Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
248 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 90 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×#64716 | C2 | semidirect |
| 5. C3×#64714 | C2 | semidirect |
| 6. #10601517 | C3 | direct (N × H) |
| 20. #64716 | C2×C3 | semidirect |
| 21. #64714 | C2×C3 | semidirect |
| 167. C3×C5 | #2239 | semidirect |
| 194. C5 | C3×#2239 | semidirect |
| 203. C3 | #10601517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#430 | 2 |
| C3×#65426 | 2 |
| C3×#64773 | 2 |
| C3×#64716 | 2 |
| C3×#64714 | 2 |
| #10601517 | 3 |
| C3×#2239 | 5 |