Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
884 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 346 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 |
|---|---|---|
| 3. #17987450 | C3 | direct (N × H) |
| 4. C3×#13095306 | C3 | semidirect |
| 5. C3×#13095306 | C3 | semidirect |
| 6. C3×#13095305 | C3 | semidirect |
| 7. C3×#13095305 | C3 | semidirect |
| 9. C3×C9×#4294 | C3 | semidirect |
| 10. C3×C19×C9⋊C9 | C3 | semidirect |
| 21. #13095306 | C32 | semidirect |
| 22. #13095306 | C32 | semidirect |
| 23. #13095305 | C32 | semidirect |
| 24. #13095305 | C32 | semidirect |
| 26. C9×#4294 | C32 | semidirect |
| 30. C19×C9⋊C9 | C32 | semidirect |
| 39. C3×C9×C19 | 3−1+2 | semidirect |
| 47. C3×#4294 | 3−1+2 | semidirect |
| 62. C3×C9⋊C9 | C19⋊C3 | semidirect |
| 75. C9×C19 | C3×3−1+2 | semidirect |
| 80. #4294 | C3×3−1+2 | semidirect |
| 98. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 101. C3×C19 | #6896 | semidirect |
| 125. C3×C9 | #10587022 | semidirect |
| 129. C19 | C3×#6896 | semidirect |
| 145. C9 | C3×#10587022 | semidirect |
| 147. C3 | #17987450 | 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 |
| C32×#10587023 | 3 |
| #17987450 | 3 |
| C3×#13095306 | 3 |
| C3×#13095305 | 3 |
| C3×#13095303 | 3 |
| C3×C9×#4294 | 3 |
| C3×C19×C9⋊C9 | 3 |
| C3×#6896 | 19 |