Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
758 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 112 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. C32×#10587025 | C3 | semidirect |
| 3. C3×C32⋊#4294 | C3 | semidirect |
| 4. C3×#13095303 | C3 | semidirect |
| 5. C3×C19×C32⋊C9 | C3 | semidirect |
| 30. C32×C19⋊C3 | 3−1+2 | semidirect |
| 39. C3×#4294 | H(3,𝔽3) | semidirect |
| 44. C3×C32⋊C9 | C19⋊C3 | semidirect |
| 104. C19 | #10624563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587025 | 3 |
| C32×C32⋊(C19⋊C3) | 3 |
| C3×C32⋊#4294 | 3 |
| C3×#13095303 | 3 |
| C3×C19×C32⋊C9 | 3 |
| #10624563 | 19 |