Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
290 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 64 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×D3×C3⋊D3 | 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. #6289 | C2 | semidirect |
| 4. C3×#624 | C2 | semidirect |
| 5. C3×D3×Dic3 | C2 | semidirect |
| 11. D3×C3⋊D3 | C4 | semidirect |
| 12. C3×C3⋊Dic3 | C22 | semidirect |
| 13. C32×Dic3 | C22 | semidirect |
| 25. #624 | D3 | direct (N × H) |
| 27. D3×Dic3 | D3 | semidirect |
| 29. C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 30. C3×C3⋊D3 | C2×C4 | semidirect |
| 31. C32×D3 | C2×C4 | semidirect |
| 49. C3⋊Dic3 | C2×D3 | semidirect |
| 54. C3×Dic3 | C2×D3 | semidirect |
| 55. C3×Dic3 | C2×D3 | semidirect |
| 56. C33 | C22×C4 | semidirect |
| 82. C3⋊D3 | C4×D3 | semidirect |
| 86. C3×D3 | C4×D3 | semidirect |
| 109. Dic3 | D32 | semidirect |
| 113. C32 | C2×C4×D3 | semidirect |
| 114. C32 | C2×C4×D3 | semidirect |
| 135. D3 | #624 | direct (N × H) |
| 145. C3 | C4×D32 | semidirect |
| 146. C3 | C2×#624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C3⋊D3 | 2 |
| #6294 | 2 |
| #6289 | 2 |
| C3×#624 | 2 |
| C3×D3×Dic3 | 2 |
| C2×#624 | 3 |
| C4×D32 | 3 |