Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
764 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 234 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 |
|---|---|---|
| 6. C3×#5069 | C3 | direct (N × H) |
| 29. #5069 | C32 | direct (N × H) |
| 110. C33 | #491 | semidirect |
| 153. C32 | #5069 | direct (N × H) |
| 154. C32 | C3×#491 | semidirect |
| 173. C3 | C3×#5069 | direct (N × H) |
| 174. C3 | C32×#491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#125 | 2 |
| C32×#869 | 2 |
| C32×#810 | 2 |
| C32×#803 | 2 |
| C32×#491 | 3 |
| C3×#5069 | 3 |