Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 2. C2×C22⋊C4×D157 | C2 | semidirect |
| 3. #23757149 | C2 | semidirect |
| 4. #23757134 | C2 | semidirect |
| 5. #23757129 | C2 | semidirect |
| 6. #379×C157 | C2 | semidirect |
| 9. C22×C22⋊D157 | C4 | semidirect |
| 12. C22×C4×D157 | C22 | semidirect |
| 14. C2×C22⋊Dic157 | C22 | semidirect |
| 15. C2×#14578931 | C22 | semidirect |
| 17. #19097678 | C22 | semidirect |
| 20. C2×C22⋊C4×C157 | C22 | semidirect |
| 28. C2×C22⋊D157 | C2×C4 | semidirect |
| 30. C22×Dic157 | C2×C4 | semidirect |
| 40. C24×C157 | C2×C4 | semidirect |
| 49. C22×D157 | C22⋊C4 | semidirect |
| 98. C157 | #2308 | semidirect |
| 105. #379 | D157 | semidirect |
| 118. C2×C22⋊C4 | C2×D157 | semidirect |
| 126. C24 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D157 | 2 |
| C2×C22⋊C4×D157 | 2 |
| #23757149 | 2 |
| #23757134 | 2 |
| #23757129 | 2 |
| #379×C157 | 2 |
| #2308 | 157 |