Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. #21461577 | C2 | semidirect |
| 4. #21460918 | C2 | semidirect |
| 6. C2×#14519864 | C4 | semidirect |
| 10. #16840766 | C4 | semidirect |
| 12. #16840736 | C4 | semidirect |
| 15. C4×D61⋊C8 | C4 | semidirect |
| 16. #16840673 | C4 | semidirect |
| 17. #16840670 | C4 | semidirect |
| 180. C61 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462541 | 2 |
| #21462111 | 2 |
| #21461577 | 2 |
| #21460918 | 2 |
| #21447481 | 2 |
| #12633 | 61 |