Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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. #135×D157 | C2 | semidirect |
| 2. #23757715 | C2 | semidirect |
| 3. #23757712 | C2 | semidirect |
| 4. #23757710 | C2 | semidirect |
| 5. #23757707 | C2 | semidirect |
| 6. #23757705 | C2 | semidirect |
| 7. #23757703 | C2 | semidirect |
| 8. C2×#19097710 | C2 | semidirect |
| 9. #508×C157 | C2 | semidirect |
| 12. #19097793 | C22 | semidirect |
| 16. Q16×D157 | C22 | semidirect |
| 18. D8×D157 | C22 | semidirect |
| 20. Dic1256 | C22 | semidirect |
| 21. #19097717 | C22 | semidirect |
| 22. #19097716 | C22 | semidirect |
| 23. #19097715 | C22 | semidirect |
| 24. #19097714 | C22 | semidirect |
| 25. D2512 | C22 | semidirect |
| 26. #19097712 | C22 | semidirect |
| 27. #19097710 | C22 | semidirect |
| 28. #19097710 | C22 | semidirect |
| 29. C2×#14578929 | C22 | semidirect |
| 30. #135×C157 | C22 | semidirect |
| 31. Q32×C157 | C22 | semidirect |
| 32. SD32×C157 | C22 | semidirect |
| 33. D16×C157 | C22 | semidirect |
| 34. C2×C16×C157 | C22 | semidirect |
| 103. C157 | #3414 | semidirect |
| 112. #508 | D157 | semidirect |
| 120. #135 | C2×D157 | semidirect |
| 127. Q32 | C2×D157 | semidirect |
| 131. SD32 | C2×D157 | semidirect |
| 134. D16 | C2×D157 | semidirect |
| 138. C2×C16 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D157 | 2 |
| #23757715 | 2 |
| #23757712 | 2 |
| #23757710 | 2 |
| #23757707 | 2 |
| #23757705 | 2 |
| #23757703 | 2 |
| C2×#19097710 | 2 |
| #508×C157 | 2 |
| #3414 | 157 |