Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 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. #23758072 | C2 | semidirect |
| 2. C2×#19097794 | C2 | semidirect |
| 3. #131×D157 | C2 | semidirect |
| 4. #23757545 | C2 | semidirect |
| 5. #23757544 | C2 | semidirect |
| 6. #23757543 | C2 | semidirect |
| 7. #23757539 | C2 | semidirect |
| 8. #23757538 | C2 | semidirect |
| 9. #108×D157 | C2 | semidirect |
| 10. #23757256 | C2 | semidirect |
| 11. #473×C157 | C2 | semidirect |
| 25. C2×#14578941 | C22 | semidirect |
| 26. C2×D1256 | C22 | semidirect |
| 37. #19097707 | C22 | semidirect |
| 38. #19097706 | C22 | semidirect |
| 39. #19097690 | C22 | semidirect |
| 40. #19097687 | C22 | semidirect |
| 41. #19097687 | C22 | semidirect |
| 43. C2×Q16×C157 | C22 | semidirect |
| 45. #108×C157 | C22 | semidirect |
| 46. #101×C157 | C22 | semidirect |
| 166. C157 | #3067 | semidirect |
| 172. #473 | D157 | semidirect |
| 193. C2×Q16 | C2×D157 | semidirect |
| 209. #108 | C2×D157 | semidirect |
| 211. #101 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758072 | 2 |
| C2×#19097794 | 2 |
| #131×D157 | 2 |
| #23757545 | 2 |
| #23757544 | 2 |
| #23757543 | 2 |
| #23757539 | 2 |
| #23757538 | 2 |
| #108×D157 | 2 |
| #23757256 | 2 |
| #473×C157 | 2 |
| #3067 | 157 |