Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
156 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 35 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. C4×#272 | C2 | semidirect |
| 2. C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. #634⋊C3 | C2 | semidirect |
| 4. #6200 | C2 | semidirect |
| 5. ((C3⋊D3)⋊C3)⋊C4 | C2 | semidirect |
| 13. C4⋊(C3⋊D3) | D3 | semidirect |
| 14. #634 | D3 | semidirect |
| 43. H(3,𝔽3) | #41 | semidirect |
| 88. C32 | #237 | semidirect |
| 89. C32 | #239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#272 | 2 |
| C4⋊((C3⋊D3)⋊C3) | 2 |
| #634⋊C3 | 2 |
| #6200 | 2 |
| ((C3⋊D3)⋊C3)⋊C4 | 2 |
| #3799 | 3 |
| #3795 | 3 |