Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 86 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×#65444 | C2 | semidirect |
| 3. C3×#65198 | C2 | semidirect |
| 4. C3×#65184 | C2 | semidirect |
| 5. C3×C5×#361 | C2 | semidirect |
| 6. C3×#64731 | C2 | semidirect |
| 7. C3×#64716 | C2 | semidirect |
| 8. #10600055 | C3 | direct (N × H) |
| 25. #65444 | C2×C3 | semidirect |
| 27. #65198 | C2×C3 | semidirect |
| 28. #65184 | C2×C3 | semidirect |
| 29. C5×#361 | C2×C3 | semidirect |
| 30. #64731 | C2×C3 | semidirect |
| 31. #64716 | C2×C3 | semidirect |
| 59. C3×#361 | D5 | semidirect |
| 135. #361 | C3×D5 | semidirect |
| 249. C3×C5 | #2212 | semidirect |
| 284. C5 | C3×#2212 | semidirect |
| 294. C3 | #10600055 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65444 | 2 |
| C3×#65436 | 2 |
| C3×#65198 | 2 |
| C3×#65184 | 2 |
| C3×C5×#361 | 2 |
| C3×#64731 | 2 |
| C3×#64716 | 2 |
| #10600055 | 3 |
| C3×#2212 | 5 |