Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #23757754 | C2 | semidirect |
| 3. #23757612 | C2 | semidirect |
| 4. #23757607 | C2 | semidirect |
| 5. #23757596 | C2 | semidirect |
| 6. #23757585 | C2 | semidirect |
| 7. #23757315 | C2 | semidirect |
| 8. C2×#19097704 | C2 | semidirect |
| 9. #23757269 | C2 | semidirect |
| 10. #23757241 | C2 | semidirect |
| 11. #417×C157 | C2 | semidirect |
| 133. C157 | #3098 | semidirect |
| 143. #417 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757851 | 2 |
| #23757754 | 2 |
| #23757612 | 2 |
| #23757607 | 2 |
| #23757596 | 2 |
| #23757585 | 2 |
| #23757315 | 2 |
| C2×#19097704 | 2 |
| #23757269 | 2 |
| #23757241 | 2 |
| #417×C157 | 2 |
| #3098 | 157 |