Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
251 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 251 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. #10624740 | C2 | semidirect |
| 2. C3⋊D3×H(3,𝔽3) | C3 | semidirect |
| 4. (C3⋊D3)⋊H(3,𝔽3) | C3 | semidirect |
| 5. C3×(C3⋊D3)⋊C9 | C3 | semidirect |
| 6. C32×H(3,𝔽3) | C2×C3 | semidirect |
| 10. C3×#732 | D3 | semidirect |
| 11. C32⋊H(3,𝔽3) | C2×C3 | semidirect |
| 12. C3×C32⋊C9 | C2×C3 | semidirect |
| 33. C3×H(3,𝔽3) | C3×D3 | semidirect |
| 35. C32×C9 | C3×D3 | semidirect |
| 90. H(3,𝔽3) | (C3⋊D3)⋊C3 | semidirect |
| 100. C3⋊D3 | #732 | semidirect |
| 139. C32 | C2×#732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624740 | 2 |
| C3⋊D3×H(3,𝔽3) | 3 |
| D3×#732 | 3 |
| (C3⋊D3)⋊H(3,𝔽3) | 3 |
| C3×(C3⋊D3)⋊C9 | 3 |