Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
145 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 145 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. #6229 | C2 | semidirect |
| 3. #634⋊C3 | C2 | semidirect |
| 5. #6196 | C2 | semidirect |
| 14. #634 | D3 | semidirect |
| 25. (C3⋊D3)⋊C3 | Q8 | semidirect |
| 41. H(3,𝔽3) | C2×Q8 | semidirect |
| 61. C3⋊D3 | Dic6 | semidirect |
| 82. C32 | C2×Dic6 | semidirect |
| 83. C32 | D3×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6229 | 2 |
| C4×(C3⋊D3)⋊C3 | 2 |
| #634⋊C3 | 2 |
| ((C3⋊D3)⋊C3)⋊C4 | 2 |
| #6196 | 2 |
| #3797 | 3 |
| D3×Dic6 | 3 |