Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19097793 | C2 | semidirect |
| 2. C2×#19097790 | C2 | semidirect |
| 3. #23757941 | C2 | semidirect |
| 4. #23757648 | C2 | semidirect |
| 5. #23757510 | C2 | semidirect |
| 6. #23757472 | C2 | semidirect |
| 7. #23757419 | C2 | semidirect |
| 8. #23757416 | C2 | semidirect |
| 9. #23757367 | C2 | semidirect |
| 10. C8×C22⋊D157 | C2 | semidirect |
| 11. #466×C157 | C2 | semidirect |
| 56. Dic628 | D4 | semidirect |
| 134. Dic157 | #135 | semidirect |
| 142. C157 | #3287 | semidirect |
| 149. #466 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097793 | 2 |
| C2×#19097790 | 2 |
| #23757941 | 2 |
| #23757648 | 2 |
| #23757510 | 2 |
| #23757472 | 2 |
| #23757419 | 2 |
| #23757416 | 2 |
| #23757367 | 2 |
| C8×C22⋊D157 | 2 |
| #466×C157 | 2 |
| #3287 | 157 |