Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
205 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 49 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. C4×#272 | C2 | semidirect |
| 3. C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. #6199 | C2 | semidirect |
| 5. ((C3⋊D3)⋊C3)⋊C4 | C2 | semidirect |
| 9. ((C3⋊D3)⋊C3)⋊C2 | C4 | direct (N × H) |
| 10. C4×H(3,𝔽3) | C22 | semidirect |
| 11. #1084 | C22 | semidirect |
| 12. (C3⋊Dic3)⋊C3 | C22 | semidirect |
| 14. C4×C3⋊D3 | D3 | semidirect |
| 22. #272 | C2×C4 | semidirect |
| 23. (C3⋊D3)⋊C3 | C2×C4 | semidirect |
| 32. C32×C4 | C2×D3 | semidirect |
| 33. C3⋊Dic3 | C2×D3 | semidirect |
| 37. H(3,𝔽3) | C22×C4 | semidirect |
| 53. C3⋊D3 | C4×D3 | semidirect |
| 76. C32 | C2×C4×D3 | semidirect |
| 96. C4 | ((C3⋊D3)⋊C3)⋊C2 | direct (N × H) |
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 |
| #6199 | 2 |
| ((C3⋊D3)⋊C3)⋊C4 | 2 |
| C4×D32 | 3 |