Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
626 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 4. #16840707 | C4 | semidirect |
| 10. #16840698 | C4 | semidirect |
| 14. C2×#14519706 | C4 | semidirect |
| 16. C2×C4×#92418 | C4 | semidirect |
| 17. C2×C4×C8×C61 | C4 | semidirect |
| 142. C2×C4×C8 | #6923 | semidirect |
| 150. C61 | #7980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462266 | 2 |
| #21460682 | 2 |
| C2×#16839813 | 2 |
| #7980 | 61 |