Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
368 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 64 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×#11923958 | C3 | semidirect |
| 2. #23782812 | C3 | semidirect |
| 3. #23782800 | C3 | semidirect |
| 4. 3−1+2×C43⋊C9 | C3 | semidirect |
| 5. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 6. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 7. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 8. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 9. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 10. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 11. #23782712 | C3 | semidirect |
| 12. #23782712 | C3 | semidirect |
| 70. 3−1+2×C43 | 3−1+2 | semidirect |
| 104. C43⋊C9 | AΣL(1,𝔽27) | semidirect |
| 153. C43 | #10624798 | semidirect |
| 169. 3−1+2 | #11923958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| #23782812 | 3 |
| #23782800 | 3 |
| 3−1+2×C43⋊C9 | 3 |
| 3−1+2⋊(C43⋊C9) | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782712 | 3 |
| C3×C43×AΣL(1,𝔽27) | 3 |
| #10624798 | 43 |