Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
680 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 680 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. C3×3−1+2×C43⋊C3 | C3 | semidirect |
| 3. C32⋊C9×C43⋊C3 | C3 | semidirect |
| 4. #23782690 | C3 | semidirect |
| 5. #23782689 | C3 | semidirect |
| 6. #23782688 | C3 | semidirect |
| 7. C43×#6857 | C3 | semidirect |
| 10. C3×#11923958 | C32 | semidirect |
| 19. C32⋊(C43⋊C9) | C32 | semidirect |
| 21. C3×3−1+2×C43 | C32 | semidirect |
| 23. C43×C32⋊C9 | C32 | semidirect |
| 78. #6857 | C43⋊C3 | direct (N × H) |
| 86. C43⋊C3 | #6857 | direct (N × H) |
| 93. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 102. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 103. C43 | C3×#6857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C43⋊C3 | 3 |
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| #23782690 | 3 |
| #23782689 | 3 |
| #23782688 | 3 |
| C43×#6857 | 3 |
| C3×#6857 | 43 |