Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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×#65167 | C2 | semidirect |
| 5. C3×#64725 | C2 | semidirect |
| 6. C3×#64721 | C2 | semidirect |
| 7. C3×#64709 | C2 | semidirect |
| 8. #10599974 | C3 | direct (N × H) |
| 22. #65167 | C2×C3 | semidirect |
| 25. #64725 | C2×C3 | semidirect |
| 26. #64721 | C2×C3 | semidirect |
| 27. #64709 | C2×C3 | semidirect |
| 201. C3×C5 | #2228 | semidirect |
| 234. C5 | C3×#2228 | semidirect |
| 246. C3 | #10599974 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D8×Dic5 | 2 |
| C3×#65167 | 2 |
| C3×C5×#357 | 2 |
| C3×#64782 | 2 |
| C3×#64725 | 2 |
| C3×#64721 | 2 |
| C3×#64709 | 2 |
| #10599974 | 3 |
| C3×#2228 | 5 |