Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
268 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 268 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 |
|---|---|---|
| 2. C3×#65414 | C2 | semidirect |
| 3. C3×#64783 | C2 | semidirect |
| 4. C3×#64773 | C2 | semidirect |
| 5. C3×#64707 | C2 | semidirect |
| 6. #10601881 | C3 | direct (N × H) |
| 18. #65414 | C2×C3 | semidirect |
| 19. #64783 | C2×C3 | semidirect |
| 20. #64773 | C2×C3 | semidirect |
| 21. #64707 | C2×C3 | semidirect |
| 175. C3×C5 | #2238 | semidirect |
| 207. C5 | C3×#2238 | semidirect |
| 218. C3 | #10601881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#469 | 2 |
| C3×#65414 | 2 |
| C3×#64783 | 2 |
| C3×#64773 | 2 |
| C3×#64707 | 2 |
| #10601881 | 3 |
| C3×#2238 | 5 |