Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. #23757980 | C2 | semidirect |
| 2. #23757619 | C2 | semidirect |
| 3. #23757589 | C2 | semidirect |
| 4. #23757563 | C2 | semidirect |
| 5. #23757500 | C2 | semidirect |
| 6. #23757470 | C2 | semidirect |
| 7. #23757424 | C2 | semidirect |
| 8. C4×#14578942 | C2 | semidirect |
| 9. D4×#11929434 | C2 | semidirect |
| 10. C2×#19097692 | C2 | semidirect |
| 13. C2×#14578942 | C22 | semidirect |
| 14. C22×#11929434 | C22 | semidirect |
| 15. #19097771 | C22 | semidirect |
| 17. #19097750 | C22 | semidirect |
| 19. C4×Dic314 | C22 | semidirect |
| 21. C2×C4⋊Dic157 | C22 | semidirect |
| 22. #19097702 | C22 | semidirect |
| 23. #19097702 | C22 | semidirect |
| 24. C4⋊#11929434 | C22 | semidirect |
| 25. #19097694 | C22 | semidirect |
| 28. #19097692 | C22 | semidirect |
| 29. #19097692 | C22 | semidirect |
| 30. #19097692 | C22 | semidirect |
| 31. C22⋊#11929434 | C22 | semidirect |
| 32. C4×#11929434 | C22 | semidirect |
| 100. D4×C157 | SD16 | semidirect |
| 136. C157 | #3295 | semidirect |
| 230. D4 | #14578942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757980 | 2 |
| #23757619 | 2 |
| #23757589 | 2 |
| #23757563 | 2 |
| #23757500 | 2 |
| #23757470 | 2 |
| #23757424 | 2 |
| C4×#14578942 | 2 |
| D4×#11929434 | 2 |
| C2×#19097692 | 2 |
| D42×C157 | 2 |
| #3295 | 157 |