Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #23757229 | C2 | semidirect |
| 5. C2×C4×#11929434 | C2 | semidirect |
| 6. #23757037 | C2 | semidirect |
| 7. #339×C157 | C2 | semidirect |
| 10. #19097779 | C4 | semidirect |
| 16. #19097699 | C4 | semidirect |
| 17. #19097694 | C4 | semidirect |
| 18. #19097691 | C4 | semidirect |
| 98. C157 | #1764 | semidirect |
| 106. #339 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097779 | 2 |
| C2×#19097699 | 2 |
| #23757267 | 2 |
| #23757229 | 2 |
| C2×C4×#11929434 | 2 |
| #23757037 | 2 |
| #339×C157 | 2 |
| #1764 | 157 |