Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1988 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 1988 conjugacy classes of subgroups — too many to draw. Only its 108 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. C3×C32⋊#4296 | C3 | semidirect |
| 2. #17987558 | C3 | direct (N × H) |
| 6. C32⋊#4296 | C32 | semidirect |
| 12. C33×C19⋊C3 | C9 | semidirect |
| 13. C33×C19⋊C3 | C9 | semidirect |
| 16. C34×C19 | C9 | semidirect |
| 22. C33×C19 | C3×C9 | semidirect |
| 38. C32×C19⋊C3 | C3×C9 | semidirect |
| 85. C34 | #4296 | semidirect |
| 92. C3×C19 | #6866 | semidirect |
| 97. C19⋊C3 | #6866 | semidirect |
| 124. C33 | C3×#4296 | semidirect |
| 127. C19 | C3×#6866 | semidirect |
| 163. C3 | #17987558 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊#4296 | 3 |
| #17987558 | 3 |
| C34×C19⋊C3 | 3 |
| C3×#6866 | 19 |