Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23757639 | C2 | semidirect |
| 3. #23757635 | C2 | semidirect |
| 4. #23757630 | C2 | semidirect |
| 5. #23757621 | C2 | semidirect |
| 6. #23757277 | C2 | semidirect |
| 7. #23757272 | C2 | semidirect |
| 8. #23757267 | C2 | semidirect |
| 9. C2×#19097691 | C2 | semidirect |
| 10. #23757229 | C2 | semidirect |
| 11. #544×C157 | C2 | semidirect |
| 21. #19097694 | C22 | semidirect |
| 22. #19097694 | C22 | semidirect |
| 23. #19097694 | C22 | semidirect |
| 28. #19097691 | C22 | semidirect |
| 29. #19097691 | C22 | semidirect |
| 30. #19097691 | C22 | semidirect |
| 31. #19097682 | C22 | semidirect |
| 32. C4×#11929434 | C22 | semidirect |
| 34. C4⋊Q8×C157 | C22 | semidirect |
| 36. #125×C157 | C22 | semidirect |
| 135. C157 | #3136 | semidirect |
| 137. #544 | D157 | semidirect |
| 153. C4⋊Q8 | C2×D157 | semidirect |
| 156. #125 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757842 | 2 |
| #23757639 | 2 |
| #23757635 | 2 |
| #23757630 | 2 |
| #23757621 | 2 |
| #23757277 | 2 |
| #23757272 | 2 |
| #23757267 | 2 |
| C2×#19097691 | 2 |
| #23757229 | 2 |
| #544×C157 | 2 |
| #3136 | 157 |