Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23757830 | C2 | semidirect |
| 3. #23757574 | C2 | semidirect |
| 4. #23757564 | C2 | semidirect |
| 5. #23757554 | C2 | semidirect |
| 6. #23757315 | C2 | semidirect |
| 8. #423×C157 | C2 | semidirect |
| 11. #19097771 | C22 | semidirect |
| 12. #19097771 | C22 | semidirect |
| 13. #19097763 | C22 | semidirect |
| 25. #19097705 | C22 | semidirect |
| 26. #19097703 | C22 | semidirect |
| 31. C4⋊C8×C157 | C22 | semidirect |
| 32. C4⋊C8×C157 | C22 | semidirect |
| 38. C2×D628 | Q8 | semidirect |
| 115. C157 | #3077 | semidirect |
| 123. #423 | D157 | semidirect |
| 145. C4⋊C8 | C2×D157 | semidirect |
| 146. C4⋊C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757830 | 2 |
| C2×C4×D628 | 2 |
| #23757574 | 2 |
| #23757564 | 2 |
| #23757554 | 2 |
| #23757315 | 2 |
| #23757279 | 2 |
| #423×C157 | 2 |
| #3077 | 157 |