Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
650 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 70 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. C3×H(3,𝔽3)×C43⋊C3 | C3 | semidirect |
| 2. C3×#16812513 | C3 | semidirect |
| 3. C3×#16812512 | C3 | semidirect |
| 4. C3×#16812512 | C3 | semidirect |
| 5. (C3×C43⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 6. C3×(C3×C43⋊C3)⋊C9 | C3 | semidirect |
| 7. C3×C43×#732 | C3 | semidirect |
| 15. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 18. C32×C43⋊C9 | C32 | semidirect |
| 25. C3×H(3,𝔽3)×C43 | C32 | semidirect |
| 26. C32×C9×C43 | C32 | semidirect |
| 50. C32⋊(C43⋊C3) | H(3,𝔽3) | semidirect |
| 60. H(3,𝔽3)×C43 | H(3,𝔽3) | semidirect |
| 97. C3×C43⋊C3 | #732 | semidirect |
| 104. C3×#732 | C43⋊C3 | semidirect |
| 130. C3×H(3,𝔽3) | C3×C43⋊C3 | semidirect |
| 132. C32×C9 | C3×C43⋊C3 | semidirect |
| 139. C43 | #10624740 | semidirect |
| 169. H(3,𝔽3) | C32⋊(C43⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| C3×#16812513 | 3 |
| C3×#16812512 | 3 |
| (C3×C43⋊C3)⋊H(3,𝔽3) | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| C3×C43×#732 | 3 |
| #10624740 | 43 |