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. #23758039 | C2 | semidirect |
| 4. #23757540 | C2 | semidirect |
| 5. #23757533 | C2 | semidirect |
| 6. #23757322 | C2 | semidirect |
| 7. #23757257 | C2 | semidirect |
| 8. C2×#19097688 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C157 | C2 | semidirect |
| 11. #19097802 | C22 | semidirect |
| 15. #19097797 | C22 | semidirect |
| 21. #19097777 | C22 | semidirect |
| 26. #19097707 | C22 | semidirect |
| 27. #19097690 | C22 | semidirect |
| 28. #19097688 | C22 | semidirect |
| 29. #19097688 | C22 | semidirect |
| 34. C2×SD16×C157 | C22 | semidirect |
| 35. C2×D8×C157 | C22 | semidirect |
| 147. C157 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D157 | semidirect |
| 171. C2×SD16 | C2×D157 | semidirect |
| 173. C2×D8 | C2×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 |
| #23758039 | 2 |
| #23757540 | 2 |
| #23757533 | 2 |
| #23757322 | 2 |
| #23757257 | 2 |
| C2×#19097688 | 2 |
| C2×AGL(1,ℤ/8)×C157 | 2 |
| #3068 | 157 |