Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
278 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624743 | C2 | semidirect |
| 2. C3⋊D3×3−1+2 | C3 | semidirect |
| 3. C32×(C3⋊D3)⋊C3 | C3 | semidirect |
| 5. #92259 | C3 | semidirect |
| 6. (C3⋊D3)⋊H(3,𝔽3) | C3 | semidirect |
| 7. C32×3−1+2 | C2×C3 | semidirect |
| 8. C32×H(3,𝔽3) | C2×C3 | semidirect |
| 13. C3×AΣL(1,𝔽27) | D3 | semidirect |
| 14. #6891 | C2×C3 | semidirect |
| 15. C32⋊H(3,𝔽3) | C2×C3 | semidirect |
| 107. 3−1+2 | (C3⋊D3)⋊C3 | semidirect |
| 130. C3⋊D3 | AΣL(1,𝔽27) | semidirect |
| 170. C32 | C2×AΣL(1,𝔽27) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624743 | 2 |
| C3⋊D3×3−1+2 | 3 |
| C32×(C3⋊D3)⋊C3 | 3 |
| D3×AΣL(1,𝔽27) | 3 |
| #92259 | 3 |
| (C3⋊D3)⋊H(3,𝔽3) | 3 |