Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
296 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 13. #16840651 | C4 | semidirect |
| 14. C4×#11758187 | C4 | semidirect |
| 18. #16839583 | C4 | semidirect |
| 19. #16839582 | C4 | semidirect |
| 20. C61×#364 | C4 | semidirect |
| 123. #364 | #6923 | semidirect |
| 129. C61 | #12667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462039 | 2 |
| C4×#14519852 | 2 |
| #21461621 | 2 |
| #21460871 | 2 |
| #364×D61 | 2 |
| #12667 | 61 |