Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
533 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 533 conjugacy classes of subgroups — too many to draw. Only its 71 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 | C3⋊#4207 |
| commutator, cosocle, hypocenter | C9×H(3,𝔽3) | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | #10624869 | C2 |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624869 | C2 | semidirect |
| 4. C9⋊#272 | C3 | semidirect |
| 8. C3×#737 | D3 | semidirect |
| 9. C33×C9 | D3 | semidirect |
| 10. #6893 | D3 | semidirect |
| 14. #6891 | D3 | semidirect |
| 18. C9×H(3,𝔽3) | C2×C3 | semidirect |
| 48. C32×C9 | C3×D3 | semidirect |
| 57. C32⋊C9 | C3×D3 | semidirect |
| 103. C3×C9 | #272 | semidirect |
| 134. C32 | #4207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624869 | 2 |
| C3×#4207 | 3 |
| C32×C3⋊D9 | 3 |
| C9⋊#272 | 3 |
| #92304 | 3 |
| #92302 | 3 |
| #92300 | 3 |