Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 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. #21457619 | C2 | semidirect |
| 3. #21448069 | C2 | semidirect |
| 4. #21447939 | C2 | semidirect |
| 5. #21447896 | C2 | semidirect |
| 6. #21447778 | C2 | semidirect |
| 7. #21447701 | C2 | semidirect |
| 8. C61×#2170 | C2 | semidirect |
| 9. #16840567 | C22 | semidirect |
| 12. #16840200 | C22 | semidirect |
| 16. C2×D976 | C22 | semidirect |
| 17. C2×D976 | C22 | semidirect |
| 18. #16840139 | C22 | semidirect |
| 20. #16840032 | C22 | semidirect |
| 22. #16839880 | C22 | semidirect |
| 23. #16839592 | C22 | semidirect |
| 24. #16839576 | C22 | semidirect |
| 25. #16839570 | C22 | semidirect |
| 26. C61×#504 | C22 | semidirect |
| 28. C61×#364 | C22 | semidirect |
| 29. C61×#350 | C22 | semidirect |
| 30. C4×C16×C61 | C22 | semidirect |
| 45. Dic488 | D4 | semidirect |
| 47. #14519722 | D4 | semidirect |
| 52. D976 | D4 | semidirect |
| 145. #2170 | D61 | semidirect |
| 160. #504 | C2×D61 | semidirect |
| 168. #364 | C2×D61 | semidirect |
| 171. #350 | 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 |
|---|---|
| #21458960 | 2 |
| #21457619 | 2 |
| #21448069 | 2 |
| #21447939 | 2 |
| #21447896 | 2 |
| #21447778 | 2 |
| #21447701 | 2 |
| C61×#2170 | 2 |
| #33858 | 61 |