Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
572 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 572 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 |
|---|---|---|
| 5. #23782725 | C3 | semidirect |
| 6. #23782724 | C3 | semidirect |
| 7. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 8. #23782722 | C3 | semidirect |
| 9. C43×3−1+2⋊C9 | C3 | semidirect |
| 15. 3−1+2×C43⋊C3 | C9 | semidirect |
| 43. #11923958 | C3×C9 | semidirect |
| 59. 3−1+2×C43 | C3×C9 | semidirect |
| 102. 3−1+2⋊C9 | C43⋊C3 | direct (N × H) |
| 111. C43⋊C3 | 3−1+2⋊C9 | direct (N × H) |
| 136. C43 | C3×3−1+2⋊C9 | semidirect |
| 151. 3−1+2 | C9×C43⋊C3 | 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 |
| C32⋊C9×C43⋊C3 | 3 |
| #23782725 | 3 |
| #23782724 | 3 |
| 3−1+2⋊(C43⋊C9) | 3 |
| #23782722 | 3 |
| C43×3−1+2⋊C9 | 3 |
| C3×3−1+2⋊C9 | 43 |