Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
352 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#14519709 | C4 | semidirect |
| 9. #16839525 | C4 | semidirect |
| 13. C61×C22⋊C16 | C4 | semidirect |
| 125. C22⋊C16 | Dic61 | semidirect |
| 129. C61 | #7262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21445844 | 2 |
| #21445536 | 2 |
| C61×#2112 | 2 |
| #7262 | 61 |