Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19097799 | C2 | semidirect |
| 2. C2×#19097791 | C2 | semidirect |
| 3. #23757837 | C2 | semidirect |
| 4. #23757754 | C2 | semidirect |
| 5. #23757498 | C2 | semidirect |
| 6. #23757491 | C2 | semidirect |
| 7. #23757472 | C2 | semidirect |
| 8. #23757467 | C2 | semidirect |
| 9. #23757301 | C2 | semidirect |
| 10. C2×#19097691 | C2 | semidirect |
| 11. #417×C157 | C2 | semidirect |
| 16. C2×#14578944 | C22 | semidirect |
| 18. C2×#14578942 | C22 | semidirect |
| 19. C2×#14578941 | C22 | semidirect |
| 21. C2×#14578939 | C22 | semidirect |
| 28. #19097736 | C22 | semidirect |
| 29. #19097733 | C22 | semidirect |
| 34. #19097700 | C22 | semidirect |
| 35. #19097700 | C22 | semidirect |
| 41. #103×C157 | C22 | semidirect |
| 42. #102×C157 | C22 | semidirect |
| 45. #14578954 | D4 | semidirect |
| 154. C157 | #3045 | semidirect |
| 165. #417 | D157 | semidirect |
| 194. #103 | C2×D157 | semidirect |
| 197. #102 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097799 | 2 |
| C2×#19097791 | 2 |
| #23757837 | 2 |
| #23757754 | 2 |
| #23757498 | 2 |
| #23757491 | 2 |
| #23757472 | 2 |
| #23757467 | 2 |
| #23757301 | 2 |
| C2×#19097691 | 2 |
| #417×C157 | 2 |
| #3045 | 157 |