Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1188 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1188 conjugacy classes of subgroups — too many to draw. Only its 220 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 |
|---|---|---|
| 1. #21462421 | C2 | semidirect |
| 2. #21462101 | C2 | semidirect |
| 3. #21462090 | C2 | semidirect |
| 14. #16840333 | C4 | semidirect |
| 16. C2×#14519775 | C4 | semidirect |
| 17. #41×Dic61 | C4 | semidirect |
| 18. C2×2−1+4×C61 | C4 | semidirect |
| 141. C2×2−1+4 | #6923 | semidirect |
| 154. C61 | #33360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462421 | 2 |
| #21462101 | 2 |
| #21462090 | 2 |
| #21459600 | 2 |
| #33360 | 61 |