Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
135 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 40 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. #3752 | C3 | semidirect |
| 9. C2×(C3⋊D3)⋊C3 | C4 | semidirect |
| 15. C2×C32×C4 | D3 | semidirect |
| 16. C2×C32×C4 | C2×C3 | semidirect |
| 17. C2×C3⋊Dic3 | C2×C3 | semidirect |
| 31. C2×C3⋊D3 | C3×C4 | semidirect |
| 40. H(3,𝔽3) | C22⋊C4 | semidirect |
| 84. C32 | (C2×D3)⋊C4 | semidirect |
| 85. C32 | C3×C22⋊C4 | semidirect |
| 88. C2×C4 | (C3⋊D3)⋊C3 | semidirect |
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 |
| #3752 | 3 |
| C3×(C2×D3)⋊C4 | 3 |