Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 308 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×#65198 | C2 | semidirect |
| 3. C3×#64989 | C2 | semidirect |
| 4. C3×#64985 | C2 | semidirect |
| 5. C3×C5×#364 | C2 | semidirect |
| 6. C3×#64737 | C2 | semidirect |
| 7. C3×#64736 | C2 | semidirect |
| 8. #10600097 | C3 | direct (N × H) |
| 25. #65198 | C2×C3 | semidirect |
| 27. #64989 | C2×C3 | semidirect |
| 28. #64985 | C2×C3 | semidirect |
| 29. C5×#364 | C2×C3 | semidirect |
| 30. #64737 | C2×C3 | semidirect |
| 31. #64736 | C2×C3 | semidirect |
| 57. C3×#364 | D5 | semidirect |
| 133. #364 | C3×D5 | semidirect |
| 249. C3×C5 | #2212 | semidirect |
| 284. C5 | C3×#2212 | semidirect |
| 294. C3 | #10600097 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65198 | 2 |
| C3×#65197 | 2 |
| C3×#64989 | 2 |
| C3×#64985 | 2 |
| C3×C5×#364 | 2 |
| C3×#64737 | 2 |
| C3×#64736 | 2 |
| #10600097 | 3 |
| C3×#2212 | 5 |