Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23758071 | C2 | semidirect |
| 2. C2×#19097799 | C2 | semidirect |
| 3. C2×#19097796 | C2 | semidirect |
| 4. #23757543 | C2 | semidirect |
| 5. #23757536 | C2 | semidirect |
| 6. #23757322 | C2 | semidirect |
| 7. #23757255 | C2 | semidirect |
| 8. C2×#19097687 | C2 | semidirect |
| 9. #568×C157 | C2 | semidirect |
| 13. #19097801 | C22 | semidirect |
| 19. #19097796 | C22 | semidirect |
| 21. C2×#14578943 | C22 | semidirect |
| 23. C2×D1256 | C22 | semidirect |
| 27. #19097707 | C22 | semidirect |
| 28. #19097689 | C22 | semidirect |
| 29. #19097687 | C22 | semidirect |
| 30. #19097687 | C22 | semidirect |
| 33. #131×C157 | C22 | semidirect |
| 147. C157 | #3068 | semidirect |
| 152. #568 | D157 | semidirect |
| 175. #131 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758071 | 2 |
| C2×#19097799 | 2 |
| C2×#19097796 | 2 |
| #23757543 | 2 |
| #23757536 | 2 |
| #23757322 | 2 |
| #23757255 | 2 |
| C2×#19097687 | 2 |
| #568×C157 | 2 |
| #3068 | 157 |