Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
272 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. C3×#65167 | C2 | semidirect |
| 3. C3×C5×#366 | C2 | semidirect |
| 5. C3×#64721 | C2 | semidirect |
| 7. C3×#64710 | C2 | semidirect |
| 8. #10600127 | C3 | direct (N × H) |
| 21. #65167 | C2×C3 | semidirect |
| 23. C5×#366 | C2×C3 | semidirect |
| 25. #64721 | C2×C3 | semidirect |
| 27. #64710 | C2×C3 | semidirect |
| 46. C3×#366 | D5 | semidirect |
| 104. #366 | C3×D5 | semidirect |
| 201. C3×C5 | #2228 | semidirect |
| 234. C5 | C3×#2228 | semidirect |
| 246. C3 | #10600127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65167 | 2 |
| C3×#65161 | 2 |
| C3×C5×#366 | 2 |
| C3×#64729 | 2 |
| C3×#64721 | 2 |
| C3×#64711 | 2 |
| C3×#64710 | 2 |
| #10600127 | 3 |
| C3×#2228 | 5 |