Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
836 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 836 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 |
|---|---|---|
| 2. #23782822 | C3 | semidirect |
| 3. #23782821 | C3 | semidirect |
| 4. #23782820 | C3 | semidirect |
| 5. #23782819 | C3 | semidirect |
| 6. C9⋊C9×C43⋊C3 | C3 | semidirect |
| 8. C43×#6895 | C3 | semidirect |
| 16. #16812500 | C32 | semidirect |
| 17. #16812499 | C32 | semidirect |
| 18. (C43⋊C9)⋊C9 | C32 | semidirect |
| 19. (C43⋊C9)⋊C9 | C32 | semidirect |
| 20. (C43⋊C9)⋊C9 | C32 | semidirect |
| 24. C43×C9⋊C9 | C32 | semidirect |
| 61. #6895 | C43⋊C3 | direct (N × H) |
| 68. C43⋊C3 | #6895 | direct (N × H) |
| 82. C9⋊C9 | C3×C43⋊C3 | semidirect |
| 86. C43 | C3×#6895 | 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 |
| #23782822 | 3 |
| #23782821 | 3 |
| #23782820 | 3 |
| #23782819 | 3 |
| C9⋊C9×C43⋊C3 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| C43×#6895 | 3 |
| C3×#6895 | 43 |