Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
758 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊(C3⋊D9) |
| commutator, cosocle, hypocenter | C9×H(3,𝔽3) | C2×C3 |
| Frattini | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | C3×C9×H(3,𝔽3) | C2 |
| socle | C33 | C3⋊(C3⋊D3) |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C9×H(3,𝔽3) | C2 | semidirect |
| 4. C9⋊#272 | C3 | direct (N × H) |
| 7. C33×C9 | D3 | semidirect |
| 11. C9×H(3,𝔽3) | C2×C3 | semidirect |
| 12. C3×C32⋊C9 | D3 | semidirect |
| 24. C3×H(3,𝔽3) | D9 | semidirect |
| 31. C32×C9 | C3×D3 | semidirect |
| 36. C32⋊C9 | C3×D3 | semidirect |
| 51. C33 | C3⋊D9 | semidirect |
| 55. H(3,𝔽3) | C3×D9 | semidirect |
| 66. C3×C9 | #272 | semidirect |
| 86. C32 | C3×C3⋊D9 | semidirect |
| 94. C9 | C3×#272 | semidirect |
| 103. C3 | C9⋊#272 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×H(3,𝔽3) | 2 |
| C3×C3⋊#272 | 3 |
| C32×C3⋊D9 | 3 |
| C9⋊#272 | 3 |
| C3×#4181 | 3 |