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. C2×#19097818 | C2 | semidirect |
| 2. #23758088 | C2 | semidirect |
| 3. #23758084 | C2 | semidirect |
| 4. #23758071 | C2 | semidirect |
| 5. C2×#19097801 | C2 | semidirect |
| 6. #23758040 | C2 | semidirect |
| 7. #585×C157 | C2 | semidirect |
| 9. #19097818 | C22 | semidirect |
| 10. C2×#14578954 | C22 | semidirect |
| 12. C22×Dic314 | C22 | semidirect |
| 14. #19097802 | C22 | semidirect |
| 15. #19097801 | C22 | semidirect |
| 16. #19097801 | C22 | semidirect |
| 17. #19097797 | C22 | semidirect |
| 18. #19097796 | C22 | semidirect |
| 19. #19097791 | C22 | semidirect |
| 20. C2×#14578944 | C22 | semidirect |
| 21. C2×#14578942 | C22 | semidirect |
| 22. #19097778 | C22 | semidirect |
| 23. C2×#14578938 | C22 | semidirect |
| 25. 2−1+4×C157 | C22 | semidirect |
| 27. H(5,𝔽2)×C157 | C22 | semidirect |
| 112. C157 | #3586 | semidirect |
| 114. #585 | D157 | semidirect |
| 124. 2−1+4 | C2×D157 | semidirect |
| 126. H(5,𝔽2) | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097818 | 2 |
| #23758088 | 2 |
| #23758084 | 2 |
| #23758071 | 2 |
| C2×#19097801 | 2 |
| #23758040 | 2 |
| #585×C157 | 2 |
| #3586 | 157 |