Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
350 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 9. #16840653 | C4 | semidirect |
| 10. #16840652 | C4 | semidirect |
| 11. #16840651 | C4 | semidirect |
| 12. #16840650 | C4 | semidirect |
| 13. #16840649 | C4 | semidirect |
| 14. #16840648 | C4 | semidirect |
| 15. C4×#11758187 | C4 | semidirect |
| 16. C16×#6923 | C4 | semidirect |
| 22. #16839540 | C4 | semidirect |
| 23. #16839539 | C4 | semidirect |
| 24. C61×#347 | C4 | semidirect |
| 115. #347 | #6923 | semidirect |
| 125. C61 | #12542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462039 | 2 |
| #21462031 | 2 |
| #21462029 | 2 |
| #21461541 | 2 |
| #21447422 | 2 |
| #12542 | 61 |