Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 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. C22×Dic628 | C2 | semidirect |
| 2. C2×#19097715 | C2 | direct (N × H) |
| 3. C22×#14578929 | C2 | semidirect |
| 7. C2×Dic628 | C22 | semidirect |
| 8. #19097715 | C22 | direct (N × H) |
| 9. C2×#14578929 | C22 | semidirect |
| 18. Dic628 | C23 | semidirect |
| 19. #14578929 | C23 | semidirect |
| 42. C22×C157 | SD32 | semidirect |
| 48. C2×C157 | C2×SD32 | semidirect |
| 50. C157 | C22×SD32 | semidirect |
| 93. C22 | #19097715 | direct (N × H) |
| 99. C2 | C2×#19097715 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic628 | 2 |
| C2×#19097715 | 2 |
| C22×#14578929 | 2 |
| C22×D8×C157 | 2 |
| C22×SD32 | 157 |