Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
2636 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 2636 conjugacy classes of subgroups — too many to draw. Only its 382 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 |
|---|---|---|
| 2. C32×#10587022 | C3 | semidirect |
| 3. #17987420 | C3 | direct (N × H) |
| 4. C3×C32⋊#4294 | C3 | semidirect |
| 5. C3×#13095303 | C3 | semidirect |
| 6. C3×C19×C32⋊C9 | C3 | semidirect |
| 14. C3×#10587022 | C32 | semidirect |
| 15. C32×#4294 | C32 | semidirect |
| 16. C32⋊#4294 | C32 | semidirect |
| 17. #13095303 | C32 | semidirect |
| 19. C32×C9×C19 | C32 | semidirect |
| 20. C19×C32⋊C9 | C32 | semidirect |
| 24. C33×C19 | 3−1+2 | semidirect |
| 37. C32×C19⋊C3 | 3−1+2 | semidirect |
| 41. C3×C9×C19 | C33 | semidirect |
| 43. C3×#4294 | C33 | semidirect |
| 50. C3×C32⋊C9 | C19⋊C3 | semidirect |
| 57. C32×C19 | C3×3−1+2 | semidirect |
| 68. C3×C19⋊C3 | C3×3−1+2 | semidirect |
| 81. C32×C9 | C3×C19⋊C3 | semidirect |
| 84. C32⋊C9 | C3×C19⋊C3 | semidirect |
| 86. C3×C19 | #6891 | semidirect |
| 107. C33 | #10587022 | semidirect |
| 114. C3×C9 | C32×C19⋊C3 | semidirect |
| 115. C19 | C3×#6891 | semidirect |
| 132. C32 | C3×#10587022 | semidirect |
| 139. C3 | #17987420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C19⋊C3 | 3 |
| C32×#10587022 | 3 |
| #17987420 | 3 |
| C3×C32⋊#4294 | 3 |
| C3×#13095303 | 3 |
| C3×C19×C32⋊C9 | 3 |
| C3×#6891 | 19 |