Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
560 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
| 3. #17987420 | C3 | semidirect |
| 4. #17987418 | C3 | semidirect |
| 5. #17987313 | C3 | semidirect |
| 6. #17987312 | C3 | semidirect |
| 7. #17987311 | C3 | semidirect |
| 8. #17987311 | C3 | semidirect |
| 9. C19×#6857 | C3 | semidirect |
| 12. C3×#10587025 | C32 | semidirect |
| 13. C3×#10587025 | C32 | semidirect |
| 23. C32⋊#4294 | C32 | semidirect |
| 29. C3×C19×3−1+2 | C32 | semidirect |
| 30. C3×C19×3−1+2 | C32 | semidirect |
| 32. C19×C32⋊C9 | C32 | semidirect |
| 74. #6857 | C19⋊C3 | semidirect |
| 116. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 117. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 130. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 173. C19 | #10624590 | semidirect |
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 |
| C3×H(3,𝔽3)×C19⋊C3 | 3 |
| #17987420 | 3 |
| #17987418 | 3 |
| #17987313 | 3 |
| #17987312 | 3 |
| #17987311 | 3 |
| C19×#6857 | 3 |
| #10624590 | 19 |