Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
2072 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 2072 conjugacy classes of subgroups — too many to draw. Only its 76 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. C34×C43⋊C3 | C3 | semidirect |
| 2. C3×#16812508 | C3 | semidirect |
| 3. C3×#16812507 | C3 | semidirect |
| 4. C3×#16812506 | C3 | semidirect |
| 5. #23782795 | C3 | semidirect |
| 6. (C3×C43⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 7. C3×C43×AΣL(1,𝔽27) | C3 | semidirect |
| 14. C3×#11923958 | C32 | semidirect |
| 16. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 22. C3×3−1+2×C43 | C32 | semidirect |
| 23. C3×H(3,𝔽3)×C43 | C32 | semidirect |
| 39. C32×C43⋊C3 | H(3,𝔽3) | semidirect |
| 51. C33×C43 | H(3,𝔽3) | semidirect |
| 81. C3×C43⋊C3 | AΣL(1,𝔽27) | semidirect |
| 88. C3×AΣL(1,𝔽27) | C43⋊C3 | semidirect |
| 108. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 111. C3×H(3,𝔽3) | C3×C43⋊C3 | semidirect |
| 117. C43 | #10624730 | semidirect |
| 137. C33 | C32⋊(C43⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C43⋊C3 | 3 |
| C3×#16812508 | 3 |
| C3×#16812507 | 3 |
| C3×#16812506 | 3 |
| #23782795 | 3 |
| (C3×C43⋊C3)⋊H(3,𝔽3) | 3 |
| C3×C43×AΣL(1,𝔽27) | 3 |
| #10624730 | 43 |