Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
788 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 788 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 |
|---|---|---|
| 6. C4×C4⋊#6923 | C4 | semidirect |
| 9. #16840698 | C4 | semidirect |
| 14. #16839785 | C4 | semidirect |
| 16. C4×#11758194 | C4 | semidirect |
| 17. C4×M16×C61 | C4 | semidirect |
| 132. C4×M16 | #6923 | semidirect |
| 139. C61 | #8048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519856 | 2 |
| #21460699 | 2 |
| #21454450 | 2 |
| #8048 | 61 |