Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
822 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 2. #21460917 | C2 | semidirect |
| 3. #21460916 | C2 | semidirect |
| 7. #16840749 | C4 | semidirect |
| 25. #14519838 | C2×C4 | semidirect |
| 210. C61 | #12585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840749 | 2 |
| #21460917 | 2 |
| #21460916 | 2 |
| #21448306 | 2 |
| #12585 | 61 |