Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
470 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16812500 | C3 | semidirect |
| 3. C3×(C43⋊C9)⋊C9 | C3 | semidirect |
| 5. C43⋊#6855 | C3 | semidirect |
| 6. C43⋊#6855 | C3 | semidirect |
| 7. C43⋊#6855 | C3 | semidirect |
| 8. C43⋊#6855 | C3 | semidirect |
| 51. C3×C43⋊C9 | 3−1+2 | semidirect |
| 67. C3×C9×C43 | 3−1+2 | semidirect |
| 131. C43 | #10624565 | semidirect |
| 172. C3×C9 | #11923958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| C3×#16812500 | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C43⋊#6855 | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624565 | 43 |