Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1304 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1304 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. C32×#10587023 | C3 | semidirect |
| 2. C3×H(3,𝔽3)×C19⋊C3 | C3 | semidirect |
| 3. #17987513 | C3 | direct (N × H) |
| 4. C3×#13095320 | C3 | semidirect |
| 5. C3×#13095319 | C3 | semidirect |
| 6. C3×C19×#732 | C3 | semidirect |
| 11. C3×#10587023 | C32 | semidirect |
| 13. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 15. H(3,𝔽3)×C19⋊C3 | C32 | semidirect |
| 16. C32×#4294 | C32 | semidirect |
| 17. #13095320 | C32 | semidirect |
| 18. #13095319 | C32 | semidirect |
| 19. C3×C19×H(3,𝔽3) | C32 | semidirect |
| 20. C32×C9×C19 | C32 | semidirect |
| 21. C19×#732 | C32 | semidirect |
| 33. C19×H(3,𝔽3) | C33 | semidirect |
| 36. C3×C9×C19 | C33 | semidirect |
| 39. C32⋊(C19⋊C3) | C33 | semidirect |
| 42. C3×#4294 | C33 | semidirect |
| 49. C3×#732 | C19⋊C3 | semidirect |
| 74. C3×H(3,𝔽3) | C3×C19⋊C3 | semidirect |
| 76. C32×C9 | C3×C19⋊C3 | semidirect |
| 79. #732 | C3×C19⋊C3 | semidirect |
| 83. C3×C19 | #6911 | semidirect |
| 101. H(3,𝔽3) | C32×C19⋊C3 | semidirect |
| 107. C3×C9 | C32×C19⋊C3 | semidirect |
| 108. C19 | C3×#6911 | semidirect |
| 129. C3 | #17987513 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587023 | 3 |
| C3×H(3,𝔽3)×C19⋊C3 | 3 |
| #17987513 | 3 |
| C3×#13095320 | 3 |
| C3×#13095319 | 3 |
| C3×C19×#732 | 3 |
| C3×#6911 | 19 |