Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
592 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 145 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×Q16×D157 | C2 | semidirect |
| 2. C2×SD16×D157 | C2 | semidirect |
| 4. #124×D157 | C2 | semidirect |
| 5. #23757658 | C2 | semidirect |
| 6. #23757657 | C2 | semidirect |
| 7. #23757656 | C2 | semidirect |
| 8. #23757655 | C2 | semidirect |
| 9. #23757654 | C2 | semidirect |
| 10. C4×C8×D157 | C2 | semidirect |
| 11. #495×C157 | C2 | semidirect |
| 14. C2×Dic628 | C22 | semidirect |
| 15. C2×#14578944 | C22 | semidirect |
| 17. C2×#14578943 | C22 | semidirect |
| 18. C2×#14578942 | C22 | semidirect |
| 19. C2×#14578941 | C22 | semidirect |
| 26. #19097760 | C22 | semidirect |
| 27. #19097759 | C22 | semidirect |
| 28. #19097758 | C22 | semidirect |
| 32. C4×#11929434 | C22 | semidirect |
| 33. C8×Dic157 | C22 | semidirect |
| 34. C8×Dic157 | C22 | semidirect |
| 35. C2×Q16×C157 | C22 | semidirect |
| 36. C2×SD16×C157 | C22 | semidirect |
| 38. #124×C157 | C22 | semidirect |
| 39. C4×C8×C157 | C22 | semidirect |
| 125. D157 | #495 | direct (N × H) |
| 126. C157 | C2×#495 | semidirect |
| 137. #495 | D157 | direct (N × H) |
| 144. C2×Q16 | C2×D157 | semidirect |
| 149. C2×SD16 | C2×D157 | semidirect |
| 160. #124 | C2×D157 | semidirect |
| 166. C4×C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D157 | 2 |
| C2×SD16×D157 | 2 |
| C2×D8×D157 | 2 |
| #124×D157 | 2 |
| #23757658 | 2 |
| #23757657 | 2 |
| #23757656 | 2 |
| #23757655 | 2 |
| #23757654 | 2 |
| C4×C8×D157 | 2 |
| #495×C157 | 2 |
| C2×#495 | 157 |