Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 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. C2×#19097794 | C2 | semidirect |
| 2. C2×D8×D157 | C2 | semidirect |
| 3. #23757916 | C2 | semidirect |
| 4. #23757511 | C2 | semidirect |
| 5. #23757506 | C2 | semidirect |
| 6. #23757485 | C2 | semidirect |
| 7. #23757422 | C2 | semidirect |
| 8. #23757417 | C2 | semidirect |
| 9. C4×D1256 | C2 | semidirect |
| 10. C8×D628 | C2 | semidirect |
| 11. #495×C157 | C2 | semidirect |
| 12. C2×#14578955 | C22 | semidirect |
| 15. C2×#14578941 | C22 | semidirect |
| 20. C2×C8×D157 | C22 | semidirect |
| 24. #19097742 | C22 | semidirect |
| 27. C4×D628 | C22 | semidirect |
| 29. #19097705 | C22 | semidirect |
| 30. C4⋊#11929434 | C22 | semidirect |
| 31. #19097695 | C22 | semidirect |
| 32. #19097693 | C22 | semidirect |
| 33. #19097692 | C22 | semidirect |
| 35. #19097683 | C22 | semidirect |
| 36. C2×Q16×C157 | C22 | semidirect |
| 37. C2×SD16×C157 | C22 | semidirect |
| 39. #124×C157 | C22 | semidirect |
| 40. C4×C8×C157 | C22 | semidirect |
| 56. D1256 | D4 | semidirect |
| 127. C2×D157 | #135 | semidirect |
| 143. C157 | #3280 | semidirect |
| 148. #495 | D157 | semidirect |
| 159. C2×Q16 | C2×D157 | semidirect |
| 161. C2×SD16 | C2×D157 | semidirect |
| 168. #124 | C2×D157 | semidirect |
| 184. C4×C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| C2×D8×D157 | 2 |
| #23757916 | 2 |
| #23757511 | 2 |
| #23757506 | 2 |
| #23757485 | 2 |
| #23757422 | 2 |
| #23757417 | 2 |
| C4×D1256 | 2 |
| C8×D628 | 2 |
| #495×C157 | 2 |
| #3280 | 157 |