Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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. #127×D157 | C2 | semidirect |
| 4. #23757659 | C2 | semidirect |
| 5. #23757650 | C2 | semidirect |
| 6. #23757649 | C2 | semidirect |
| 7. #23757647 | C2 | semidirect |
| 8. C4×#14578937 | C2 | semidirect |
| 9. #492×C157 | C2 | semidirect |
| 14. C2×#14578941 | C22 | semidirect |
| 15. C2×D1256 | C22 | semidirect |
| 16. C2×#14578939 | C22 | semidirect |
| 19. #19097768 | C22 | semidirect |
| 22. #19097760 | C22 | semidirect |
| 26. #19097681 | C22 | semidirect |
| 27. C4×#11929434 | C22 | semidirect |
| 28. C2×SD16×C157 | C22 | semidirect |
| 29. C4⋊Q8×C157 | C22 | semidirect |
| 31. C4×C8×C157 | C22 | semidirect |
| 49. #14578937 | D4 | semidirect |
| 78. #11929434 | C2×D4 | semidirect |
| 86. C8×C157 | C2×D4 | semidirect |
| 98. C4×C157 | AGL(1,ℤ/8) | semidirect |
| 108. C157 | #3151 | semidirect |
| 117. #492 | D157 | semidirect |
| 124. C2×SD16 | C2×D157 | semidirect |
| 128. C4⋊Q8 | C2×D157 | semidirect |
| 140. C4×C8 | C2×D157 | semidirect |
| 195. C8 | D4×D157 | semidirect |
| 209. 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 |
| #127×D157 | 2 |
| #23757659 | 2 |
| #23757650 | 2 |
| #23757649 | 2 |
| #23757647 | 2 |
| C4×#14578937 | 2 |
| #492×C157 | 2 |
| #3151 | 157 |