Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
380 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 5. #23782694 | C3 | semidirect |
| 6. #23782693 | C3 | semidirect |
| 7. #23782692 | C3 | semidirect |
| 8. #23782691 | C3 | semidirect |
| 9. C43×#6858 | C3 | semidirect |
| 91. #6858 | C43⋊C3 | direct (N × H) |
| 99. C43⋊C3 | #6858 | direct (N × H) |
| 122. C43 | C3×#6858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C43⋊C3 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| #23782694 | 3 |
| #23782693 | 3 |
| #23782692 | 3 |
| #23782691 | 3 |
| C43×#6858 | 3 |
| C3×#6858 | 43 |