Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
592 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 5. C3×#4476 | C3 | direct (N × H) |
| 7. C22×C32×Dic3 | C4 | semidirect |
| 11. C32×#217 | C4 | semidirect |
| 30. #4476 | C32 | direct (N × H) |
| 35. C22×C3×Dic3 | C3×C4 | semidirect |
| 45. C3×#217 | C3×C4 | semidirect |
| 95. C22×Dic3 | C32×C4 | semidirect |
| 105. #217 | C32×C4 | semidirect |
| 134. C33 | #352 | semidirect |
| 202. C32 | #4476 | direct (N × H) |
| 203. C32 | C3×#352 | semidirect |
| 235. C3 | C3×#4476 | direct (N × H) |
| 236. C3 | C32×#352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#935 | 2 |
| C33×#100 | 2 |
| C32×#834 | 2 |
| C32×#352 | 3 |
| C3×#4476 | 3 |