Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19097798 | C2 | semidirect |
| 2. #23757824 | C2 | semidirect |
| 3. C4×D4×D157 | C2 | semidirect |
| 4. #23757491 | C2 | semidirect |
| 5. #23757490 | C2 | semidirect |
| 6. #23757475 | C2 | semidirect |
| 7. #23757469 | C2 | semidirect |
| 8. #23757468 | C2 | semidirect |
| 9. #23757295 | C2 | semidirect |
| 10. #23757273 | C2 | semidirect |
| 11. #461×C157 | C2 | semidirect |
| 20. #19097768 | C22 | semidirect |
| 21. #19097760 | C22 | semidirect |
| 34. C4⋊#11929434 | C22 | semidirect |
| 35. #19097700 | C22 | semidirect |
| 36. #19097695 | C22 | semidirect |
| 37. #19097693 | C22 | semidirect |
| 38. #19097691 | C22 | semidirect |
| 40. C4⋊Q8×C157 | C22 | semidirect |
| 42. C4⋊C8×C157 | C22 | semidirect |
| 43. #103×C157 | C22 | semidirect |
| 54. D4×D157 | D4 | semidirect |
| 146. C4×C157 | AGL(1,ℤ/8) | semidirect |
| 160. C157 | #3036 | semidirect |
| 168. #461 | D157 | semidirect |
| 182. C4⋊Q8 | C2×D157 | semidirect |
| 200. C4⋊C8 | C2×D157 | semidirect |
| 202. #103 | C2×D157 | semidirect |
| 311. C4 | #19097798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097798 | 2 |
| #23757824 | 2 |
| C4×D4×D157 | 2 |
| #23757491 | 2 |
| #23757490 | 2 |
| #23757475 | 2 |
| #23757469 | 2 |
| #23757468 | 2 |
| #23757295 | 2 |
| #23757273 | 2 |
| #461×C157 | 2 |
| #3036 | 157 |