Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 116 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×#65725 | C2 | semidirect |
| 3. C3×#64898 | C2 | semidirect |
| 4. C3×#64889 | C2 | semidirect |
| 5. C3×#64886 | C2 | semidirect |
| 6. #10604084 | C3 | direct (N × H) |
| 18. #65725 | C2×C3 | semidirect |
| 20. #64898 | C2×C3 | semidirect |
| 21. #64889 | C2×C3 | semidirect |
| 22. #64886 | C2×C3 | semidirect |
| 164. C3×C5 | #2171 | semidirect |
| 188. C5 | C3×#2171 | semidirect |
| 195. C3 | #10604084 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65725 | 2 |
| C3×#65184 | 2 |
| C3×#64898 | 2 |
| C3×#64889 | 2 |
| C3×#64886 | 2 |
| #10604084 | 3 |
| C3×#2171 | 5 |