Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23782783 | C3 | semidirect |
| 3. C3×#16812500 | C3 | semidirect |
| 4. #23782719 | C3 | semidirect |
| 5. #23782716 | C3 | semidirect |
| 6. C43×#6868 | C3 | semidirect |
| 11. #16812513 | C9 | semidirect |
| 19. C32⋊(C43⋊C3) | C3×C9 | semidirect |
| 30. C3×C9×C43 | C3×C9 | semidirect |
| 50. #6868 | C43⋊C3 | semidirect |
| 67. C43 | #10624722 | semidirect |
| 81. 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 |
|---|---|
| C3×#16812513 | 3 |
| #23782783 | 3 |
| C3×#16812500 | 3 |
| #23782719 | 3 |
| #23782716 | 3 |
| C43×#6868 | 3 |
| #10624722 | 43 |