Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19097796 | C2 | semidirect |
| 2. C22×D1256 | C2 | semidirect |
| 3. #23757543 | C2 | direct (N × H) |
| 4. C2×#19097707 | C2 | semidirect |
| 5. C2×#19097687 | C2 | semidirect |
| 6. C2×#131×C157 | C2 | semidirect |
| 9. #19097796 | C22 | semidirect |
| 14. C2×D1256 | C22 | semidirect |
| 17. #19097707 | C22 | semidirect |
| 18. #19097687 | C22 | semidirect |
| 21. #131×C157 | C22 | semidirect |
| 105. C2×C157 | #472 | semidirect |
| 108. C157 | C2×#472 | semidirect |
| 112. C2×#131 | D157 | semidirect |
| 127. #131 | C2×D157 | semidirect |
| 215. C2 | #23757543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097796 | 2 |
| C22×D1256 | 2 |
| #23757543 | 2 |
| C2×#19097707 | 2 |
| C2×#19097687 | 2 |
| C2×#131×C157 | 2 |
| C2×#472 | 157 |