Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 4. C3×#64971 | C2 | semidirect |
| 5. C3×#64970 | C2 | semidirect |
| 6. C3×#64970 | C2 | semidirect |
| 7. C3×C5×#322 | C2 | semidirect |
| 8. #10598886 | C3 | direct (N × H) |
| 26. #64971 | C2×C3 | semidirect |
| 27. #64970 | C2×C3 | semidirect |
| 28. #64970 | C2×C3 | semidirect |
| 29. C5×#322 | C2×C3 | semidirect |
| 53. C3×#322 | D5 | semidirect |
| 120. #322 | C3×D5 | semidirect |
| 224. C3×C5 | #1719 | semidirect |
| 259. C5 | C3×#1719 | semidirect |
| 270. C3 | #10598886 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64983 | 2 |
| C3×#64982 | 2 |
| C3×#64971 | 2 |
| C3×#64970 | 2 |
| C3×C5×#322 | 2 |
| #10598886 | 3 |
| C3×#1719 | 5 |