Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1196 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1196 conjugacy classes of subgroups — too many to draw. Only its 292 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. C32×C32⋊(C43⋊C3) | C3 | semidirect |
| 3. C32×C32⋊(C43⋊C3) | C3 | semidirect |
| 4. #23782883 | C3 | direct (N × H) |
| 5. C3×#16812508 | C3 | semidirect |
| 6. C32×3−1+2×C43 | C3 | semidirect |
| 8. C33×C43⋊C3 | C32 | semidirect |
| 12. C3×#11923958 | C32 | semidirect |
| 13. C3×#11923958 | C32 | semidirect |
| 22. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 23. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 25. #16812508 | C32 | semidirect |
| 30. C3×3−1+2×C43 | C32 | semidirect |
| 31. C3×3−1+2×C43 | C32 | semidirect |
| 39. C32×C43⋊C3 | C33 | semidirect |
| 43. #11923958 | C33 | semidirect |
| 63. 3−1+2×C43 | C33 | semidirect |
| 89. C32×3−1+2 | C43⋊C3 | semidirect |
| 99. C3×C43 | #6909 | semidirect |
| 114. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 115. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 129. C43 | C3×#6909 | semidirect |
| 151. 3−1+2 | C32×C43⋊C3 | semidirect |
| 191. C3 | #23782883 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| C32×C32⋊(C43⋊C3) | 3 |
| #23782883 | 3 |
| C3×#16812508 | 3 |
| C32×3−1+2×C43 | 3 |
| C3×#6909 | 43 |