Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 10. #13095342 | C9 | semidirect |
| 11. #13095342 | C9 | semidirect |
| 18. #13095312 | C9 | semidirect |
| 22. C19×C27⋊C3 | C9 | semidirect |
| 73. C27⋊C3 | #4296 | semidirect |
| 104. C19 | #10624467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C19⋊C3)⋊(C27⋊C3) | 3 |
| C3×C9×#4296 | 3 |
| C19⋊C3×C27⋊C3 | 3 |
| #10624467 | 19 |