Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
118 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 44 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. C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. C32×C3⋊C8 | C2 | semidirect |
| 6. #3711 | C3 | direct (N × H) |
| 15. C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 20. C3×C3⋊C8 | D3 | semidirect |
| 21. C3×C3⋊C8 | C2×C3 | semidirect |
| 42. C33 | M16 | semidirect |
| 54. C3⋊C8 | C3×D3 | semidirect |
| 86. C32 | ΓL(1,𝔽25) | semidirect |
| 87. C32 | #208 | semidirect |
| 88. C32 | C3×M16 | semidirect |
| 110. C3 | #3711 | direct (N × H) |
| 111. C3 | C3×ΓL(1,𝔽25) | semidirect |
| 112. C3 | C3×#208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D3 | 2 |
| C3×C3⋊(C3⋊C8) | 2 |
| C32×C3⋊C8 | 2 |
| C3×#208 | 3 |
| C3×ΓL(1,𝔽25) | 3 |
| #3711 | 3 |