Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 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×#19097797 | C2 | semidirect |
| 2. C22×#14578939 | C2 | semidirect |
| 3. #23757842 | C2 | semidirect |
| 4. #23757488 | C2 | semidirect |
| 5. #23757468 | C2 | semidirect |
| 6. #23757300 | C2 | semidirect |
| 7. #23757277 | C2 | semidirect |
| 8. #23757267 | C2 | semidirect |
| 9. #518×C157 | C2 | semidirect |
| 13. C2×#14578942 | C22 | semidirect |
| 16. C2×#14578939 | C22 | semidirect |
| 19. #19097768 | C22 | semidirect |
| 20. #19097759 | C22 | semidirect |
| 23. C4⋊#11929434 | C22 | semidirect |
| 24. #19097694 | C22 | semidirect |
| 25. #19097691 | C22 | semidirect |
| 26. #19097691 | C22 | semidirect |
| 29. C4×D4×C157 | C22 | semidirect |
| 56. C2×D4×C157 | D4 | semidirect |
| 121. C157 | #3041 | semidirect |
| 126. #518 | D157 | semidirect |
| 147. C4×D4 | C2×D157 | semidirect |
| 169. C2×D4 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097797 | 2 |
| C22×#14578939 | 2 |
| #23757842 | 2 |
| #23757488 | 2 |
| #23757468 | 2 |
| #23757300 | 2 |
| #23757277 | 2 |
| #23757267 | 2 |
| #518×C157 | 2 |
| #3041 | 157 |