Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
250 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 4. #10589500 | C3 | direct (N × H) |
| 34. C3×C22⋊C9 | Q16 | semidirect |
| 93. C22⋊C9 | C3×Q16 | semidirect |
| 147. C22×C3 | Dic36 | semidirect |
| 182. C22 | C3×Dic36 | semidirect |
| 188. C3 | #10589500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×(C22⋊C9)⋊Q8 | 2 |
| C3×C8×C22⋊C9 | 2 |
| C3×#5116 | 3 |
| #10589500 | 3 |
| C3×Dic36 | 4 |