Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23757829 | C2 | semidirect |
| 3. #23757643 | C2 | semidirect |
| 4. #23757642 | C2 | semidirect |
| 5. #23757637 | C2 | semidirect |
| 6. #23757631 | C2 | semidirect |
| 7. #23757266 | C2 | semidirect |
| 8. #97×D157 | C2 | semidirect |
| 9. #490×C157 | C2 | semidirect |
| 90. C157 | #3135 | semidirect |
| 97. #490 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757829 | 2 |
| #23757821 | 2 |
| #23757643 | 2 |
| #23757642 | 2 |
| #23757637 | 2 |
| #23757631 | 2 |
| #23757266 | 2 |
| #97×D157 | 2 |
| #490×C157 | 2 |
| #3135 | 157 |