Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19097802 | C2 | semidirect |
| 3. C2×#19097760 | C2 | semidirect |
| 4. #23757741 | C2 | semidirect |
| 5. #23757498 | C2 | semidirect |
| 6. #23757491 | C2 | semidirect |
| 7. #23757296 | C2 | semidirect |
| 8. #23757277 | C2 | semidirect |
| 9. #419×C157 | C2 | semidirect |
| 14. C2×#14578944 | C22 | semidirect |
| 16. C2×#14578941 | C22 | semidirect |
| 22. #19097736 | C22 | semidirect |
| 23. #19097733 | C22 | semidirect |
| 29. #19097700 | C22 | semidirect |
| 34. #103×C157 | C22 | semidirect |
| 125. C157 | #3040 | semidirect |
| 134. #419 | D157 | semidirect |
| 159. #103 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097802 | 2 |
| C2×#19097799 | 2 |
| C2×#19097760 | 2 |
| #23757741 | 2 |
| #23757498 | 2 |
| #23757491 | 2 |
| #23757296 | 2 |
| #23757277 | 2 |
| #419×C157 | 2 |
| #3040 | 157 |