Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
554 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 175 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. C3×#13095307 | C3 | semidirect |
| 4. #17987308 | C3 | semidirect |
| 16. C19×C32⋊C9 | C9 | semidirect |
| 28. C3×C9×C19 | C3×C9 | semidirect |
| 51. C32×C19 | C9⋊C9 | semidirect |
| 73. C32⋊C9 | #4294 | semidirect |
| 103. C3×C9 | C3×#4294 | semidirect |
| 104. C19 | #10624556 | semidirect |
| 111. C32 | #13095307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#4294 | 3 |
| C3×#13095307 | 3 |
| C3×C32⋊#4294 | 3 |
| #17987308 | 3 |
| C3×C19×C32⋊C9 | 3 |
| #10624556 | 19 |