Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
500 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 500 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. C3×3−1+2×C43⋊C3 | C3 | semidirect |
| 2. C3×#16812511 | C3 | semidirect |
| 3. C3×#16812511 | C3 | semidirect |
| 4. C3×#16812510 | C3 | semidirect |
| 5. C3×#16812509 | C3 | semidirect |
| 6. #23782795 | C3 | semidirect |
| 8. C3×(C3×C43⋊C3)⋊C9 | C3 | semidirect |
| 9. C3×C43×#731 | C3 | semidirect |
| 52. #11923958 | H(3,𝔽3) | semidirect |
| 73. 3−1+2×C43 | H(3,𝔽3) | semidirect |
| 109. C3×C43⋊C3 | #731 | semidirect |
| 121. C3×#731 | C43⋊C3 | semidirect |
| 164. C43 | #10624745 | semidirect |
| 187. 3−1+2 | C32⋊(C43⋊C3) | 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 |
| C3×#16812511 | 3 |
| C3×#16812510 | 3 |
| C3×#16812509 | 3 |
| #23782795 | 3 |
| (C3×C43⋊C3)⋊H(3,𝔽3) | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| C3×C43×#731 | 3 |
| #10624745 | 43 |