Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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×#19097796 | C2 | semidirect |
| 2. C22×#14578939 | C2 | semidirect |
| 3. #23757747 | C2 | semidirect |
| 4. #23757485 | C2 | semidirect |
| 5. #23757465 | C2 | semidirect |
| 6. #23757300 | C2 | semidirect |
| 7. #23757278 | C2 | semidirect |
| 8. #23757269 | C2 | semidirect |
| 9. #535×C157 | C2 | semidirect |
| 12. C2×#14578941 | C22 | semidirect |
| 15. C2×#14578939 | C22 | semidirect |
| 18. C4×D628 | C22 | semidirect |
| 22. C4⋊#11929434 | C22 | semidirect |
| 23. #19097695 | C22 | semidirect |
| 24. #19097692 | C22 | semidirect |
| 25. #19097692 | C22 | semidirect |
| 28. #127×C157 | C22 | semidirect |
| 29. #124×C157 | C22 | semidirect |
| 36. C2×D628 | D4 | semidirect |
| 121. C157 | #3041 | semidirect |
| 125. #535 | D157 | semidirect |
| 142. #127 | C2×D157 | semidirect |
| 143. #124 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097796 | 2 |
| C22×#14578939 | 2 |
| #23757747 | 2 |
| #23757485 | 2 |
| #23757465 | 2 |
| #23757300 | 2 |
| #23757278 | 2 |
| #23757269 | 2 |
| #535×C157 | 2 |
| #3041 | 157 |