Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
198 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. C3×#634 | C2 | semidirect |
| 3. C32×Dic6 | C2 | semidirect |
| 4. C3×#627 | C2 | semidirect |
| 8. D3×Dic6 | C3 | direct (N × H) |
| 16. #634 | C2×C3 | semidirect |
| 28. C3×Dic6 | D3 | direct (N × H) |
| 29. C3×Dic6 | C2×C3 | semidirect |
| 30. #627 | C2×C3 | semidirect |
| 33. C32×D3 | Q8 | semidirect |
| 60. C33 | C2×Q8 | semidirect |
| 78. Dic6 | C3×D3 | direct (N × H) |
| 88. C3×D3 | Dic6 | direct (N × H) |
| 89. C3×D3 | C3×Q8 | semidirect |
| 118. C32 | C2×Dic6 | semidirect |
| 119. C32 | D3×Q8 | semidirect |
| 120. C32 | C2×C3×Q8 | semidirect |
| 136. D3 | C3×Dic6 | direct (N × H) |
| 146. C3 | D3×Dic6 | direct (N × H) |
| 147. C3 | C2×C3×Dic6 | semidirect |
| 148. C3 | C3×D3×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#634 | 2 |
| C32×C4×D3 | 2 |
| C32×Dic6 | 2 |
| C3×#627 | 2 |
| C3×D3×Dic3 | 2 |
| C3×D3×Q8 | 3 |
| C2×C3×Dic6 | 3 |
| D3×Dic6 | 3 |