Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
372 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 64 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. C32×#11923957 | C3 | semidirect |
| 3. #23782818 | C3 | semidirect |
| 4. H(3,𝔽3)×C43⋊C9 | C3 | semidirect |
| 5. #23782725 | C3 | semidirect |
| 6. #23782724 | C3 | semidirect |
| 7. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 8. #23782711 | C3 | semidirect |
| 9. C43×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 50. H(3,𝔽3)×C43 | 3−1+2 | semidirect |
| 78. C43⋊C9 | AΣL(1,𝔽27) | semidirect |
| 86. H(3,𝔽3)⋊C9 | C43⋊C3 | semidirect |
| 114. C43 | #10624794 | semidirect |
| 128. H(3,𝔽3) | #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×#16812506 | 3 |
| #23782818 | 3 |
| H(3,𝔽3)×C43⋊C9 | 3 |
| #23782725 | 3 |
| #23782724 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782711 | 3 |
| C43×H(3,𝔽3)⋊C9 | 3 |
| #10624794 | 43 |