Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1196 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1196 conjugacy classes of subgroups — too many to draw. Only its 274 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. C3×3−1+2×C19⋊C3 | C3 | semidirect |
| 2. C32×C32⋊(C19⋊C3) | C3 | semidirect |
| 3. C3×H(3,𝔽3)×C19⋊C3 | C3 | semidirect |
| 4. #17987502 | C3 | direct (N × H) |
| 5. C3×#13095315 | C3 | semidirect |
| 6. C3×#13095314 | C3 | semidirect |
| 7. C3×#13095313 | C3 | semidirect |
| 8. C3×C19×AΣL(1,𝔽27) | C3 | semidirect |
| 11. C33×C19⋊C3 | C32 | semidirect |
| 12. C3×#10587025 | C32 | semidirect |
| 16. 3−1+2×C19⋊C3 | C32 | semidirect |
| 22. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 24. H(3,𝔽3)×C19⋊C3 | C32 | semidirect |
| 26. #13095315 | C32 | semidirect |
| 27. #13095314 | C32 | semidirect |
| 28. #13095313 | C32 | semidirect |
| 29. C34×C19 | C32 | semidirect |
| 30. C3×C19×3−1+2 | C32 | semidirect |
| 32. C19×AΣL(1,𝔽27) | C32 | semidirect |
| 39. C33×C19 | C33 | semidirect |
| 51. C32×C19⋊C3 | C33 | semidirect |
| 53. C19×3−1+2 | C33 | semidirect |
| 63. #10587025 | C33 | semidirect |
| 75. C3×AΣL(1,𝔽27) | C19⋊C3 | semidirect |
| 104. C34 | C3×C19⋊C3 | semidirect |
| 110. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 124. AΣL(1,𝔽27) | C3×C19⋊C3 | semidirect |
| 129. C3×C19 | #6909 | semidirect |
| 152. C33 | C32×C19⋊C3 | semidirect |
| 158. 3−1+2 | C32×C19⋊C3 | semidirect |
| 169. C19 | C3×#6909 | semidirect |
| 203. C3 | #17987502 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C19⋊C3 | 3 |
| C32×C32⋊(C19⋊C3) | 3 |
| C3×H(3,𝔽3)×C19⋊C3 | 3 |
| #17987502 | 3 |
| C3×#13095315 | 3 |
| C3×#13095314 | 3 |
| C3×#13095313 | 3 |
| C3×C19×AΣL(1,𝔽27) | 3 |
| C3×#6909 | 19 |