Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23757983 | C2 | semidirect |
| 3. #23757620 | C2 | semidirect |
| 4. #23757593 | C2 | semidirect |
| 5. #23757563 | C2 | semidirect |
| 6. #23757505 | C2 | semidirect |
| 7. #23757473 | C2 | semidirect |
| 8. #23757422 | C2 | semidirect |
| 9. C8×D628 | C2 | semidirect |
| 10. #102×D157 | C2 | semidirect |
| 11. C4×SD16×C157 | C2 | semidirect |
| 14. C2×#14578941 | C22 | semidirect |
| 15. C2×C8×D157 | C22 | semidirect |
| 16. #19097771 | C22 | semidirect |
| 20. #19097747 | C22 | semidirect |
| 26. C4⋊C4×D157 | C22 | semidirect |
| 27. #19097702 | C22 | semidirect |
| 28. C4⋊#11929434 | C22 | semidirect |
| 29. #19097693 | C22 | semidirect |
| 30. #19097693 | C22 | semidirect |
| 32. #19097691 | C22 | semidirect |
| 33. #19097683 | C22 | semidirect |
| 35. C4×Q8×C157 | C22 | semidirect |
| 37. #106×C157 | C22 | semidirect |
| 38. #103×C157 | C22 | semidirect |
| 40. C4×C8×C157 | C22 | semidirect |
| 88. D628 | SD16 | semidirect |
| 136. C157 | #3295 | semidirect |
| 146. C4×SD16 | D157 | semidirect |
| 162. C4×Q8 | C2×D157 | semidirect |
| 168. #106 | C2×D157 | semidirect |
| 170. #103 | C2×D157 | semidirect |
| 177. C4×C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757983 | 2 |
| D4×D628 | 2 |
| #23757620 | 2 |
| #23757593 | 2 |
| #23757563 | 2 |
| #23757505 | 2 |
| #23757473 | 2 |
| #23757422 | 2 |
| C8×D628 | 2 |
| #102×D157 | 2 |
| C4×SD16×C157 | 2 |
| #3295 | 157 |