Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
368 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23782816 | C3 | semidirect |
| 3. #23782802 | C3 | semidirect |
| 4. C9×#11923958 | C3 | semidirect |
| 5. #23782724 | C3 | semidirect |
| 6. #23782724 | C3 | semidirect |
| 7. #23782721 | C3 | semidirect |
| 8. #23782712 | C3 | semidirect |
| 9. C32×3−1+2×C43 | C3 | semidirect |
| 33. #11923958 | 3−1+2 | semidirect |
| 71. C9×C43 | AΣL(1,𝔽27) | semidirect |
| 77. C32×3−1+2 | C43⋊C3 | semidirect |
| 112. C43 | #10624798 | semidirect |
| 159. C9 | #16812507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812507 | 3 |
| #23782816 | 3 |
| #23782802 | 3 |
| C9×#11923958 | 3 |
| #23782724 | 3 |
| #23782721 | 3 |
| #23782712 | 3 |
| C32×3−1+2×C43 | 3 |
| #10624798 | 43 |