Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
476 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. #23782716 | C3 | semidirect |
| 4. #23782715 | C3 | semidirect |
| 5. C43×#6868 | C3 | semidirect |
| 12. C3×C9×C43⋊C3 | C9 | semidirect |
| 26. C3×C43⋊C9 | C3×C9 | semidirect |
| 34. C3×C9×C43 | C3×C9 | semidirect |
| 57. #6868 | C43⋊C3 | direct (N × H) |
| 64. C43⋊C3 | #6868 | direct (N × H) |
| 76. C43 | C3×#6868 | semidirect |
| 94. C3×C9 | C9×C43⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C43⋊C3 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| #23782716 | 3 |
| #23782715 | 3 |
| C43×#6868 | 3 |
| C3×#6868 | 43 |