Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
328 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 88 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. C9×C32⋊(C43⋊C3) | C3 | semidirect |
| 3. C3×C9×C43⋊C9 | C3 | semidirect |
| 4. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 5. #23782719 | C3 | semidirect |
| 6. #23782715 | C3 | semidirect |
| 7. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 12. #16812512 | C9 | direct (N × H) |
| 24. C32⋊(C43⋊C3) | C3×C9 | semidirect |
| 30. C3×C43⋊C9 | C3×C9 | semidirect |
| 35. H(3,𝔽3)×C43 | C3×C9 | semidirect |
| 55. C9×C43 | #732 | semidirect |
| 61. C9×H(3,𝔽3) | C43⋊C3 | semidirect |
| 87. C43 | C9×#732 | semidirect |
| 94. H(3,𝔽3) | C9×C43⋊C3 | semidirect |
| 123. C9 | #16812512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812512 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| C3×C9×C43⋊C9 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782719 | 3 |
| #23782715 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| C9×#732 | 43 |