Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
152 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 152 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. #6229 | C2 | semidirect |
| 2. C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. #6198 | C2 | semidirect |
| 5. ((C3⋊D3)⋊C3)⋊C4 | C2 | semidirect |
| 13. C4⋊(C3⋊D3) | D3 | semidirect |
| 14. C4×C3⋊D3 | D3 | semidirect |
| 42. H(3,𝔽3) | #41 | semidirect |
| 85. C32 | #235 | semidirect |
| 86. C32 | #237 | 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 |
| C4×(C3⋊D3)⋊C3 | 2 |
| #6198 | 2 |
| ((C3⋊D3)⋊C3)⋊C4 | 2 |
| #3799 | 3 |
| #3796 | 3 |