Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #23757671 | C2 | semidirect |
| 4. #23757615 | C2 | semidirect |
| 5. #23757604 | C2 | semidirect |
| 6. #23757569 | C2 | semidirect |
| 7. #23757559 | C2 | semidirect |
| 8. #23757531 | C2 | semidirect |
| 9. C4×Dic628 | C2 | semidirect |
| 10. #23757315 | C2 | semidirect |
| 116. C157 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757993 | 2 |
| #23757980 | 2 |
| #23757671 | 2 |
| #23757615 | 2 |
| #23757604 | 2 |
| #23757569 | 2 |
| #23757559 | 2 |
| #23757531 | 2 |
| C4×Dic628 | 2 |
| #23757315 | 2 |
| #436×C157 | 2 |
| #3356 | 157 |