Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23757818 | C2 | semidirect |
| 2. C2×D4×Dic157 | C2 | semidirect |
| 3. #23757587 | C2 | semidirect |
| 4. #23757584 | C2 | semidirect |
| 5. #23757551 | C2 | semidirect |
| 6. #23757466 | C2 | semidirect |
| 7. #23757407 | C2 | semidirect |
| 8. D8×Dic157 | C2 | semidirect |
| 9. #23757353 | C2 | semidirect |
| 10. #23757323 | C2 | semidirect |
| 11. #447×C157 | C2 | semidirect |
| 15. #19097770 | C22 | semidirect |
| 16. #19097767 | C22 | semidirect |
| 24. D4×Dic157 | C22 | semidirect |
| 25. #19097733 | C22 | semidirect |
| 30. #19097705 | C22 | semidirect |
| 31. #19097704 | C22 | semidirect |
| 32. #19097700 | C22 | semidirect |
| 33. #19097693 | C22 | semidirect |
| 35. #19097692 | C22 | semidirect |
| 37. C8×Dic157 | C22 | semidirect |
| 96. C2×Dic157 | D8 | semidirect |
| 113. D4×C157 | #41 | semidirect |
| 149. C157 | #3100 | semidirect |
| 158. #447 | D157 | semidirect |
| 249. D4 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757818 | 2 |
| C2×D4×Dic157 | 2 |
| #23757587 | 2 |
| #23757584 | 2 |
| #23757551 | 2 |
| #23757466 | 2 |
| #23757407 | 2 |
| D8×Dic157 | 2 |
| #23757353 | 2 |
| #23757323 | 2 |
| #447×C157 | 2 |
| #3100 | 157 |