | semidirect |
| 112. C61 | #12668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462166 | 2 |
| #21461621 | 2 |
| #21460889 | 2 |
| #21460887 | 2 |
| C4×#14519716 | 2 |
| #12668 | 61 |