Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
476 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 3. #23782713 | C3 | direct (N × H) |
| 10. C32×C43⋊C9 | C9 | semidirect |
| 25. C3×C43⋊C9 | C3×C9 | semidirect |
| 63. C3×C43 | #6867 | semidirect |
| 80. C43 | C3×#6867 | semidirect |
| 121. C3 | #23782713 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C43⋊C9 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| #23782713 | 3 |
| C3×C43×C32⋊C9 | 3 |
| C3×#6867 | 43 |