Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
210 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 56 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×C32×Dic3 | C2 | semidirect |
| 4. #3722 | C3 | direct (N × H) |
| 7. C2×C3×C3⋊D3 | C4 | semidirect |
| 14. C2×C3×Dic3 | D3 | semidirect |
| 15. C2×C3×Dic3 | C2×C3 | semidirect |
| 27. C2×C3⋊D3 | C3×C4 | semidirect |
| 37. C33 | C22⋊C4 | semidirect |
| 44. C2×Dic3 | C3×D3 | semidirect |
| 80. C32 | (C2×D3)⋊C4 | semidirect |
| 81. C32 | C3×C22⋊C4 | semidirect |
| 106. C3 | #3722 | direct (N × H) |
| 107. C3 | C3×(C2×D3)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C3⋊D3 | 2 |
| C2×C32×Dic3 | 2 |
| C3×(C2×D3)⋊C4 | 3 |
| #3722 | 3 |