Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23757983 | C2 | semidirect |
| 3. #23757619 | C2 | semidirect |
| 4. #23757590 | C2 | semidirect |
| 5. #23757564 | C2 | semidirect |
| 6. #23757499 | C2 | semidirect |
| 7. #23757422 | C2 | semidirect |
| 8. C4×#14578941 | C2 | semidirect |
| 9. #23757338 | C2 | semidirect |
| 10. #102×D157 | C2 | semidirect |
| 11. #460×C157 | C2 | semidirect |
| 15. C2×C8×D157 | C22 | semidirect |
| 16. #19097771 | C22 | semidirect |
| 19. #19097747 | C22 | semidirect |
| 26. C4⋊C4×D157 | C22 | semidirect |
| 27. #19097703 | C22 | semidirect |
| 28. #19097702 | C22 | semidirect |
| 29. #19097695 | C22 | semidirect |
| 31. #19097692 | C22 | semidirect |
| 32. #19097692 | C22 | semidirect |
| 34. #19097683 | C22 | semidirect |
| 35. C4×#11929434 | C22 | semidirect |
| 36. C2×SD16×C157 | C22 | semidirect |
| 38. C4×Q8×C157 | C22 | semidirect |
| 39. C4⋊C8×C157 | C22 | semidirect |
| 40. #102×C157 | C22 | semidirect |
| 84. D628 | SD16 | semidirect |
| 136. C157 | #3295 | semidirect |
| 144. #460 | D157 | semidirect |
| 152. C2×SD16 | C2×D157 | semidirect |
| 162. C4×Q8 | C2×D157 | semidirect |
| 169. C4⋊C8 | C2×D157 | semidirect |
| 175. #102 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757983 | 2 |
| #23757908 | 2 |
| #23757619 | 2 |
| #23757590 | 2 |
| #23757564 | 2 |
| #23757499 | 2 |
| #23757422 | 2 |
| C4×#14578941 | 2 |
| #23757338 | 2 |
| #102×D157 | 2 |
| #460×C157 | 2 |
| #3295 | 157 |