Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23756492 | C2 | semidirect |
| 2. #23756490 | C2 | semidirect |
| 3. #23756487 | C2 | semidirect |
| 4. #23756483 | C2 | semidirect |
| 5. #23756482 | C2 | semidirect |
| 6. #23756479 | C2 | semidirect |
| 7. #23756475 | C2 | semidirect |
| 9. C4×Dic626 | C2 | semidirect |
| 10. C4×D1252 | C2 | semidirect |
| 11. C4×C22⋊D313 | C2 | semidirect |
| 12. C4×C22⋊D313 | C2 | semidirect |
| 13. #23756454 | C2 | semidirect |
| 14. C42×D313 | C2 | semidirect |
| 15. #117×C313 | C2 | semidirect |
| 103. C313 | #529 | semidirect |
| 118. #117 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756492 | 2 |
| #23756490 | 2 |
| #23756487 | 2 |
| #23756483 | 2 |
| #23756482 | 2 |
| #23756479 | 2 |
| #23756475 | 2 |
| #23756470 | 2 |
| C4×Dic626 | 2 |
| C4×D1252 | 2 |
| C4×C22⋊D313 | 2 |
| #23756454 | 2 |
| C42×D313 | 2 |
| #117×C313 | 2 |
| #529 | 313 |