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. C2×#19097796 | C2 | semidirect |
| 3. C22×D1256 | C2 | semidirect |
| 4. #23757842 | C2 | semidirect |
| 5. #23757421 | C2 | semidirect |
| 6. #23757408 | C2 | semidirect |
| 7. #23757277 | C2 | semidirect |
| 8. #23757239 | C2 | semidirect |
| 9. #416×C157 | C2 | semidirect |
| 12. C2×#14578955 | C22 | semidirect |
| 17. C22×D628 | C22 | semidirect |
| 19. C2×D4×D157 | C22 | semidirect |
| 21. C2×#14578941 | C22 | semidirect |
| 23. C2×D1256 | C22 | semidirect |
| 24. C2×#14578939 | C22 | semidirect |
| 25. C2×#14578938 | C22 | semidirect |
| 28. #19097746 | C22 | semidirect |
| 30. #19097691 | C22 | semidirect |
| 31. #19097683 | C22 | semidirect |
| 33. C22×C8×C157 | C22 | semidirect |
| 34. #117×C157 | C22 | semidirect |
| 35. #103×C157 | C22 | semidirect |
| 36. #102×C157 | C22 | semidirect |
| 55. C2×D628 | D4 | semidirect |
| 72. #41×C157 | D4 | semidirect |
| 151. C157 | #3008 | semidirect |
| 160. #416 | D157 | semidirect |
| 179. C22×C8 | C2×D157 | semidirect |
| 184. #117 | C2×D157 | semidirect |
| 185. #103 | C2×D157 | semidirect |
| 187. #102 | C2×D157 | semidirect |
| 198. #41 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097817 | 2 |
| C2×#19097796 | 2 |
| C22×D1256 | 2 |
| #23757842 | 2 |
| #23757421 | 2 |
| #23757408 | 2 |
| #23757277 | 2 |
| #23757239 | 2 |
| #416×C157 | 2 |
| #3008 | 157 |