Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14578944 | C2 | semidirect |
| 2. C22×#14578942 | C2 | semidirect |
| 3. C22×#14578941 | C2 | semidirect |
| 5. C2×#19097759 | C2 | semidirect |
| 6. #23757655 | C2 | direct (N × H) |
| 7. C2×C4×#11929434 | C2 | semidirect |
| 8. C2×#124×C157 | C2 | semidirect |
| 12. C2×#14578944 | C22 | semidirect |
| 14. C2×#14578942 | C22 | semidirect |
| 16. C2×#14578941 | C22 | semidirect |
| 22. #19097759 | C22 | semidirect |
| 24. C4×#11929434 | C22 | semidirect |
| 28. #124×C157 | C22 | semidirect |
| 112. C2×C157 | #495 | semidirect |
| 116. C157 | C2×#495 | semidirect |
| 123. C2×#124 | D157 | semidirect |
| 143. #124 | C2×D157 | semidirect |
| 230. C2 | #23757655 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578944 | 2 |
| C22×#14578942 | 2 |
| C22×#14578941 | 2 |
| C22×#14578939 | 2 |
| C2×#19097759 | 2 |
| #23757655 | 2 |
| C2×C4×#11929434 | 2 |
| C2×#124×C157 | 2 |
| C2×#495 | 157 |