Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19097796 | C2 | semidirect |
| 2. C22×D1256 | C2 | semidirect |
| 3. #23757837 | C2 | semidirect |
| 4. #23757747 | C2 | semidirect |
| 5. #23757491 | C2 | semidirect |
| 6. #23757467 | C2 | semidirect |
| 7. #23757299 | C2 | semidirect |
| 8. #23757277 | C2 | semidirect |
| 9. #416×C157 | C2 | semidirect |
| 13. C2×#14578941 | C22 | semidirect |
| 16. C2×#14578939 | C22 | semidirect |
| 18. #19097767 | C22 | semidirect |
| 19. #19097760 | C22 | semidirect |
| 23. #19097733 | C22 | semidirect |
| 26. #19097700 | C22 | semidirect |
| 27. #19097691 | C22 | semidirect |
| 31. #103×C157 | C22 | semidirect |
| 32. #102×C157 | C22 | semidirect |
| 40. C2×D628 | D4 | semidirect |
| 121. C157 | #3041 | semidirect |
| 131. #416 | D157 | semidirect |
| 152. #103 | C2×D157 | semidirect |
| 154. #102 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097796 | 2 |
| C22×D1256 | 2 |
| #23757837 | 2 |
| #23757747 | 2 |
| #23757491 | 2 |
| #23757467 | 2 |
| #23757299 | 2 |
| #23757277 | 2 |
| #416×C157 | 2 |
| #3041 | 157 |