Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23757828 | C2 | semidirect |
| 3. #23757636 | C2 | semidirect |
| 4. #23757621 | C2 | semidirect |
| 5. #23757620 | C2 | semidirect |
| 6. #23757619 | C2 | semidirect |
| 7. #23757276 | C2 | semidirect |
| 8. C4×#14578937 | C2 | semidirect |
| 9. #486×C157 | C2 | semidirect |
| 14. #19097771 | C22 | semidirect |
| 19. #19097762 | C22 | semidirect |
| 26. #19097693 | C22 | semidirect |
| 27. #19097692 | C22 | semidirect |
| 28. #19097691 | C22 | semidirect |
| 29. #19097681 | C22 | semidirect |
| 30. C4×#11929434 | C22 | semidirect |
| 31. C4⋊Q8×C157 | C22 | semidirect |
| 33. #102×C157 | C22 | semidirect |
| 34. C4×C8×C157 | C22 | semidirect |
| 123. C157 | #3138 | semidirect |
| 131. #486 | D157 | semidirect |
| 139. C4⋊Q8 | C2×D157 | semidirect |
| 155. #102 | C2×D157 | semidirect |
| 158. C4×C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757828 | 2 |
| #127×D157 | 2 |
| #23757636 | 2 |
| #23757621 | 2 |
| #23757620 | 2 |
| #23757619 | 2 |
| #23757276 | 2 |
| C4×#14578937 | 2 |
| #486×C157 | 2 |
| #3138 | 157 |