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 |
|---|---|---|
| 2. #125×D157 | C2 | semidirect |
| 3. #23757641 | C2 | semidirect |
| 4. #23757639 | C2 | semidirect |
| 5. #23757638 | C2 | semidirect |
| 6. #23757629 | C2 | semidirect |
| 7. #23757273 | C2 | semidirect |
| 8. #23757225 | C2 | semidirect |
| 9. #491×C157 | C2 | semidirect |
| 90. C157 | #3142 | semidirect |
| 95. #491 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757824 | 2 |
| #125×D157 | 2 |
| #23757641 | 2 |
| #23757639 | 2 |
| #23757638 | 2 |
| #23757629 | 2 |
| #23757273 | 2 |
| #23757225 | 2 |
| #491×C157 | 2 |
| #3142 | 157 |