Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 82 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. D61⋊#362 | C2 | semidirect |
| 4. #21461981 | C2 | semidirect |
| 5. #21460889 | C2 | semidirect |
| 6. #21460868 | C2 | semidirect |
| 24. C2×Dic488 | C4 | semidirect |
| 25. C2×#14519723 | C4 | semidirect |
| 26. C2×#14519721 | C4 | semidirect |
| 28. C2×SD32×C61 | C4 | semidirect |
| 195. C2×SD32 | #6923 | semidirect |
| 208. C61 | #13035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462595 | 2 |
| D61⋊#362 | 2 |
| #21462134 | 2 |
| #21461981 | 2 |
| #21460889 | 2 |
| #21460868 | 2 |
| C2×#16840201 | 2 |
| #13035 | 61 |