Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
472 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. #21458956 | C2 | semidirect |
| 2. #21448132 | C2 | semidirect |
| 3. #21448130 | C2 | semidirect |
| 4. #21448128 | C2 | semidirect |
| 5. #21448125 | C2 | semidirect |
| 6. D32×D61 | C2 | semidirect |
| 7. #21448112 | C2 | semidirect |
| 8. C2×C61×D32 | C2 | semidirect |
| 12. #16840194 | C22 | semidirect |
| 13. #16840191 | C22 | semidirect |
| 14. D16×D61 | C22 | semidirect |
| 16. Dic976 | C22 | semidirect |
| 17. #16839601 | C22 | semidirect |
| 18. #16839600 | C22 | semidirect |
| 19. D1952 | C22 | semidirect |
| 20. #16839597 | C22 | semidirect |
| 21. #16839596 | C22 | semidirect |
| 22. #16839595 | C22 | semidirect |
| 23. C32×D61 | C22 | semidirect |
| 24. C2×D16×C61 | C22 | semidirect |
| 25. C61×D32 | C22 | semidirect |
| 26. C61×D32 | C22 | semidirect |
| 27. C2×C32×C61 | C22 | semidirect |
| 108. C2×D32 | D61 | semidirect |
| 121. C2×D16 | C2×D61 | semidirect |
| 128. D32 | C2×D61 | semidirect |
| 129. D32 | C2×D61 | semidirect |
| 133. C2×C32 | C2×D61 | semidirect |
| 134. C61 | #33982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458956 | 2 |
| #21448132 | 2 |
| #21448130 | 2 |
| #21448128 | 2 |
| #21448125 | 2 |
| D32×D61 | 2 |
| #21448112 | 2 |
| C2×C61×D32 | 2 |
| #33982 | 61 |