Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×C3×Dic40 | C2 | semidirect |
| 3. C3×#64742 | C2 | semidirect |
| 4. C3×#64740 | C2 | semidirect |
| 5. C3×#64719 | C2 | semidirect |
| 6. #10602303 | C3 | direct (N × H) |
| 18. C2×Dic40 | C2×C3 | semidirect |
| 19. #64742 | C2×C3 | semidirect |
| 20. #64740 | C2×C3 | semidirect |
| 21. #64719 | C2×C3 | semidirect |
| 145. C3×C5 | #2264 | semidirect |
| 168. C5 | C3×#2264 | semidirect |
| 175. C3 | #10602303 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#508 | 2 |
| C2×C3×Dic40 | 2 |
| C3×#64742 | 2 |
| C3×#64740 | 2 |
| C3×#64719 | 2 |
| #10602303 | 3 |
| C3×#2264 | 5 |