Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
542 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×D3 |
| commutator, socle, cosocle | C33 | C2×C33 |
| Fitting | C3×#6893 | C2 |
| prime radical | C3×D3×H(3,𝔽3) | C3 |
| hypercenter | #6893 | D3 |
| hypocenter | C3 | C2×#6893 |
| LCS | G ▷ C33 ▷ C3 | |
| UCS | C1 ◁ C32 ◁ #6893 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#6893 | C2 | semidirect |
| 2. C3×D3×3−1+2 | C3 | semidirect |
| 4. C32×D3×C9 | C3 | semidirect |
| 6. D3×C32⋊C9 | C3 | semidirect |
| 7. C32×3−1+2 | C2×C3 | semidirect |
| 9. C33×C9 | C2×C3 | semidirect |
| 14. #6893 | D3 | direct (N × H) |
| 15. C3×C32⋊C9 | C2×C3 | semidirect |
| 33. C3×3−1+2 | C3×D3 | semidirect |
| 43. C32×C9 | C3×D3 | semidirect |
| 49. C32⋊C9 | C3×D3 | semidirect |
| 132. D3 | #6893 | direct (N × H) |
| 139. C3 | C2×#6893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6893 | 2 |
| C3×D3×3−1+2 | 3 |
| C3×D3×H(3,𝔽3) | 3 |
| C32×D3×C9 | 3 |
| C2×#6893 | 3 |
| D3×C32⋊C9 | 3 |