Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
560 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 61 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. C43⋊H(5,𝔽3) | C3 | semidirect |
| 2. #23782892 | C3 | semidirect |
| 3. #23782891 | C3 | semidirect |
| 4. #23782883 | C3 | semidirect |
| 5. C3×#16812507 | C3 | semidirect |
| 6. #23782794 | C3 | semidirect |
| 7. C3×C43×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C3×#11923958 | C32 | semidirect |
| 13. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 20. C34×C43 | C32 | semidirect |
| 21. C3×3−1+2×C43 | C32 | semidirect |
| 27. C32×C43⋊C3 | H(3,𝔽3) | semidirect |
| 39. C32⋊(C43⋊C3) | H(3,𝔽3) | semidirect |
| 50. H(3,𝔽3)×C43 | H(3,𝔽3) | semidirect |
| 78. C3×AΣL(1,𝔽27) | C43⋊C3 | semidirect |
| 89. C34 | C3×C43⋊C3 | semidirect |
| 91. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 105. C43 | UT(4,𝔽3) | semidirect |
| 131. 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 |
|---|---|
| C43⋊H(5,𝔽3) | 3 |
| #23782892 | 3 |
| #23782891 | 3 |
| #23782883 | 3 |
| C3×#16812507 | 3 |
| #23782794 | 3 |
| C3×C43×AΣL(1,𝔽27) | 3 |
| UT(4,𝔽3) | 43 |