Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
560 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23782796 | C3 | semidirect |
| 4. #23782795 | C3 | semidirect |
| 5. #23782690 | C3 | semidirect |
| 6. #23782689 | C3 | semidirect |
| 7. #23782688 | C3 | semidirect |
| 8. #23782688 | C3 | semidirect |
| 9. C43×#6857 | C3 | semidirect |
| 12. C3×#11923958 | C32 | semidirect |
| 13. C3×#11923958 | C32 | semidirect |
| 23. C32⋊(C43⋊C9) | C32 | semidirect |
| 29. C3×3−1+2×C43 | C32 | semidirect |
| 30. C3×3−1+2×C43 | C32 | semidirect |
| 32. C43×C32⋊C9 | C32 | semidirect |
| 107. #6857 | C43⋊C3 | semidirect |
| 126. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 127. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 140. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 141. C43 | #10624590 | 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 |
| #23782796 | 3 |
| #23782795 | 3 |
| #23782690 | 3 |
| #23782689 | 3 |
| #23782688 | 3 |
| C43×#6857 | 3 |
| #10624590 | 43 |