Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14578943 | C2 | semidirect |
| 2. C2×#19097777 | C2 | semidirect |
| 3. #23757849 | C2 | semidirect |
| 5. #23757520 | C2 | semidirect |
| 6. #23757503 | C2 | semidirect |
| 7. #23757281 | C2 | semidirect |
| 8. #23757277 | C2 | semidirect |
| 9. #427×C157 | C2 | semidirect |
| 18. C2×#14578937 | C22 | semidirect |
| 19. C2×C8×D157 | C22 | semidirect |
| 25. #19097751 | C22 | semidirect |
| 28. #19097694 | C22 | semidirect |
| 33. #107×C157 | C22 | semidirect |
| 34. #106×C157 | C22 | semidirect |
| 62. C2×C8×C157 | D4 | semidirect |
| 120. C157 | #3057 | semidirect |
| 128. #427 | D157 | semidirect |
| 152. #107 | C2×D157 | semidirect |
| 153. #106 | C2×D157 | semidirect |
| 180. C2×C8 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578943 | 2 |
| C2×#19097777 | 2 |
| #23757849 | 2 |
| #23757842 | 2 |
| #23757520 | 2 |
| #23757503 | 2 |
| #23757281 | 2 |
| #23757277 | 2 |
| #427×C157 | 2 |
| #3057 | 157 |