Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
118 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 118 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 |
|---|---|---|
| 2. C2×C3×C4×C9 | C2 | semidirect |
| 3. C2×C3×Dic9 | C2 | semidirect |
| 5. (C2×D9)⋊C4 | C3 | direct (N × H) |
| 9. C2×C3×D9 | C4 | semidirect |
| 17. C2×C4×C9 | C2×C3 | semidirect |
| 18. C2×Dic9 | C2×C3 | semidirect |
| 35. C2×D9 | C3×C4 | semidirect |
| 39. C3×C9 | C22⋊C4 | semidirect |
| 44. C2×C3×C4 | D9 | semidirect |
| 75. C9 | C3×C22⋊C4 | semidirect |
| 78. C2×C4 | C3×D9 | semidirect |
| 97. C3 | (C2×D9)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D9 | 2 |
| C2×C3×C4×C9 | 2 |
| C2×C3×Dic9 | 2 |
| C3×(C2×D3)⋊C4 | 3 |
| (C2×D9)⋊C4 | 3 |