Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1052 conjugacy classes of subgroups; only the 490 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 490 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. #23782779 | C3 | direct (N × H) |
| 3. C3×(C43⋊C9)⋊C9 | C3 | semidirect |
| 5. C3×C9×C43⋊C9 | C3 | semidirect |
| 7. C32×C43⋊C9 | C9 | semidirect |
| 12. (C43⋊C9)⋊C9 | C32 | semidirect |
| 14. C9×C43⋊C9 | C32 | semidirect |
| 21. C3×C43⋊C9 | C3×C9 | semidirect |
| 52. C3×C43 | #6887 | semidirect |
| 67. C43 | C3×#6887 | semidirect |
| 95. C3 | #23782779 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C43⋊C9 | 3 |
| #23782779 | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C3×C9×C43⋊C9 | 3 |
| C3×C43×C32⋊C9 | 3 |
| C3×#6887 | 43 |