Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
446 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 50 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. #10624930 | C2 | semidirect |
| 2. #92394 | C3 | semidirect |
| 3. #92392 | C3 | semidirect |
| 4. C32×#272 | C3 | semidirect |
| 6. 3−1+4 | C2×C3 | semidirect |
| 7. H(5,𝔽3) | C2×C3 | semidirect |
| 8. C32×H(3,𝔽3) | C2×C3 | semidirect |
| 12. C3×AΣL(1,𝔽27) | D3 | semidirect |
| 21. C34 | C3×D3 | semidirect |
| 25. C3×3−1+2 | C3×D3 | semidirect |
| 32. C3×H(3,𝔽3) | C3×D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624930 | 2 |
| #92394 | 3 |
| #92392 | 3 |
| C32×#272 | 3 |
| D3×AΣL(1,𝔽27) | 3 |