Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
270 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D33 |
| commutator, hypocenter | C33 | C22×C4 |
| Fitting, socle, cosocle | C2×C33 | C23 |
| prime radical | C2×C3×D32 | C2 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #6294 | C2 | semidirect |
| 3. Dic3×C3⋊D3 | C2 | semidirect |
| 4. D3×C3⋊Dic3 | C2 | semidirect |
| 5. C3×D3×Dic3 | C2 | semidirect |
| 10. C3×D32 | C4 | semidirect |
| 11. C3⋊(C3⋊Dic3) | C22 | semidirect |
| 12. C3×C3⋊Dic3 | C22 | semidirect |
| 13. C32×Dic3 | C22 | semidirect |
| 27. D3×Dic3 | D3 | direct (N × H) |
| 29. C3×C3⋊D3 | C2×C4 | semidirect |
| 30. C32×D3 | C2×C4 | semidirect |
| 41. D32 | Dic3 | direct (N × H) |
| 48. C3⋊Dic3 | C2×D3 | semidirect |
| 53. C3×Dic3 | C2×D3 | semidirect |
| 54. C33 | C22×C4 | semidirect |
| 75. C3⋊D3 | C2×Dic3 | semidirect |
| 79. C3×D3 | C4×D3 | semidirect |
| 80. C3×D3 | C2×Dic3 | semidirect |
| 102. Dic3 | D32 | direct (N × H) |
| 106. C32 | C2×C4×D3 | semidirect |
| 107. C32 | C22×Dic3 | semidirect |
| 124. D3 | D3×Dic3 | direct (N × H) |
| 134. C3 | C4×D32 | semidirect |
| 135. C3 | C2×D3×Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D32 | 2 |
| #6294 | 2 |
| Dic3×C3⋊D3 | 2 |
| D3×C3⋊Dic3 | 2 |
| C3×D3×Dic3 | 2 |
| C2×D3×Dic3 | 3 |
| C4×D32 | 3 |