Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #23757901 | C2 | semidirect |
| 3. #23757574 | C2 | semidirect |
| 4. #23757574 | C2 | semidirect |
| 5. #23757564 | C2 | semidirect |
| 6. #23757554 | C2 | semidirect |
| 7. #23757315 | C2 | semidirect |
| 8. #23757311 | C2 | semidirect |
| 11. #424×C157 | C2 | semidirect |
| 13. #19097771 | C22 | semidirect |
| 15. #19097763 | C22 | semidirect |
| 26. #19097705 | C22 | semidirect |
| 27. #19097705 | C22 | semidirect |
| 28. #19097705 | C22 | semidirect |
| 29. #19097703 | C22 | semidirect |
| 30. #19097703 | C22 | semidirect |
| 31. #19097703 | C22 | semidirect |
| 39. C4⋊C8×C157 | C22 | semidirect |
| 40. C4⋊C8×C157 | C22 | semidirect |
| 45. C2×D628 | Q8 | semidirect |
| 124. C157 | #3081 | semidirect |
| 134. #424 | D157 | semidirect |
| 160. C4⋊C8 | C2×D157 | semidirect |
| 161. C4⋊C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757901 | 2 |
| #23757747 | 2 |
| #23757574 | 2 |
| #23757564 | 2 |
| #23757554 | 2 |
| #23757315 | 2 |
| #23757311 | 2 |
| #23757279 | 2 |
| C2×#19097693 | 2 |
| #424×C157 | 2 |
| #3081 | 157 |