Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
292 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 90 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. #23758236 | C2 | semidirect |
| 4. C2×#19097825 | C2 | semidirect |
| 5. #23758148 | C2 | semidirect |
| 6. #23758145 | C2 | semidirect |
| 12. #19097836 | C4 | semidirect |
| 13. #19097835 | C4 | semidirect |
| 14. #19097834 | C4 | semidirect |
| 15. #19097833 | C4 | semidirect |
| 22. #19097779 | C4 | semidirect |
| 23. #19097778 | C4 | semidirect |
| 25. #19097777 | C4 | semidirect |
| 30. #131×C157 | C4 | semidirect |
| 127. C157 | #1765 | semidirect |
| 142. #131 | #10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D157⋊#104 | 2 |
| #23758263 | 2 |
| #23758236 | 2 |
| C2×#19097825 | 2 |
| #23758148 | 2 |
| #23758145 | 2 |
| #131×D157 | 2 |
| #1765 | 157 |