Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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. #23758109 | C2 | semidirect |
| 2. C2×#19097818 | C2 | semidirect |
| 3. #23758090 | C2 | semidirect |
| 4. #23758085 | C2 | semidirect |
| 5. #23758073 | C2 | semidirect |
| 6. C2×#19097804 | C2 | semidirect |
| 7. #568×C157 | C2 | semidirect |
| 10. #19097818 | C22 | semidirect |
| 11. #19097818 | C22 | semidirect |
| 12. #19097817 | C22 | semidirect |
| 15. C2×#14578954 | C22 | semidirect |
| 18. C22×Dic314 | C22 | semidirect |
| 20. #19097804 | C22 | semidirect |
| 21. #19097804 | C22 | semidirect |
| 22. #19097804 | C22 | semidirect |
| 23. #19097799 | C22 | semidirect |
| 24. #19097799 | C22 | semidirect |
| 25. #19097793 | C22 | semidirect |
| 26. C2×Dic628 | C22 | semidirect |
| 27. C2×#14578943 | C22 | semidirect |
| 29. #131×C157 | C22 | semidirect |
| 30. C2×M16×C157 | C22 | semidirect |
| 112. C157 | #3586 | semidirect |
| 120. #568 | D157 | semidirect |
| 142. #131 | C2×D157 | semidirect |
| 143. C2×M16 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758109 | 2 |
| C2×#19097818 | 2 |
| #23758090 | 2 |
| #23758085 | 2 |
| #23758073 | 2 |
| C2×#19097804 | 2 |
| #568×C157 | 2 |
| #3586 | 157 |