Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
506 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 142 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×(C43⋊C9)⋊C9 | C3 | semidirect |
| 5. C3×C9×C43⋊C9 | C3 | semidirect |
| 6. C43⋊#6855 | C3 | semidirect |
| 7. C43⋊#6855 | C3 | semidirect |
| 8. C43⋊#6855 | C3 | semidirect |
| 9. C43×#6855 | C3 | semidirect |
| 14. C3×#11923957 | C9 | semidirect |
| 55. C3×C43⋊C9 | 3−1+2 | semidirect |
| 67. C3×C9×C43 | 3−1+2 | semidirect |
| 94. C43⋊C9 | C32⋊C9 | semidirect |
| 103. #6855 | C43⋊C3 | semidirect |
| 131. C43 | #10624560 | semidirect |
| 172. C3×C9 | #11923957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923957 | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| C3×C9×C43⋊C9 | 3 |
| C43⋊#6855 | 3 |
| C43×#6855 | 3 |
| #10624560 | 43 |