Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 7. #16839559 | C4 | semidirect |
| 9. #16839557 | C4 | semidirect |
| 13. C2×C4×C8×C61 | C4 | semidirect |
| 14. C61×#382 | C4 | semidirect |
| 131. C2×C4×C8 | Dic61 | semidirect |
| 132. #382 | Dic61 | semidirect |
| 137. C61 | #7502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839559 | 2 |
| C2×#16839557 | 2 |
| C61×#1958 | 2 |
| #7502 | 61 |