Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. #23757927 | C2 | semidirect |
| 2. #23757619 | C2 | semidirect |
| 3. #23757584 | C2 | semidirect |
| 4. #23757553 | C2 | semidirect |
| 5. #23757507 | C2 | semidirect |
| 6. #23757465 | C2 | semidirect |
| 7. #23757407 | C2 | semidirect |
| 8. C4×#14578939 | C2 | semidirect |
| 9. D4×#11929434 | C2 | semidirect |
| 10. C2×#19097692 | C2 | semidirect |
| 11. D42×C157 | C2 | semidirect |
| 14. C2×#14578939 | C22 | semidirect |
| 15. C22×#11929434 | C22 | semidirect |
| 16. #19097771 | C22 | semidirect |
| 19. #19097745 | C22 | semidirect |
| 20. C4×D628 | C22 | semidirect |
| 21. C2×C4⋊Dic157 | C22 | semidirect |
| 22. #19097704 | C22 | semidirect |
| 23. #19097704 | C22 | semidirect |
| 24. C4⋊#11929434 | C22 | semidirect |
| 27. #19097692 | C22 | semidirect |
| 28. #19097692 | C22 | semidirect |
| 29. #19097692 | C22 | semidirect |
| 30. #19097691 | C22 | semidirect |
| 31. C22⋊#11929434 | C22 | semidirect |
| 32. C4×#11929434 | C22 | semidirect |
| 103. D4×C157 | D8 | semidirect |
| 104. D4×C157 | #41 | semidirect |
| 142. C157 | #3294 | semidirect |
| 145. D42 | D157 | semidirect |
| 239. D4 | #14578939 | semidirect |
| 240. D4 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757927 | 2 |
| #23757619 | 2 |
| #23757584 | 2 |
| #23757553 | 2 |
| #23757507 | 2 |
| #23757465 | 2 |
| #23757407 | 2 |
| C4×#14578939 | 2 |
| D4×#11929434 | 2 |
| C2×#19097692 | 2 |
| D42×C157 | 2 |
| #3294 | 157 |