Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19097791 | C2 | semidirect |
| 2. C2×#19097778 | C2 | semidirect |
| 3. #23757851 | C2 | semidirect |
| 4. #23757529 | C2 | semidirect |
| 5. #23757524 | C2 | semidirect |
| 6. #23757504 | C2 | semidirect |
| 7. #23757500 | C2 | semidirect |
| 8. C2×#19097702 | C2 | semidirect |
| 9. #23757274 | C2 | semidirect |
| 10. #23757272 | C2 | semidirect |
| 11. #537×C157 | C2 | semidirect |
| 58. C2×#11929434 | D4 | semidirect |
| 152. C157 | #3060 | semidirect |
| 157. #537 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097791 | 2 |
| C2×#19097778 | 2 |
| #23757851 | 2 |
| #23757529 | 2 |
| #23757524 | 2 |
| #23757504 | 2 |
| #23757500 | 2 |
| C2×#19097702 | 2 |
| #23757274 | 2 |
| #23757272 | 2 |
| #537×C157 | 2 |
| #3060 | 157 |