Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#19097790 | C2 | semidirect |
| 2. C2×#19097777 | C2 | semidirect |
| 3. #23757852 | C2 | semidirect |
| 4. #23757518 | C2 | semidirect |
| 5. #23757517 | C2 | semidirect |
| 6. #23757515 | C2 | semidirect |
| 7. #23757514 | C2 | semidirect |
| 8. #23757506 | C2 | semidirect |
| 9. #107×D157 | C2 | semidirect |
| 10. #23757271 | C2 | semidirect |
| 11. #466×C157 | C2 | semidirect |
| 64. C8×D157 | D4 | semidirect |
| 143. C157 | #3061 | semidirect |
| 153. #466 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097790 | 2 |
| C2×#19097777 | 2 |
| #23757852 | 2 |
| #23757518 | 2 |
| #23757517 | 2 |
| #23757515 | 2 |
| #23757514 | 2 |
| #23757506 | 2 |
| #107×D157 | 2 |
| #23757271 | 2 |
| #466×C157 | 2 |
| #3061 | 157 |