Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#19097797 | C2 | semidirect |
| 2. #23757823 | C2 | semidirect |
| 3. #23757488 | C2 | semidirect |
| 4. #23757478 | C2 | semidirect |
| 5. #23757468 | C2 | semidirect |
| 6. #23757297 | C2 | semidirect |
| 7. #23757272 | C2 | semidirect |
| 8. C2×C4×D4×C157 | C2 | semidirect |
| 14. #19097771 | C22 | semidirect |
| 15. #19097768 | C22 | semidirect |
| 16. #19097759 | C22 | semidirect |
| 21. C4⋊#11929434 | C22 | semidirect |
| 22. C4⋊#11929434 | C22 | semidirect |
| 23. #19097694 | C22 | semidirect |
| 24. #19097691 | C22 | semidirect |
| 53. C2×D4×C157 | D4 | semidirect |
| 119. C4×C157 | AGL(1,ℤ/8) | semidirect |
| 129. C157 | #3036 | semidirect |
| 133. C2×C4×D4 | D157 | semidirect |
| 174. C2×D4 | D628 | semidirect |
| 250. C4 | #19097797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097797 | 2 |
| #23757823 | 2 |
| #23757488 | 2 |
| #23757478 | 2 |
| #23757468 | 2 |
| #23757297 | 2 |
| #23757272 | 2 |
| C2×C4×D4×C157 | 2 |
| #3036 | 157 |