Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 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×#11923958 | C3 | semidirect |
| 3. C3×C9×C43⋊C9 | C3 | semidirect |
| 4. #23782725 | C3 | semidirect |
| 6. #23782713 | C3 | semidirect |
| 11. #16812509 | C9 | direct (N × H) |
| 23. #11923958 | C3×C9 | semidirect |
| 30. C3×C43⋊C9 | C3×C9 | semidirect |
| 51. C9×C43 | #731 | semidirect |
| 83. C43 | C9×#731 | semidirect |
| 116. C9 | #16812509 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812509 | 3 |
| C9×#11923958 | 3 |
| C3×C9×C43⋊C9 | 3 |
| #23782725 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782713 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| C9×#731 | 43 |