Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
462 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 151 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. #21458960 | C2 | semidirect |
| 2. #21448137 | C2 | semidirect |
| 3. #21448131 | C2 | semidirect |
| 4. #21448126 | C2 | semidirect |
| 5. C2×#16839599 | C2 | semidirect |
| 6. #21448113 | C2 | semidirect |
| 7. C61×#3417 | C2 | semidirect |
| 12. #16839602 | C22 | semidirect |
| 13. #16839600 | C22 | semidirect |
| 14. #16839599 | C22 | semidirect |
| 15. #16839599 | C22 | semidirect |
| 16. #16839597 | C22 | semidirect |
| 17. #16839596 | C22 | semidirect |
| 18. C2×#14519683 | C22 | semidirect |
| 21. C61×#508 | C22 | semidirect |
| 22. C2×Q32×C61 | C22 | semidirect |
| 92. #3417 | D61 | semidirect |
| 108. #508 | C2×D61 | semidirect |
| 109. C2×Q32 | C2×D61 | semidirect |
| 119. C61 | #33983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458960 | 2 |
| #21448137 | 2 |
| #21448131 | 2 |
| #21448126 | 2 |
| C2×#16839599 | 2 |
| #21448113 | 2 |
| C61×#3417 | 2 |
| #33983 | 61 |