Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. C2×#16839557 | C2 | semidirect |
| 3. #21443971 | C2 | semidirect |
| 4. C61×#1533 | C2 | semidirect |
| 5. C2×#14519825 | C4 | semidirect |
| 9. #16839934 | C4 | semidirect |
| 12. C2×#14519696 | C4 | semidirect |
| 15. #16839557 | C22 | semidirect |
| 19. C61×#329 | C22 | semidirect |
| 23. #14519825 | C2×C4 | semidirect |
| 38. #14519696 | C2×C4 | semidirect |
| 172. #1533 | D61 | semidirect |
| 195. #329 | C2×D61 | semidirect |
| 196. C61 | #13569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839934 | 2 |
| C2×#16839557 | 2 |
| #21443971 | 2 |
| C61×#1533 | 2 |
| #13569 | 61 |