Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23757828 | C2 | semidirect |
| 3. #23757629 | C2 | semidirect |
| 4. #23757623 | C2 | semidirect |
| 5. #23757621 | C2 | semidirect |
| 6. #23757620 | C2 | semidirect |
| 7. #23757268 | C2 | semidirect |
| 8. C4×C8×D157 | C2 | semidirect |
| 9. #487×C157 | C2 | semidirect |
| 111. C157 | #3131 | semidirect |
| 117. #487 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757828 | 2 |
| #23757824 | 2 |
| #23757629 | 2 |
| #23757623 | 2 |
| #23757621 | 2 |
| #23757620 | 2 |
| #23757268 | 2 |
| C4×C8×D157 | 2 |
| #487×C157 | 2 |
| #3131 | 157 |