Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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×#19097799 | C2 | semidirect |
| 2. C2×#19097791 | C2 | semidirect |
| 3. C22×#14578939 | C2 | semidirect |
| 4. #23757840 | C2 | semidirect |
| 5. #23757837 | C2 | semidirect |
| 6. #23757661 | C2 | semidirect |
| 7. #23757659 | C2 | semidirect |
| 8. #23757654 | C2 | semidirect |
| 9. #23757648 | C2 | semidirect |
| 10. #23757231 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C157 | C2 | semidirect |
| 16. C2×#14578944 | C22 | semidirect |
| 17. C2×#14578943 | C22 | semidirect |
| 18. C2×#14578942 | C22 | semidirect |
| 19. C2×#14578941 | C22 | semidirect |
| 20. C2×D1256 | C22 | semidirect |
| 24. C2×#14578939 | C22 | semidirect |
| 26. #19097767 | C22 | semidirect |
| 27. #19097767 | C22 | semidirect |
| 28. #19097760 | C22 | semidirect |
| 29. #19097758 | C22 | semidirect |
| 35. #19097681 | C22 | semidirect |
| 36. C8×Dic157 | C22 | semidirect |
| 40. C2×SD16×C157 | C22 | semidirect |
| 41. C2×D8×C157 | C22 | semidirect |
| 64. C2×#11929434 | D4 | semidirect |
| 86. M16×C157 | D4 | semidirect |
| 153. C157 | #3155 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D157 | semidirect |
| 177. C2×SD16 | C2×D157 | semidirect |
| 183. C2×D8 | C2×D157 | semidirect |
| 232. M16 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097799 | 2 |
| C2×#19097791 | 2 |
| C22×#14578939 | 2 |
| #23757840 | 2 |
| #23757837 | 2 |
| #23757661 | 2 |
| #23757659 | 2 |
| #23757654 | 2 |
| #23757648 | 2 |
| #23757231 | 2 |
| C2×AGL(1,ℤ/8)×C157 | 2 |
| #3155 | 157 |