Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
174 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 174 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 |
|---|---|---|
| 5. #16840695 | C4 | semidirect |
| 12. #16839592 | C4 | semidirect |
| 14. C61×#368 | C4 | semidirect |
| 90. #368 | #6923 | semidirect |
| 93. C61 | #7478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊M64 | 2 |
| C2×#16840688 | 2 |
| #368×D61 | 2 |
| #7478 | 61 |