Finite Group DatabasebetaFinite Group Databasebeta← C2×Dic3×AΣL(1,𝔽27) #14517450
Order 1944.
535 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 535 conjugacy classes of subgroups — too many to draw. Only its 104 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. Dic3×AΣL(1,𝔽27) | C2 | direct (N × H) |
| 3. C2×C33×Dic3 | C3 | semidirect |
| 4. C2×Dic3×3−1+2 | C3 | semidirect |
| 5. C2×Dic3×H(3,𝔽3) | C3 | semidirect |
| 7. C2×C3×AΣL(1,𝔽27) | C4 | semidirect |
| 10. C33×Dic3 | C2×C3 | semidirect |
| 13. Dic3×3−1+2 | C2×C3 | semidirect |
| 14. Dic3×H(3,𝔽3) | C2×C3 | semidirect |
| 20. C3×AΣL(1,𝔽27) | C2×C4 | semidirect |
| 29. C2×C34 | C3×C4 | semidirect |
| 31. C2×C3×3−1+2 | C3×C4 | semidirect |
| 33. C2×C3×H(3,𝔽3) | C3×C4 | semidirect |
| 41. C2×AΣL(1,𝔽27) | Dic3 | direct (N × H) |
| 66. C34 | C2×C3×C4 | semidirect |
| 67. C3×3−1+2 | C2×C3×C4 | semidirect |
| 68. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 72. AΣL(1,𝔽27) | C2×Dic3 | direct (N × H) |
| 94. C2×C33 | C3×Dic3 | semidirect |
| 102. C2×3−1+2 | C3×Dic3 | semidirect |
| 108. C2×H(3,𝔽3) | C3×Dic3 | semidirect |
| 146. C33 | C2×C3×Dic3 | semidirect |
| 150. 3−1+2 | C2×C3×Dic3 | semidirect |
| 153. H(3,𝔽3) | C2×C3×Dic3 | semidirect |
| 159. C2×Dic3 | AΣL(1,𝔽27) | direct (N × H) |
| 211. Dic3 | C2×AΣL(1,𝔽27) | direct (N × H) |
| 246. C2×C3 | C4×AΣL(1,𝔽27) | semidirect |
| 259. C3 | C2×C4×AΣL(1,𝔽27) | semidirect |
| 261. C2 | Dic3×AΣL(1,𝔽27) | 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 |
| Dic3×AΣL(1,𝔽27) | 2 |
| C2×C33×Dic3 | 3 |
| C2×Dic3×3−1+2 | 3 |
| C2×Dic3×H(3,𝔽3) | 3 |
| C2×C4×AΣL(1,𝔽27) | 3 |