Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
535 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 535 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 2. C3×#66322 | C2 | direct (N × H) |
| 3. C2×C3×C3⋊(C3⋊Dic3) | C3 | semidirect |
| 5. C2×#66322 | C3 | direct (N × H) |
| 6. C2×C3×AΣL(1,𝔽27) | C4 | semidirect |
| 9. C3×C3⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 15. #66322 | C2×C3 | direct (N × H) |
| 16. C3×AΣL(1,𝔽27) | C2×C4 | semidirect |
| 17. C2×C3⋊(C3⋊Dic3) | C32 | semidirect |
| 23. C2×C34 | C3×C4 | semidirect |
| 27. C2×C3×H(3,𝔽3) | Dic3 | semidirect |
| 31. C2×AΣL(1,𝔽27) | C3×C4 | semidirect |
| 41. C3⋊(C3⋊Dic3) | C2×C32 | semidirect |
| 52. C34 | C2×C3×C4 | semidirect |
| 54. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 56. AΣL(1,𝔽27) | C2×C3×C4 | semidirect |
| 78. C2×C33 | C32×C4 | semidirect |
| 87. C2×H(3,𝔽3) | C3×Dic3 | semidirect |
| 123. C33 | C2×C32×C4 | semidirect |
| 127. H(3,𝔽3) | C2×C3×Dic3 | semidirect |
| 211. C2×C3 | #66322 | direct (N × H) |
| 223. C3 | C2×#66322 | direct (N × H) |
| 225. C2 | C3×#66322 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×AΣL(1,𝔽27) | 2 |
| C3×#66322 | 2 |
| C2×C3×C3⋊(C3⋊Dic3) | 3 |
| C2×C3×(C3⋊Dic3)⋊C3 | 3 |
| C2×#66322 | 3 |