Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
178 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 8. #16840689 | C4 | semidirect |
| 9. #16840688 | C4 | semidirect |
| 11. #16839596 | C4 | semidirect |
| 14. C61×M64 | C4 | semidirect |
| 84. M64 | #6923 | semidirect |
| 90. C61 | #7477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462170 | 2 |
| C2×#16840689 | 2 |
| M64×D61 | 2 |
| #7477 | 61 |