Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
410 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 126 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. #21462031 | C2 | semidirect |
| 4. #21460871 | C2 | semidirect |
| 8. C2×#14519852 | C4 | semidirect |
| 10. C2×#14519851 | C4 | semidirect |
| 11. C2×D61⋊C16 | C4 | semidirect |
| 13. C22×#11758187 | C4 | semidirect |
| 22. #16839544 | C4 | semidirect |
| 23. #16839543 | C4 | semidirect |
| 24. C61×#349 | C4 | semidirect |
| 157. #349 | #6923 | semidirect |
| 161. C61 | #12613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840821 | 2 |
| #21462031 | 2 |
| #21461575 | 2 |
| #21460871 | 2 |
| #21447438 | 2 |
| #12613 | 61 |