Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1088 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 292 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×#11923958 | C3 | semidirect |
| 3. #23782887 | C3 | direct (N × H) |
| 4. C3×#16812510 | C3 | semidirect |
| 5. C32×3−1+2×C43 | C3 | semidirect |
| 10. C3×#11923958 | C32 | semidirect |
| 11. C3×#11923958 | C32 | semidirect |
| 17. #16812510 | C32 | semidirect |
| 22. C3×3−1+2×C43 | C32 | semidirect |
| 23. C32×C9×C43 | C32 | semidirect |
| 30. #11923958 | C33 | semidirect |
| 46. C3×C9×C43 | C33 | semidirect |
| 64. C32×3−1+2 | C43⋊C3 | semidirect |
| 72. C3×C43 | #6910 | semidirect |
| 85. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 91. C32×C9 | C3×C43⋊C3 | semidirect |
| 93. C43 | C3×#6910 | semidirect |
| 116. C3×C9 | C32×C43⋊C3 | semidirect |
| 137. C3 | #23782887 | 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 |
| C32×C32⋊(C43⋊C3) | 3 |
| #23782887 | 3 |
| C3×#16812510 | 3 |
| C32×3−1+2×C43 | 3 |
| C3×#6910 | 43 |