Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
192 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×#157 |
| commutator, hypocenter | C33 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33 | C2×C4 |
| prime radical | C2×D3×C3⋊D3 | C2 |
| cosocle | C3×C3⋊D3 | C23 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊#157 | C2 | semidirect |
| 3. C2×C3×#157 | C2 | semidirect |
| 4. D3×#157 | C2 | direct (N × H) |
| 6. C2×C3⋊(C3⋊D3) | C4 | semidirect |
| 8. C2×C32×D3 | C4 | semidirect |
| 9. D3×C3⋊D3 | C4 | semidirect |
| 11. C3⋊#157 | C22 | semidirect |
| 12. C3×#157 | C22 | semidirect |
| 17. C2×#157 | D3 | direct (N × H) |
| 18. C2×C33 | C2×C4 | semidirect |
| 19. C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 20. C3×C3⋊D3 | C2×C4 | semidirect |
| 22. C32×D3 | C2×C4 | semidirect |
| 36. #157 | C2×D3 | direct (N × H) |
| 37. C33 | C22×C4 | semidirect |
| 46. C2×C32 | C4×D3 | semidirect |
| 50. C3⋊D3 | C4×D3 | semidirect |
| 66. C2×D3 | #157 | direct (N × H) |
| 71. C32 | C2×C4×D3 | semidirect |
| 81. C2×C3 | C2×#157 | semidirect |
| 87. D3 | C2×#157 | direct (N × H) |
| 97. C3 | C22×#157 | semidirect |
| 102. C2 | D3×#157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C3⋊D3 | 2 |
| C2×C3⋊#157 | 2 |
| C2×C3×#157 | 2 |
| D3×#157 | 2 |
| C22×#157 | 3 |
| C2×C4×D3 | 9 |