Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
770 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 770 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 |
|---|---|---|
| 1. C32×C32⋊(C43⋊C3) | C3 | semidirect |
| 2. C3×H(3,𝔽3)×C43⋊C3 | C3 | semidirect |
| 3. C3×#16812508 | C3 | semidirect |
| 4. C3×#16812507 | C3 | semidirect |
| 5. C3×#16812506 | C3 | semidirect |
| 6. #23782795 | C3 | semidirect |
| 7. C3×C43×AΣL(1,𝔽27) | C3 | semidirect |
| 10. C33×C43⋊C3 | C32 | semidirect |
| 11. C3×#11923958 | C32 | semidirect |
| 24. C34×C43 | C32 | semidirect |
| 25. C3×3−1+2×C43 | C32 | semidirect |
| 54. C32⋊(C43⋊C3) | H(3,𝔽3) | semidirect |
| 67. H(3,𝔽3)×C43 | H(3,𝔽3) | semidirect |
| 106. C3×C43⋊C3 | AΣL(1,𝔽27) | semidirect |
| 114. C3×AΣL(1,𝔽27) | C43⋊C3 | semidirect |
| 131. C34 | C3×C43⋊C3 | semidirect |
| 133. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 148. C43 | #10624742 | semidirect |
| 187. H(3,𝔽3) | C32⋊(C43⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C43⋊C3) | 3 |
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| C3×#16812508 | 3 |
| C3×#16812507 | 3 |
| C3×#16812506 | 3 |
| #23782795 | 3 |
| C3×C43×AΣL(1,𝔽27) | 3 |
| #10624742 | 43 |