Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
400 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 166 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 |
|---|---|---|
| 3. #11746730 | C2 | semidirect |
| 4. C3×#64859 | C2 | semidirect |
| 5. #11746542 | C2 | semidirect |
| 12. D3×#674 | C4 | semidirect |
| 22. #64859 | D3 | direct (N × H) |
| 34. C3⋊#674 | C2×C4 | semidirect |
| 35. C3×#674 | C2×C4 | semidirect |
| 86. #674 | C4×D3 | semidirect |
| 137. C5×D3 | #346 | semidirect |
| 171. C3×C5 | C2×#346 | semidirect |
| 197. D3 | #64859 | direct (N × H) |
| 198. C5 | D3×#346 | semidirect |
| 207. C3 | C2×#64859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#674 | 2 |
| C4×D3×#168 | 2 |
| #11746730 | 2 |
| C3×#64859 | 2 |
| #11746542 | 2 |
| C2×#64859 | 3 |
| D3×#346 | 5 |