Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #23758040 | C2 | semidirect |
| 3. #23757291 | C2 | semidirect |
| 4. C2×#19097699 | C2 | semidirect |
| 5. C4×#41×C157 | C2 | semidirect |
| 7. #19097818 | C4 | semidirect |
| 8. #19097817 | C4 | semidirect |
| 13. C2×#14578938 | C22 | semidirect |
| 14. #19097699 | C22 | semidirect |
| 15. #19097699 | C22 | semidirect |
| 19. #117×C157 | C22 | semidirect |
| 20. C2×C42×C157 | C22 | semidirect |
| 24. #14578954 | C2×C4 | semidirect |
| 27. C2×Dic314 | C2×C4 | semidirect |
| 29. C2×D628 | C2×C4 | semidirect |
| 83. C157 | #2901 | semidirect |
| 87. C4×#41 | D157 | semidirect |
| 101. #117 | C2×D157 | semidirect |
| 102. C2×C42 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758109 | 2 |
| #23758040 | 2 |
| #23757291 | 2 |
| C2×#19097699 | 2 |
| C4×#41×C157 | 2 |
| #2901 | 157 |