Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
980 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 271 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 |
|---|---|---|
| 3. #23782896 | C3 | semidirect |
| 4. #23782895 | C3 | semidirect |
| 5. #23782894 | C3 | semidirect |
| 6. #23782893 | C3 | semidirect |
| 7. #733×C43⋊C3 | C3 | semidirect |
| 8. C43×#6912 | C3 | semidirect |
| 30. #16812515 | C32 | semidirect |
| 31. #16812514 | C32 | semidirect |
| 34. C43×#733 | C32 | semidirect |
| 94. #6912 | C43⋊C3 | direct (N × H) |
| 103. C43⋊C3 | #6912 | direct (N × H) |
| 129. #733 | C3×C43⋊C3 | semidirect |
| 130. C43 | C3×#6912 | 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 |
| #23782896 | 3 |
| #23782895 | 3 |
| #23782894 | 3 |
| #23782893 | 3 |
| #733×C43⋊C3 | 3 |
| C43×#6912 | 3 |
| C3×#6912 | 43 |