Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
535 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 535 conjugacy classes of subgroups — too many to draw. Only its 72 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. C22×C3×AΣL(1,𝔽27) | C2 | semidirect |
| 2. C2×D3×AΣL(1,𝔽27) | C2 | semidirect |
| 3. Dic3×AΣL(1,𝔽27) | C2 | semidirect |
| 4. C33×#67 | C3 | semidirect |
| 5. #67×3−1+2 | C3 | semidirect |
| 6. #67×H(3,𝔽3) | C3 | semidirect |
| 11. C22×C34 | C2×C3 | semidirect |
| 12. C2×C33×D3 | C2×C3 | semidirect |
| 13. C33×Dic3 | C2×C3 | semidirect |
| 14. C22×C3×3−1+2 | C2×C3 | semidirect |
| 15. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 16. C2×D3×3−1+2 | C2×C3 | semidirect |
| 17. C2×D3×H(3,𝔽3) | C2×C3 | semidirect |
| 18. Dic3×3−1+2 | C2×C3 | semidirect |
| 19. Dic3×H(3,𝔽3) | C2×C3 | semidirect |
| 24. C22×AΣL(1,𝔽27) | D3 | semidirect |
| 26. C3×AΣL(1,𝔽27) | D4 | semidirect |
| 60. C22×C33 | C3×D3 | semidirect |
| 74. C22×3−1+2 | C3×D3 | semidirect |
| 78. C22×H(3,𝔽3) | C3×D3 | semidirect |
| 84. C34 | C3×D4 | semidirect |
| 85. C3×3−1+2 | C3×D4 | semidirect |
| 86. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 90. AΣL(1,𝔽27) | #67 | direct (N × H) |
| 181. C33 | C3×#67 | semidirect |
| 185. 3−1+2 | C3×#67 | semidirect |
| 188. H(3,𝔽3) | C3×#67 | semidirect |
| 194. #67 | AΣL(1,𝔽27) | direct (N × H) |
| 253. C22×C3 | C2×AΣL(1,𝔽27) | semidirect |
| 255. C2×D3 | C2×AΣL(1,𝔽27) | semidirect |
| 260. Dic3 | C2×AΣL(1,𝔽27) | semidirect |
| 305. C22 | D3×AΣL(1,𝔽27) | semidirect |
| 314. C3 | D4×AΣL(1,𝔽27) | semidirect |
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 |
| C2×D3×AΣL(1,𝔽27) | 2 |
| Dic3×AΣL(1,𝔽27) | 2 |
| C33×#67 | 3 |
| #67×3−1+2 | 3 |
| #67×H(3,𝔽3) | 3 |
| D4×AΣL(1,𝔽27) | 3 |