Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
800 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 247 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. C22×Dic60 | C2 | semidirect |
| 3. C2×#91111 | C2 | direct (N × H) |
| 4. C22×C3⋊#672 | C2 | semidirect |
| 12. C2×Dic60 | C22 | semidirect |
| 13. #91111 | C22 | direct (N × H) |
| 14. C2×C3⋊#672 | C22 | semidirect |
| 32. Dic60 | C23 | semidirect |
| 33. C3⋊#672 | C23 | semidirect |
| 89. C22×C3×C5 | SD32 | semidirect |
| 130. C2×C3×C5 | C2×SD32 | semidirect |
| 146. C22×C5 | #827 | semidirect |
| 165. C3×C5 | C22×SD32 | semidirect |
| 168. C22×C3 | #3959 | semidirect |
| 174. C2×C5 | C2×#827 | semidirect |
| 189. C2×C3 | C2×#3959 | semidirect |
| 191. C5 | C22×#827 | semidirect |
| 194. C22 | #91111 | direct (N × H) |
| 199. C3 | C22×#3959 | semidirect |
| 201. C2 | C2×#91111 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×D8 | 2 |
| C22×Dic60 | 2 |
| C2×#91111 | 2 |
| C22×C3⋊#672 | 2 |
| C22×#3959 | 3 |
| C22×#827 | 5 |