Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1326 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 352 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 |
|---|---|---|
| 5. #16840707 | C4 | semidirect |
| 10. #16839632 | C4 | semidirect |
| 11. #16839631 | C4 | semidirect |
| 12. C61×#384 | C4 | semidirect |
| 42. C42×C61 | C42 | semidirect |
| 45. C4×Dic61 | C42 | semidirect |
| 88. #384 | #6923 | semidirect |
| 92. C61 | #13830 | semidirect |
| 125. C42 | C4×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840707 | 2 |
| #21460998 | 2 |
| #384×D61 | 2 |
| #13830 | 61 |