Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
292 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 14. #16840687 | C4 | semidirect |
| 15. #16840686 | C4 | semidirect |
| 16. #16840653 | C4 | semidirect |
| 17. #16840653 | C4 | semidirect |
| 23. #16839592 | C4 | semidirect |
| 24. #16839591 | C4 | semidirect |
| 25. #16839591 | C4 | semidirect |
| 26. C61×#368 | C4 | semidirect |
| 145. #368 | #6923 | semidirect |
| 152. C61 | #12678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462166 | 2 |
| C2×#16840653 | 2 |
| #21461640 | 2 |
| #21461628 | 2 |
| #21460899 | 2 |
| #21460896 | 2 |
| #21447612 | 2 |
| #12678 | 61 |