Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 2. C3×#65759 | C2 | semidirect |
| 3. C3×#65754 | C2 | semidirect |
| 4. C3×#64915 | C2 | semidirect |
| 5. #10604978 | C3 | direct (N × H) |
| 23. #65759 | C2×C3 | semidirect |
| 24. #65754 | C2×C3 | semidirect |
| 25. #64915 | C2×C3 | semidirect |
| 265. C3×C5 | #1469 | semidirect |
| 313. C5 | C3×#1469 | semidirect |
| 329. C3 | #10604978 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#4093 | 2 |
| C3×#65759 | 2 |
| C3×#65754 | 2 |
| C3×#64915 | 2 |
| #10604978 | 3 |
| C3×#1469 | 5 |