Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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. #23757926 | C2 | semidirect |
| 2. D4×D628 | C2 | semidirect |
| 3. #23757621 | C2 | semidirect |
| 4. #23757588 | C2 | semidirect |
| 5. #23757510 | C2 | semidirect |
| 6. #23757469 | C2 | semidirect |
| 7. #23757408 | C2 | semidirect |
| 8. C4×#14578939 | C2 | semidirect |
| 9. #23757338 | C2 | semidirect |
| 10. #102×D157 | C2 | semidirect |
| 11. #474×C157 | C2 | semidirect |
| 15. C2×D1256 | C22 | semidirect |
| 17. C2×C8×D157 | C22 | semidirect |
| 22. #19097746 | C22 | semidirect |
| 26. C4×D628 | C22 | semidirect |
| 27. C4⋊C4×D157 | C22 | semidirect |
| 28. #19097704 | C22 | semidirect |
| 29. #19097693 | C22 | semidirect |
| 31. #19097691 | C22 | semidirect |
| 32. #19097691 | C22 | semidirect |
| 33. #19097691 | C22 | semidirect |
| 34. #19097683 | C22 | semidirect |
| 35. C4×#11929434 | C22 | semidirect |
| 36. C4⋊Q8×C157 | C22 | semidirect |
| 38. #107×C157 | C22 | semidirect |
| 39. C4⋊C8×C157 | C22 | semidirect |
| 92. D628 | D8 | semidirect |
| 105. D4×C157 | #41 | semidirect |
| 142. C157 | #3294 | semidirect |
| 148. #474 | D157 | semidirect |
| 161. C4⋊Q8 | C2×D157 | semidirect |
| 174. #107 | C2×D157 | semidirect |
| 175. C4⋊C8 | C2×D157 | semidirect |
| 240. D4 | #14578955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757926 | 2 |
| D4×D628 | 2 |
| #23757621 | 2 |
| #23757588 | 2 |
| #23757510 | 2 |
| #23757469 | 2 |
| #23757408 | 2 |
| C4×#14578939 | 2 |
| #23757338 | 2 |
| #102×D157 | 2 |
| #474×C157 | 2 |
| #3294 | 157 |