Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
334 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #16840237 | C4 | semidirect |
| 7. C2×#14519694 | C4 | semidirect |
| 10. #16839506 | C4 | semidirect |
| 14. C61×#353 | C4 | semidirect |
| 145. #353 | Dic61 | semidirect |
| 149. C61 | #7493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446218 | 2 |
| #21444533 | 2 |
| C2×C61×#353 | 2 |
| #7493 | 61 |