Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
459 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 459 conjugacy classes of subgroups — too many to draw. Only its 150 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 |
|---|---|---|
| 3. C22×C42×C9 | C3 | semidirect |
| 4. C42×C22⋊C9 | C3 | semidirect |
| 6. C4×C9⋊A4 | C4 | direct (N × H) |
| 25. C22×C4×C9 | C3×C4 | semidirect |
| 26. C4×C22⋊C9 | C3×C4 | semidirect |
| 30. C42×C9 | A4 | semidirect |
| 32. C9⋊A4 | C42 | direct (N × H) |
| 51. C22×C42 | 3−1+2 | semidirect |
| 72. C22×C9 | C3×C42 | semidirect |
| 74. C22⋊C9 | C3×C42 | semidirect |
| 77. C4×C9 | C4×A4 | semidirect |
| 102. C22×C4 | C4×3−1+2 | semidirect |
| 105. C42 | C9⋊A4 | direct (N × H) |
| 119. C9 | C42×A4 | semidirect |
| 137. C22 | C42×3−1+2 | semidirect |
| 140. C4 | C4×C9⋊A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C9⋊A4 | 2 |
| C3×C42×A4 | 3 |
| C22×C42×C9 | 3 |
| C42×C22⋊C9 | 3 |
| C42×3−1+2 | 4 |