Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
551 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32 | C3×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C2×C33 |
| Frattini | C32 | C33×D3 |
| Fitting | C3×#6909 | C2 |
| hypercenter | C33 | (C3⋊D3)⋊C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C32 ◁ C33 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#6909 | C2 | semidirect |
| 2. C32×#272 | C3 | semidirect |
| 4. #92281 | C3 | direct (N × H) |
| 5. C3×#4174 | C3 | semidirect |
| 7. C32×H(3,𝔽3) | D3 | semidirect |
| 8. C32×H(3,𝔽3) | C2×C3 | semidirect |
| 10. #6909 | C2×C3 | semidirect |
| 12. C3×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 18. C3×#272 | C32 | semidirect |
| 20. #4174 | C32 | semidirect |
| 23. C34 | C3×D3 | semidirect |
| 36. C3×H(3,𝔽3) | C3×D3 | semidirect |
| 38. C3×H(3,𝔽3) | C2×C32 | semidirect |
| 42. AΣL(1,𝔽27) | C2×C32 | semidirect |
| 69. C33 | C32×D3 | semidirect |
| 133. C3 | #92281 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6909 | 2 |
| C32×#272 | 3 |
| C3×D3×H(3,𝔽3) | 3 |
| #92281 | 3 |
| C3×#4174 | 3 |