Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19097804 | C2 | semidirect |
| 3. #23757844 | C2 | semidirect |
| 4. #23757754 | C2 | semidirect |
| 5. #23757494 | C2 | semidirect |
| 6. #23757487 | C2 | semidirect |
| 7. #23757482 | C2 | semidirect |
| 8. #23757477 | C2 | semidirect |
| 9. #23757301 | C2 | semidirect |
| 10. C2×#19097694 | C2 | semidirect |
| 11. #417×C157 | C2 | semidirect |
| 146. C157 | #3046 | semidirect |
| 157. #417 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097804 | 2 |
| C2×#19097791 | 2 |
| #23757844 | 2 |
| #23757754 | 2 |
| #23757494 | 2 |
| #23757487 | 2 |
| #23757482 | 2 |
| #23757477 | 2 |
| #23757301 | 2 |
| C2×#19097694 | 2 |
| #417×C157 | 2 |
| #3046 | 157 |