Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
134 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | #626 |
| commutator, cosocle | C32×C4 | C22×C3 |
| Frattini | C4 | C3×D32 |
| Fitting | C33×C4 | C22 |
| socle | C2×C33 | D4 |
| hypercenter | C3×C4 | D32 |
| hypocenter | C32 | C3×D8 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C32×D12 | C2 | semidirect |
| 3. C32×C3⋊C8 | C2 | semidirect |
| 6. #3714 | C3 | direct (N × H) |
| 11. C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 16. C3×D12 | D3 | semidirect |
| 17. C3×D12 | C2×C3 | semidirect |
| 20. C3×C3⋊C8 | D3 | semidirect |
| 21. C3×C3⋊C8 | C2×C3 | semidirect |
| 43. C33 | D8 | semidirect |
| 51. D12 | C3×D3 | semidirect |
| 55. C3⋊C8 | C3×D3 | semidirect |
| 91. C32 | D24 | semidirect |
| 92. C32 | #213 | semidirect |
| 93. C32 | C3×D8 | semidirect |
| 119. C3 | #3714 | direct (N × H) |
| 120. C3 | C3×D24 | semidirect |
| 121. C3 | C3×#213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊(C3⋊D3) | 2 |
| C32×D12 | 2 |
| C32×C3⋊C8 | 2 |
| C3×#213 | 3 |
| C3×D24 | 3 |
| #3714 | 3 |