Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
832 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
| 6. C2×C3×AΣL(1,𝔽27) | C4 | semidirect |
| 9. C3⋊(C3⋊(C3⋊Dic3)) | C2×C3 | semidirect |
| 16. C3×AΣL(1,𝔽27) | C2×C4 | semidirect |
| 25. C2×C34 | C3×C4 | semidirect |
| 29. C2×C3×H(3,𝔽3) | Dic3 | semidirect |
| 33. C2×AΣL(1,𝔽27) | Dic3 | semidirect |
| 55. C34 | C2×C3×C4 | semidirect |
| 57. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 59. AΣL(1,𝔽27) | C2×Dic3 | semidirect |
| 79. C2×C33 | C3×Dic3 | semidirect |
| 90. C2×H(3,𝔽3) | C3⋊Dic3 | semidirect |
| 121. C33 | C2×C3×Dic3 | semidirect |
| 126. H(3,𝔽3) | C2×C3⋊Dic3 | semidirect |
| 194. C2×C3 | #66322 | semidirect |
| 205. C3 | C2×#66322 | semidirect |
| 207. 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 |