Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
205 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×H(3,𝔽3) | C2 | semidirect |
| 3. C2×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. C4×(C3⋊D3)⋊C3 | C2 | direct (N × H) |
| 5. C2×C4×C3⋊D3 | C3 | semidirect |
| 8. C2×(C3⋊D3)⋊C3 | C4 | direct (N × H) |
| 10. C4×H(3,𝔽3) | C22 | semidirect |
| 11. (C3⋊Dic3)⋊C3 | C22 | semidirect |
| 15. C2×C32×C4 | D3 | semidirect |
| 16. C2×C32×C4 | C2×C3 | semidirect |
| 17. C2×C3⋊Dic3 | C2×C3 | semidirect |
| 18. C4×C3⋊D3 | C2×C3 | semidirect |
| 21. C2×H(3,𝔽3) | C2×C4 | semidirect |
| 23. (C3⋊D3)⋊C3 | C2×C4 | direct (N × H) |
| 30. C2×C3⋊D3 | C3×C4 | semidirect |
| 35. C32×C4 | C2×D3 | semidirect |
| 36. C32×C4 | C22×C3 | semidirect |
| 37. C3⋊Dic3 | C22×C3 | semidirect |
| 39. H(3,𝔽3) | C22×C4 | semidirect |
| 55. C2×C32 | C4×D3 | semidirect |
| 56. C2×C32 | C2×C3×C4 | semidirect |
| 59. C3⋊D3 | C2×C3×C4 | semidirect |
| 80. C32 | C2×C4×D3 | semidirect |
| 81. C32 | C22×C3×C4 | semidirect |
| 85. C2×C4 | (C3⋊D3)⋊C3 | direct (N × H) |
| 101. C4 | C2×(C3⋊D3)⋊C3 | direct (N × H) |
| 107. C2 | C4×(C3⋊D3)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C3⋊D3)⋊C3 | 2 |
| C2×C4×H(3,𝔽3) | 2 |
| C2×(C3⋊Dic3)⋊C3 | 2 |
| C4×(C3⋊D3)⋊C3 | 2 |
| C2×C4×C3⋊D3 | 3 |
| C2×C3×C4×D3 | 3 |