Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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. C2×#19097799 | C2 | semidirect |
| 2. #23757823 | C2 | semidirect |
| 3. C2×C4×D628 | C2 | semidirect |
| 4. #23757489 | C2 | semidirect |
| 5. #23757479 | C2 | semidirect |
| 6. #23757469 | C2 | semidirect |
| 7. #23757275 | C2 | semidirect |
| 8. #423×C157 | C2 | semidirect |
| 15. #19097771 | C22 | semidirect |
| 16. #19097768 | C22 | semidirect |
| 17. #19097759 | C22 | semidirect |
| 28. #19097696 | C22 | semidirect |
| 29. #19097693 | C22 | semidirect |
| 32. C4⋊C8×C157 | C22 | semidirect |
| 33. C4⋊C8×C157 | C22 | semidirect |
| 42. C2×D628 | D4 | semidirect |
| 118. C4×C157 | AGL(1,ℤ/8) | semidirect |
| 129. C157 | #3036 | semidirect |
| 137. #423 | D157 | semidirect |
| 160. C4⋊C8 | C2×D157 | semidirect |
| 161. C4⋊C8 | C2×D157 | semidirect |
| 250. C4 | #19097799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097799 | 2 |
| #23757823 | 2 |
| C2×C4×D628 | 2 |
| #23757489 | 2 |
| #23757479 | 2 |
| #23757469 | 2 |
| #23757275 | 2 |
| #423×C157 | 2 |
| #3036 | 157 |