Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
416 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 2. C3×#16812505 | C3 | semidirect |
| 3. #23782717 | C3 | direct (N × H) |
| 4. C3×C43×C27⋊C3 | C3 | semidirect |
| 16. #16812505 | C32 | semidirect |
| 20. C43×C27⋊C3 | C32 | semidirect |
| 64. C3×C27⋊C3 | C43⋊C3 | semidirect |
| 68. C3×C43 | #6869 | semidirect |
| 85. C27⋊C3 | C3×C43⋊C3 | semidirect |
| 88. C43 | C3×#6869 | semidirect |
| 131. C3 | #23782717 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C43⋊C3 | 3 |
| C3×#16812505 | 3 |
| #23782717 | 3 |
| C3×C43×C27⋊C3 | 3 |
| C3×#6869 | 43 |