Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
628 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 100 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×#65365 | C2 | semidirect |
| 3. #11746882 | C2 | semidirect |
| 4. #11746365 | C2 | semidirect |
| 5. #11745837 | C2 | semidirect |
| 13. C3×#4015 | C22 | semidirect |
| 14. C4⋊(C3⋊#168) | C22 | semidirect |
| 15. C3×C4×#168 | C22 | semidirect |
| 20. #65365 | D3 | semidirect |
| 52. #4015 | C2×D3 | semidirect |
| 56. C4×#168 | C2×D3 | semidirect |
| 70. C5×D12 | SD16 | semidirect |
| 187. D12 | #687 | semidirect |
| 221. C3×C5 | #1629 | semidirect |
| 261. C5 | #71266 | semidirect |
| 274. C3 | #10602700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5717 | 2 |
| C3×#65365 | 2 |
| #11746882 | 2 |
| #11746365 | 2 |
| #11745837 | 2 |
| #10602700 | 3 |
| #71266 | 5 |