Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1688 conjugacy classes of subgroups; only the 468 normal subgroups are shown.
This group has 1688 conjugacy classes of subgroups — too many to draw. Only its 468 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. H(3,𝔽3)×#4296 | C3 | direct (N × H) |
| 3. C3×C32⋊#4296 | C3 | semidirect |
| 8. C32×#4296 | C32 | semidirect |
| 9. C32⋊#4296 | C32 | semidirect |
| 11. C3×C32⋊(C19⋊C3) | C9 | semidirect |
| 12. H(3,𝔽3)×C19⋊C3 | C9 | semidirect |
| 14. C3×C19×H(3,𝔽3) | C9 | semidirect |
| 16. C33×C19 | C3×C9 | semidirect |
| 19. C32×C19⋊C3 | C3×C9 | semidirect |
| 20. C32×C19⋊C3 | C3×C9 | semidirect |
| 25. C3×#4296 | H(3,𝔽3) | direct (N × H) |
| 28. C19×H(3,𝔽3) | C3×C9 | semidirect |
| 29. C32⋊(C19⋊C3) | C3×C9 | semidirect |
| 36. C32×C19 | C32×C9 | semidirect |
| 42. C3×C19⋊C3 | C32×C9 | semidirect |
| 47. #4296 | C3×H(3,𝔽3) | direct (N × H) |
| 52. C3×H(3,𝔽3) | #4296 | direct (N × H) |
| 59. C3×C19 | C9×H(3,𝔽3) | semidirect |
| 62. C19⋊C3 | C9×H(3,𝔽3) | semidirect |
| 71. C33 | C3×#4296 | semidirect |
| 73. H(3,𝔽3) | C3×#4296 | direct (N × H) |
| 79. C19 | C3×C9×H(3,𝔽3) | semidirect |
| 91. C32 | C32×#4296 | semidirect |
| 99. C3 | H(3,𝔽3)×#4296 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#4296 | 3 |
| H(3,𝔽3)×#4296 | 3 |
| C3×C32⋊#4296 | 3 |
| C3×H(3,𝔽3)×C19⋊C3 | 3 |
| C3×C9×H(3,𝔽3) | 19 |