Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #23758071 | C2 | semidirect |
| 2. C2×#19097797 | C2 | semidirect |
| 3. #23758040 | C2 | semidirect |
| 4. #23757541 | C2 | semidirect |
| 5. #23757534 | C2 | semidirect |
| 6. #23757321 | C2 | semidirect |
| 7. #23757255 | C2 | semidirect |
| 8. C2×#19097688 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C157 | C2 | semidirect |
| 12. #19097801 | C22 | semidirect |
| 16. #19097796 | C22 | semidirect |
| 18. C2×#14578942 | C22 | semidirect |
| 19. C2×#14578939 | C22 | semidirect |
| 21. #19097778 | C22 | semidirect |
| 26. #19097706 | C22 | semidirect |
| 27. #19097689 | C22 | semidirect |
| 28. #19097688 | C22 | semidirect |
| 29. #19097687 | C22 | semidirect |
| 147. C157 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758071 | 2 |
| C2×#19097797 | 2 |
| #23758040 | 2 |
| #23757541 | 2 |
| #23757534 | 2 |
| #23757321 | 2 |
| #23757255 | 2 |
| C2×#19097688 | 2 |
| C2×AGL(1,ℤ/8)×C157 | 2 |
| #3068 | 157 |