Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
560 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 61 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. C19⋊H(5,𝔽3) | C3 | semidirect |
| 2. #17987515 | C3 | semidirect |
| 3. #17987514 | C3 | semidirect |
| 4. #17987506 | C3 | semidirect |
| 5. C3×#13095314 | C3 | semidirect |
| 6. #17987417 | C3 | semidirect |
| 7. C3×C19×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C3×#10587025 | C32 | semidirect |
| 13. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 20. C34×C19 | C32 | semidirect |
| 21. C3×C19×3−1+2 | C32 | semidirect |
| 34. C32×C19⋊C3 | H(3,𝔽3) | semidirect |
| 38. C19×H(3,𝔽3) | H(3,𝔽3) | semidirect |
| 49. C32⋊(C19⋊C3) | H(3,𝔽3) | semidirect |
| 58. C3×AΣL(1,𝔽27) | C19⋊C3 | semidirect |
| 80. C34 | C3×C19⋊C3 | semidirect |
| 82. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 130. H(3,𝔽3) | C32⋊(C19⋊C3) | semidirect |
| 133. C19 | UT(4,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19⋊H(5,𝔽3) | 3 |
| #17987515 | 3 |
| #17987514 | 3 |
| #17987506 | 3 |
| C3×#13095314 | 3 |
| #17987417 | 3 |
| C3×C19×AΣL(1,𝔽27) | 3 |
| UT(4,𝔽3) | 19 |