Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
486 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 104 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. #21462036 | C2 | semidirect |
| 4. #21461625 | C2 | semidirect |
| 5. #21460892 | C2 | semidirect |
| 6. #21460883 | C2 | semidirect |
| 13. #16840680 | C4 | semidirect |
| 14. #16840674 | C4 | semidirect |
| 20. #16839875 | C4 | semidirect |
| 21. #16839874 | C4 | semidirect |
| 22. #16839873 | C4 | semidirect |
| 28. C61×#442 | C4 | semidirect |
| 32. #14519852 | C2×C4 | semidirect |
| 36. D61⋊C16 | C2×C4 | semidirect |
| 38. #14519847 | C2×C4 | semidirect |
| 39. #14519846 | C2×C4 | semidirect |
| 205. #442 | #6923 | semidirect |
| 217. C61 | #12647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#361 | 2 |
| #21462128 | 2 |
| #21462036 | 2 |
| #21461625 | 2 |
| #21460892 | 2 |
| #21460883 | 2 |
| #442×D61 | 2 |
| #12647 | 61 |