Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
314 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92391 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624888 | C2 |
| prime radical | #92300 | C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624888 | C2 | semidirect |
| 2. #92305 | C3 | semidirect |
| 7. #6893 | C2×C3 | semidirect |
| 13. C9×H(3,𝔽3) | D3 | semidirect |
| 14. C3×C32⋊C9 | D3 | semidirect |
| 33. C32×C9 | C3×D3 | semidirect |
| 45. C32⋊C9 | C3×D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624888 | 2 |
| #92305 | 3 |
| #92300 | 3 |
| C9×(C3⋊D3)⋊C3 | 3 |
| C3×(C3⋊D3)⋊C9 | 3 |