Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 122 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. C3×#64971 | C2 | semidirect |
| 3. C3×#64782 | C2 | semidirect |
| 4. C3×C4×#672 | C2 | semidirect |
| 5. #10602081 | C3 | direct (N × H) |
| 16. #64971 | C2×C3 | semidirect |
| 17. #64782 | C2×C3 | semidirect |
| 18. C4×#672 | C2×C3 | semidirect |
| 158. C3×C5 | #2240 | semidirect |
| 188. C5 | C3×#2240 | semidirect |
| 198. C3 | #10602081 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#493 | 2 |
| C3×#64971 | 2 |
| C3×#64782 | 2 |
| C3×C4×#672 | 2 |
| #10602081 | 3 |
| C3×#2240 | 5 |