Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
472 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 472 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. C33×#4296 | C3 | semidirect |
| 2. 3−1+2×#4296 | C3 | semidirect |
| 3. H(3,𝔽3)×#4296 | C3 | semidirect |
| 4. 3−1+2⋊#4296 | C3 | semidirect |
| 5. H(3,𝔽3)⋊#4296 | C3 | semidirect |
| 6. #17987558 | C3 | semidirect |
| 23. #13095315 | C9 | semidirect |
| 24. #13095314 | C9 | semidirect |
| 25. #13095313 | C9 | semidirect |
| 26. C19×AΣL(1,𝔽27) | C9 | semidirect |
| 28. C33×C19 | C3×C9 | semidirect |
| 34. C32×C19⋊C3 | C3×C9 | semidirect |
| 46. C19×3−1+2 | C3×C9 | semidirect |
| 47. C19×H(3,𝔽3) | C3×C9 | semidirect |
| 49. C32⋊(C19⋊C3) | C3×C9 | semidirect |
| 50. #10587025 | C3×C9 | semidirect |
| 81. #4296 | AΣL(1,𝔽27) | direct (N × H) |
| 96. AΣL(1,𝔽27) | #4296 | direct (N × H) |
| 119. C33 | C3×#4296 | semidirect |
| 123. 3−1+2 | C3×#4296 | semidirect |
| 126. H(3,𝔽3) | C3×#4296 | semidirect |
| 138. C19 | C9×AΣL(1,𝔽27) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#4296 | 3 |
| 3−1+2×#4296 | 3 |
| H(3,𝔽3)×#4296 | 3 |
| 3−1+2⋊#4296 | 3 |
| H(3,𝔽3)⋊#4296 | 3 |
| #17987558 | 3 |
| C19⋊C3×AΣL(1,𝔽27) | 3 |
| C9×AΣL(1,𝔽27) | 19 |