Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
572 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 4. #23782724 | C3 | direct (N × H) |
| 9. C3×#11923958 | C9 | semidirect |
| 26. #11923958 | C3×C9 | semidirect |
| 78. C3×C43 | 3−1+2⋊C9 | semidirect |
| 100. C43 | C3×3−1+2⋊C9 | semidirect |
| 150. C3 | #23782724 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| #23782724 | 3 |
| C33×C9×C43 | 3 |
| C3×3−1+2⋊C9 | 43 |