Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
543 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 84 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×#63690 | C2 | direct (N × H) |
| 3. C2×C3×#3688 | C2 | semidirect |
| 5. C2×#63690 | C3 | direct (N × H) |
| 9. C3×#3688 | C22 | semidirect |
| 19. #63690 | C2×C3 | direct (N × H) |
| 20. C2×#3688 | C2×C3 | semidirect |
| 47. #3688 | C22×C3 | semidirect |
| 249. C2×C3 | #63690 | direct (N × H) |
| 261. C3 | C2×#63690 | direct (N × H) |
| 264. C2 | C3×#63690 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41⋊C9 | 2 |
| C3×#63690 | 2 |
| C2×C3×#3688 | 2 |
| C2×C3×#951 | 3 |
| C2×#63690 | 3 |
| C2×C3×Dic18 | 4 |