Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19097706 | C2 | semidirect |
| 3. C2×#19097699 | C2 | semidirect |
| 4. #23757241 | C2 | semidirect |
| 5. #23757240 | C2 | semidirect |
| 6. C2×C4×#11929434 | C2 | semidirect |
| 7. C2×#104×C157 | C2 | semidirect |
| 11. C2×#14578944 | C4 | semidirect |
| 12. C2×#14578942 | C4 | semidirect |
| 13. C2×#14578941 | C4 | semidirect |
| 14. C2×#14578939 | C4 | semidirect |
| 119. C157 | #1974 | semidirect |
| 124. C2×#104 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097791 | 2 |
| C2×#19097706 | 2 |
| C2×#19097699 | 2 |
| #23757241 | 2 |
| #23757240 | 2 |
| C2×C4×#11929434 | 2 |
| C2×#104×C157 | 2 |
| #1974 | 157 |