Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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. C22×#14578939 | C2 | semidirect |
| 2. C2×#19097778 | C2 | semidirect |
| 3. #23757837 | C2 | semidirect |
| 4. #23757524 | C2 | semidirect |
| 5. #23757507 | C2 | semidirect |
| 6. #23757309 | C2 | semidirect |
| 7. #23757278 | C2 | semidirect |
| 8. #23757277 | C2 | semidirect |
| 9. #535×C157 | C2 | semidirect |
| 16. C2×#14578938 | C22 | semidirect |
| 18. C22×#11929434 | C22 | semidirect |
| 21. #19097745 | C22 | semidirect |
| 24. #19097704 | C22 | semidirect |
| 25. #19097702 | C22 | semidirect |
| 26. #19097692 | C22 | semidirect |
| 27. #19097691 | C22 | semidirect |
| 32. #121×C157 | C22 | semidirect |
| 46. C2×#11929434 | D4 | semidirect |
| 125. C157 | #3058 | semidirect |
| 130. #535 | D157 | semidirect |
| 152. #121 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578939 | 2 |
| C2×#19097778 | 2 |
| #23757837 | 2 |
| #23757524 | 2 |
| #23757507 | 2 |
| #23757309 | 2 |
| #23757278 | 2 |
| #23757277 | 2 |
| #535×C157 | 2 |
| #3058 | 157 |