Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 236 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 |
|---|---|---|
| 4. C2×#90946 | C2 | direct (N × H) |
| 14. #90946 | C22 | direct (N × H) |
| 86. C22×C3×C5 | Q32 | semidirect |
| 126. C2×C3×C5 | C2×Q32 | semidirect |
| 139. C22×C5 | #829 | semidirect |
| 159. C3×C5 | C22×Q32 | semidirect |
| 160. C22×C3 | #3961 | semidirect |
| 166. C2×C5 | C2×#829 | semidirect |
| 179. C2×C3 | C2×#3961 | semidirect |
| 181. C5 | C22×#829 | semidirect |
| 182. C22 | #90946 | direct (N × H) |
| 188. C3 | C22×#3961 | semidirect |
| 189. C2 | C2×#90946 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic12 | 2 |
| C22×C3×Dic20 | 2 |
| C22×C3⋊#672 | 2 |
| C2×#90946 | 2 |
| C22×#3961 | 3 |
| C22×#829 | 5 |