Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 512 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. C2×C3×#3959 | C2 | semidirect |
| 3. C3×#65405 | C2 | semidirect |
| 4. C3×#64782 | C2 | semidirect |
| 5. C3×C22⋊#672 | C2 | semidirect |
| 6. #10602829 | C3 | direct (N × H) |
| 13. C2×C3×Dic20 | C22 | semidirect |
| 15. C3×#3950 | C22 | semidirect |
| 17. C2×C3×#672 | C22 | semidirect |
| 20. C2×#3959 | C2×C3 | semidirect |
| 21. #65405 | C2×C3 | semidirect |
| 22. #64782 | C2×C3 | semidirect |
| 23. C22⋊#672 | C2×C3 | semidirect |
| 53. C2×Dic20 | C22×C3 | semidirect |
| 55. #3950 | C22×C3 | semidirect |
| 57. C2×#672 | C22×C3 | semidirect |
| 117. C22×C3×C5 | SD32 | semidirect |
| 200. C22×C5 | C3×SD32 | semidirect |
| 225. C3×C5 | #2187 | semidirect |
| 232. C22×C3 | #3959 | semidirect |
| 267. C5 | C3×#2187 | semidirect |
| 274. C22 | C3×#3959 | semidirect |
| 281. C3 | #10602829 | 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 |
| C2×C3×#3959 | 2 |
| C3×#65405 | 2 |
| C3×#64782 | 2 |
| C3×C22⋊#672 | 2 |
| #10602829 | 3 |
| C3×#2187 | 5 |