Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
126 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | D32 |
| commutator, hypocenter | C32 | C2×C3×C8 |
| Frattini | C4 | C3×D32 |
| Fitting | C33×C4 | C22 |
| socle | C2×C33 | C2×C4 |
| prime radical | C2×C32×D3 | C4 |
| cosocle | C32×C4 | C22×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C3×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. C32×C3⋊C8 | C2 | semidirect |
| 6. D3×C3⋊C8 | C3 | direct (N × H) |
| 15. C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 20. C3×C3⋊C8 | D3 | direct (N × H) |
| 21. C3×C3⋊C8 | C2×C3 | semidirect |
| 23. C32×D3 | C8 | semidirect |
| 42. C33 | C2×C8 | semidirect |
| 54. C3⋊C8 | C3×D3 | direct (N × H) |
| 64. C3×D3 | C3⋊C8 | direct (N × H) |
| 65. C3×D3 | C3×C8 | semidirect |
| 86. C32 | D3×C8 | semidirect |
| 87. C32 | C2×C3⋊C8 | semidirect |
| 88. C32 | C2×C3×C8 | semidirect |
| 102. D3 | C3×C3⋊C8 | direct (N × H) |
| 110. C3 | D3×C3⋊C8 | direct (N × H) |
| 111. C3 | C3×D3×C8 | semidirect |
| 112. C3 | C2×C3×C3⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D3 | 2 |
| C3×C3⋊(C3⋊C8) | 2 |
| C32×C3⋊C8 | 2 |
| C2×C3×C3⋊C8 | 3 |
| C3×D3×C8 | 3 |
| D3×C3⋊C8 | 3 |