Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21457618 | C2 | semidirect |
| 3. #21447936 | C2 | semidirect |
| 4. #21447892 | C2 | semidirect |
| 5. #21447775 | C2 | semidirect |
| 6. #21447701 | C2 | semidirect |
| 7. #21447657 | C2 | semidirect |
| 8. C61×#2246 | C2 | semidirect |
| 10. #16840563 | C22 | semidirect |
| 11. #16840198 | C22 | semidirect |
| 16. #16840178 | C22 | semidirect |
| 18. #16840029 | C22 | semidirect |
| 21. #16839880 | C22 | semidirect |
| 22. #16839592 | C22 | semidirect |
| 23. #16839583 | C22 | semidirect |
| 24. #16839575 | C22 | semidirect |
| 25. #16839570 | C22 | semidirect |
| 26. #16839545 | C22 | semidirect |
| 27. C2×D16×C61 | C22 | semidirect |
| 28. C2×D16×C61 | C22 | semidirect |
| 29. C61×#493 | C22 | semidirect |
| 30. C4×C16×C61 | C22 | semidirect |
| 44. Dic488 | D4 | semidirect |
| 45. #14519722 | D4 | semidirect |
| 47. D976 | D4 | semidirect |
| 140. #2246 | D61 | semidirect |
| 158. C2×D16 | C2×D61 | semidirect |
| 159. C2×D16 | C2×D61 | semidirect |
| 161. #493 | C2×D61 | semidirect |
| 172. C4×C16 | C2×D61 | semidirect |
| 173. C61 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458956 | 2 |
| #21457618 | 2 |
| #21447936 | 2 |
| #21447892 | 2 |
| #21447775 | 2 |
| #21447701 | 2 |
| #21447657 | 2 |
| C61×#2246 | 2 |
| #33858 | 61 |