Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
608 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 80 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 | #92297 |
| commutator, cosocle, hypocenter | C32×C9 | C2×C32 |
| Frattini | C32 | C32×C3⋊D3 |
| Fitting | C3×C9×H(3,𝔽3) | C2 |
| socle | C33 | C3×C3⋊D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C9×H(3,𝔽3) | C2 | semidirect |
| 2. C3×C3⋊(C3⋊D9) | C3 | semidirect |
| 5. #92297 | C3 | direct (N × H) |
| 9. C33×C9 | D3 | semidirect |
| 10. C33×C9 | C2×C3 | semidirect |
| 14. C9×H(3,𝔽3) | C2×C3 | semidirect |
| 17. C3×C32⋊C9 | D3 | semidirect |
| 20. C3⋊(C3⋊D9) | C32 | semidirect |
| 35. C3×H(3,𝔽3) | D9 | semidirect |
| 53. C32×C9 | C3×D3 | semidirect |
| 54. C32×C9 | C2×C32 | semidirect |
| 60. C32⋊C9 | C3×D3 | semidirect |
| 96. C33 | C3×D9 | semidirect |
| 97. C33 | C3⋊D9 | semidirect |
| 104. H(3,𝔽3) | C3×D9 | semidirect |
| 124. C3×C9 | (C3⋊D3)⋊C3 | semidirect |
| 169. C32 | C32×D9 | semidirect |
| 171. C32 | C3×C3⋊D9 | semidirect |
| 180. C9 | C3×(C3⋊D3)⋊C3 | semidirect |
| 195. C3 | #92297 | 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⋊(C3⋊D9) | 3 |
| C3×C3⋊((C3⋊D3)⋊C3) | 3 |
| C32×C3⋊D9 | 3 |
| #92297 | 3 |
| C3×#4169 | 3 |