Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23757804 | C2 | semidirect |
| 2. #23757674 | C2 | semidirect |
| 3. #23757656 | C2 | semidirect |
| 4. #23757626 | C2 | semidirect |
| 5. #23757514 | C2 | semidirect |
| 6. #23757500 | C2 | semidirect |
| 7. #23757367 | C2 | semidirect |
| 8. #23757364 | C2 | semidirect |
| 9. D8×Dic157 | C2 | semidirect |
| 10. C2×C8×Dic157 | C2 | semidirect |
| 118. C157 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757804 | 2 |
| #23757674 | 2 |
| #23757656 | 2 |
| #23757626 | 2 |
| #23757514 | 2 |
| #23757500 | 2 |
| #23757367 | 2 |
| #23757364 | 2 |
| D8×Dic157 | 2 |
| C2×C8×Dic157 | 2 |
| #466×C157 | 2 |
| #3168 | 157 |