Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#19097797 | C2 | semidirect |
| 2. C2×#19097778 | C2 | semidirect |
| 3. #23757851 | C2 | semidirect |
| 4. #23757524 | C2 | semidirect |
| 5. #23757517 | C2 | semidirect |
| 6. #23757507 | C2 | semidirect |
| 7. #23757500 | C2 | semidirect |
| 8. #23757316 | C2 | semidirect |
| 9. #23757267 | C2 | semidirect |
| 10. C2×#19097692 | C2 | semidirect |
| 11. #535×C157 | C2 | semidirect |
| 18. C2×#14578938 | C22 | semidirect |
| 20. C22×#11929434 | C22 | semidirect |
| 21. #19097750 | C22 | semidirect |
| 23. #19097745 | C22 | semidirect |
| 27. #19097704 | C22 | semidirect |
| 28. #19097702 | C22 | semidirect |
| 29. #19097694 | C22 | semidirect |
| 30. #19097694 | C22 | semidirect |
| 33. #19097691 | C22 | semidirect |
| 34. #19097691 | C22 | semidirect |
| 54. #14578938 | D4 | semidirect |
| 151. C157 | #3062 | semidirect |
| 156. #535 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097797 | 2 |
| C2×#19097778 | 2 |
| #23757851 | 2 |
| #23757524 | 2 |
| #23757517 | 2 |
| #23757507 | 2 |
| #23757500 | 2 |
| #23757316 | 2 |
| #23757267 | 2 |
| C2×#19097692 | 2 |
| #535×C157 | 2 |
| #3062 | 157 |