Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
554 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 554 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. C32×C32⋊(C19⋊C3) | C3 | semidirect |
| 2. #17987515 | C3 | semidirect |
| 3. #17987514 | C3 | semidirect |
| 4. #17987511 | C3 | semidirect |
| 5. #17987510 | C3 | semidirect |
| 6. #17987506 | C3 | semidirect |
| 7. #17987505 | C3 | semidirect |
| 8. C3×#13095314 | C3 | semidirect |
| 9. C3×C19×AΣL(1,𝔽27) | C3 | semidirect |
| 11. C3×#10587025 | C32 | semidirect |
| 12. C3×#10587025 | C32 | semidirect |
| 18. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 28. C3×C19×3−1+2 | C32 | semidirect |
| 29. C3×C19×3−1+2 | C32 | semidirect |
| 30. C3×C19×H(3,𝔽3) | C32 | semidirect |
| 79. C3×AΣL(1,𝔽27) | C19⋊C3 | semidirect |
| 107. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 108. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 115. C3×H(3,𝔽3) | C3×C19⋊C3 | semidirect |
| 173. C19 | #10624754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C19⋊C3) | 3 |
| #17987515 | 3 |
| #17987514 | 3 |
| #17987511 | 3 |
| #17987510 | 3 |
| #17987506 | 3 |
| #17987505 | 3 |
| C3×#13095314 | 3 |
| C3×C19×AΣL(1,𝔽27) | 3 |
| #10624754 | 19 |