Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
205 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 1. C2×((C3⋊D3)⋊C3)⋊C2 | C2 | semidirect |
| 2. C4⋊#272 | C2 | semidirect |
| 3. C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 4. C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 5. #6200 | C2 | semidirect |
| 8. C2×#272 | C22 | semidirect |
| 10. C2×(C3⋊D3)⋊C3 | C22 | semidirect |
| 12. C4×H(3,𝔽3) | C22 | semidirect |
| 13. (C3⋊Dic3)⋊C3 | C22 | semidirect |
| 16. C4⋊(C3⋊D3) | D3 | semidirect |
| 17. C4×C3⋊D3 | D3 | semidirect |
| 28. (C3⋊D3)⋊C3 | D4 | semidirect |
| 33. C2×C3⋊D3 | C2×D3 | semidirect |
| 42. C32×C4 | C2×D3 | semidirect |
| 43. C32×C4 | C2×D3 | semidirect |
| 44. C3⋊Dic3 | C2×D3 | semidirect |
| 46. H(3,𝔽3) | C2×D4 | semidirect |
| 67. C3⋊D3 | D12 | semidirect |
| 95. C32 | C2×D12 | semidirect |
| 96. C32 | D3×D4 | semidirect |
| 121. C4 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×((C3⋊D3)⋊C3)⋊C2 | 2 |
| C4⋊#272 | 2 |
| C4⋊((C3⋊D3)⋊C3) | 2 |
| C4×(C3⋊D3)⋊C3 | 2 |
| #6200 | 2 |
| #3802 | 3 |
| D3×D12 | 3 |