Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1088 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1088 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×#10587022 | C3 | semidirect |
| 2. C3×3−1+2×C19⋊C3 | C3 | semidirect |
| 4. #17987508 | C3 | direct (N × H) |
| 5. C3×#13095318 | C3 | semidirect |
| 6. C3×#13095317 | C3 | semidirect |
| 7. C3×#13095316 | C3 | semidirect |
| 8. C3×C19×#731 | C3 | semidirect |
| 11. C3×#10587025 | C32 | semidirect |
| 16. C3×#10587022 | C32 | semidirect |
| 19. 3−1+2×C19⋊C3 | C32 | semidirect |
| 24. C32×#4294 | C32 | semidirect |
| 26. #13095318 | C32 | semidirect |
| 27. #13095317 | C32 | semidirect |
| 28. #13095316 | C32 | semidirect |
| 29. C3×C19×3−1+2 | C32 | semidirect |
| 31. C32×C9×C19 | C32 | semidirect |
| 32. C19×#731 | C32 | semidirect |
| 45. C19×3−1+2 | C33 | semidirect |
| 51. C3×C9×C19 | C33 | semidirect |
| 56. #10587025 | C33 | semidirect |
| 60. C3×#4294 | C33 | semidirect |
| 73. C3×#731 | C19⋊C3 | semidirect |
| 104. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 112. C32×C9 | C3×C19⋊C3 | semidirect |
| 116. #731 | C3×C19⋊C3 | semidirect |
| 120. C3×C19 | #6910 | semidirect |
| 142. 3−1+2 | C32×C19⋊C3 | semidirect |
| 156. C3×C9 | C32×C19⋊C3 | semidirect |
| 157. C19 | C3×#6910 | semidirect |
| 183. C3 | #17987508 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587022 | 3 |
| C3×3−1+2×C19⋊C3 | 3 |
| C3×H(3,𝔽3)×C19⋊C3 | 3 |
| #17987508 | 3 |
| C3×#13095318 | 3 |
| C3×#13095317 | 3 |
| C3×#13095316 | 3 |
| C3×C19×#731 | 3 |
| C3×#6910 | 19 |