Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
118 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C2×C3×C4×C9 | C2 | semidirect |
| 3. C2×C9×Dic3 | C2 | semidirect |
| 9. C2×D3×C9 | C4 | semidirect |
| 18. C2×C4×C9 | D3 | semidirect |
| 24. (C2×D3)⋊C4 | C9 | direct (N × H) |
| 39. C3×C9 | C22⋊C4 | semidirect |
| 44. C2×C3×C4 | C2×C9 | semidirect |
| 46. C2×Dic3 | C2×C9 | semidirect |
| 67. C2×D3 | C4×C9 | semidirect |
| 75. C9 | (C2×D3)⋊C4 | direct (N × H) |
| 78. C2×C4 | D3×C9 | semidirect |
| 97. C3 | C9×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C9 | 2 |
| C2×C3×C4×C9 | 2 |
| C2×C9×Dic3 | 2 |
| C3×(C2×D3)⋊C4 | 3 |
| C9×C22⋊C4 | 3 |