Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
666 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 346 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. #10588615 | C3 | direct (N × H) |
| 7. C3×C42×C9 | C4 | semidirect |
| 29. C42×C9 | C3×C4 | semidirect |
| 34. C3×C4×C9 | C4⋊C4 | semidirect |
| 66. C3×C42 | Dic9 | semidirect |
| 81. C4×C9 | C3×C4⋊C4 | semidirect |
| 85. C3×C9 | #384 | semidirect |
| 112. C42 | C3×Dic9 | semidirect |
| 124. C3×C4 | C4⋊Dic9 | semidirect |
| 129. C9 | C3×#384 | semidirect |
| 148. C4 | C3×C4⋊Dic9 | semidirect |
| 150. C3 | #10588615 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C9 | 2 |
| C2×C3×C4⋊Dic9 | 2 |
| C3×#4935 | 3 |
| #10588615 | 3 |