Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19097817 | C2 | semidirect |
| 2. C22×#14578939 | C2 | semidirect |
| 3. #23757840 | C2 | semidirect |
| 4. #23757417 | C2 | semidirect |
| 5. #23757405 | C2 | semidirect |
| 6. #23757279 | C2 | semidirect |
| 7. #23757269 | C2 | semidirect |
| 8. #23757241 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C157 | C2 | semidirect |
| 12. C2×#14578955 | C22 | semidirect |
| 18. C2×D4×D157 | C22 | semidirect |
| 20. C2×#14578939 | C22 | semidirect |
| 21. C22×#11929434 | C22 | semidirect |
| 24. #19097742 | C22 | semidirect |
| 26. #19097730 | C22 | semidirect |
| 27. #19097695 | C22 | semidirect |
| 28. #19097693 | C22 | semidirect |
| 29. #19097692 | C22 | semidirect |
| 30. #19097683 | C22 | semidirect |
| 32. C22×D4×C157 | C22 | semidirect |
| 34. C2×SD16×C157 | C22 | semidirect |
| 35. C2×D8×C157 | C22 | semidirect |
| 36. C2×M16×C157 | C22 | semidirect |
| 50. C2×D628 | D4 | semidirect |
| 69. #41×C157 | D4 | semidirect |
| 151. C157 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D157 | semidirect |
| 172. C22×D4 | C2×D157 | semidirect |
| 174. C2×SD16 | C2×D157 | semidirect |
| 177. C2×D8 | C2×D157 | semidirect |
| 178. C2×M16 | C2×D157 | semidirect |
| 198. #41 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097817 | 2 |
| C22×#14578939 | 2 |
| #23757840 | 2 |
| #23757417 | 2 |
| #23757405 | 2 |
| #23757279 | 2 |
| #23757269 | 2 |
| #23757241 | 2 |
| C2×AGL(1,ℤ/8)×C157 | 2 |
| #3008 | 157 |