Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
1334 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C34 | C2×C32 |
| Frattini | C32 | C32×C3⋊D3 |
| Fitting | C3×C32⋊H(3,𝔽3) | C2 |
| socle | C33 | C32×D3 |
| LCS | G ▷ C34 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C32⋊H(3,𝔽3) | C2 | semidirect |
| 3. C3⋊(C3⋊((C3⋊D3)⋊C3)) | C3 | semidirect |
| 5. C35 | D3 | semidirect |
| 7. C32×H(3,𝔽3) | C2×C3 | semidirect |
| 9. C32⋊H(3,𝔽3) | D3 | semidirect |
| 10. C3⋊(C3⋊(C3⋊D3)) | C32 | semidirect |
| 21. C34 | C3⋊D3 | semidirect |
| 22. C34 | C2×C32 | semidirect |
| 30. C3×H(3,𝔽3) | C3×D3 | semidirect |
| 56. C33 | (C3⋊D3)⋊C3 | semidirect |
| 58. C33 | C32×D3 | semidirect |
| 92. C32 | C3⋊((C3⋊D3)⋊C3) | semidirect |
| 103. C3 | #92258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊H(3,𝔽3) | 2 |
| C32×C3⋊(C3⋊D3) | 3 |
| C3⋊(C3⋊((C3⋊D3)⋊C3)) | 3 |
| #92258 | 3 |