Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
342 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 14. #16840626 | C4 | semidirect |
| 15. #16840623 | C4 | semidirect |
| 23. #16839514 | C4 | semidirect |
| 24. #16839514 | C4 | semidirect |
| 25. #16839513 | C4 | semidirect |
| 26. C61×#334 | C4 | semidirect |
| 150. #334 | #6923 | semidirect |
| 155. C61 | #8270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461532 | 2 |
| #21461367 | 2 |
| #21461035 | 2 |
| #21461025 | 2 |
| #21460646 | 2 |
| #21444564 | 2 |
| #8270 | 61 |