Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
848 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 432 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. #17987599 | C3 | direct (N × H) |
| 2. C3×#13095344 | C3 | semidirect |
| 3. C3×#13095343 | C3 | semidirect |
| 4. C3×#13095342 | C3 | semidirect |
| 5. C3×(C19⋊C3)⋊C27 | C3 | semidirect |
| 6. C32×#10587020 | C3 | semidirect |
| 8. #13095344 | C32 | semidirect |
| 9. #13095343 | C32 | semidirect |
| 10. #13095342 | C32 | semidirect |
| 11. (C19⋊C3)⋊C27 | C32 | semidirect |
| 16. C3×#10587020 | C32 | semidirect |
| 84. C3×C19 | #6903 | semidirect |
| 107. C19 | C3×#6903 | semidirect |
| 121. C3 | #17987599 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987599 | 3 |
| C3×#13095344 | 3 |
| C3×#13095343 | 3 |
| C3×#13095342 | 3 |
| C3×(C19⋊C3)⋊C27 | 3 |
| C32×#10587020 | 3 |
| C3×#13095333 | 3 |
| C3×#6903 | 19 |