Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
356 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. #21462179 | C2 | semidirect |
| 2. C4×#14519845 | C2 | semidirect |
| 3. #21460808 | C2 | semidirect |
| 13. #16840146 | C4 | semidirect |
| 18. #16839856 | C4 | semidirect |
| 20. #16839844 | C4 | semidirect |
| 22. C61×#499 | C4 | semidirect |
| 150. #499 | #6923 | semidirect |
| 166. C61 | #11741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462179 | 2 |
| C4×#14519845 | 2 |
| #21460808 | 2 |
| #21460806 | 2 |
| #21456391 | 2 |
| #11741 | 61 |