Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 388 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. #21462175 | C2 | semidirect |
| 4. #21461929 | C2 | semidirect |
| 5. #21460901 | C2 | semidirect |
| 6. #21460865 | C2 | semidirect |
| 27. #16839573 | C4 | semidirect |
| 28. #16839572 | C4 | semidirect |
| 29. #16839571 | C4 | semidirect |
| 30. C61×#360 | C4 | semidirect |
| 219. #360 | #6923 | semidirect |
| 223. C61 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#444 | 2 |
| #21462175 | 2 |
| #21462133 | 2 |
| #21461929 | 2 |
| #21460901 | 2 |
| #21460865 | 2 |
| #21447553 | 2 |
| #12944 | 61 |