Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
680 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 680 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 |
|---|---|---|
| 2. C32×C9×C43⋊C3 | C3 | semidirect |
| 3. C32⋊C9×C43⋊C3 | C3 | semidirect |
| 4. #23782721 | C3 | semidirect |
| 5. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 6. #23782719 | C3 | semidirect |
| 7. C43×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 13. H(3,𝔽3)×C43⋊C3 | C9 | semidirect |
| 14. C32×C43⋊C9 | C32 | semidirect |
| 19. C32⋊(C43⋊C9) | C32 | semidirect |
| 22. C32×C9×C43 | C32 | semidirect |
| 23. C43×C32⋊C9 | C32 | semidirect |
| 38. C32⋊(C43⋊C3) | C3×C9 | semidirect |
| 48. H(3,𝔽3)×C43 | C3×C9 | semidirect |
| 88. H(3,𝔽3)⋊C9 | C43⋊C3 | direct (N × H) |
| 98. C43⋊C3 | H(3,𝔽3)⋊C9 | direct (N × H) |
| 111. C32×C9 | C3×C43⋊C3 | semidirect |
| 114. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 115. C43 | C3×H(3,𝔽3)⋊C9 | semidirect |
| 134. H(3,𝔽3) | C9×C43⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| C32×C9×C43⋊C3 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| #23782721 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782719 | 3 |
| C43×H(3,𝔽3)⋊C9 | 3 |
| C3×H(3,𝔽3)⋊C9 | 43 |