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. C2×#19097796 | C2 | semidirect |
| 2. C2×#19097796 | C2 | semidirect |
| 3. #23758040 | C2 | semidirect |
| 4. #23757541 | C2 | semidirect |
| 5. #23757538 | C2 | semidirect |
| 6. #23757321 | C2 | semidirect |
| 7. #23757257 | C2 | semidirect |
| 8. C2×#19097687 | C2 | semidirect |
| 9. #575×C157 | C2 | semidirect |
| 16. C2×#14578941 | C22 | semidirect |
| 18. C2×#14578939 | C22 | semidirect |
| 20. #19097778 | C22 | semidirect |
| 25. #19097706 | C22 | semidirect |
| 26. #19097690 | C22 | semidirect |
| 27. #19097688 | C22 | semidirect |
| 28. #19097687 | C22 | semidirect |
| 32. #137×C157 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C157 | C22 | semidirect |
| 147. C157 | #3068 | semidirect |
| 149. #575 | D157 | semidirect |
| 162. #137 | C2×D157 | semidirect |
| 168. AGL(1,ℤ/8) | 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 |
| #23758040 | 2 |
| #23757541 | 2 |
| #23757538 | 2 |
| #23757321 | 2 |
| #23757257 | 2 |
| C2×#19097687 | 2 |
| #575×C157 | 2 |
| #3068 | 157 |