Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
690 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 135 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. #66153⋊C3 | C2 | direct (N × H) |
| 3. C2×#4094⋊C3 | C2 | semidirect |
| 4. C2×#66153 | C3 | semidirect |
| 11. #4094⋊C3 | C22 | semidirect |
| 15. #66153 | C2×C3 | semidirect |
| 17. C2×#4094 | C2×C3 | semidirect |
| 45. #4094 | C22×C3 | semidirect |
| 279. C2×C5 | #568⋊C3 | semidirect |
| 321. C5 | C2×#568⋊C3 | semidirect |
| 343. C2 | #66153⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41⋊C3 | 2 |
| #66153⋊C3 | 2 |
| C2×#4094⋊C3 | 2 |
| C2×#66153 | 3 |
| C2×C3×#681 | 4 |
| C2×#568⋊C3 | 5 |