Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23782858 | C3 | semidirect |
| 3. #23782857 | C3 | semidirect |
| 4. C3×#16812504 | C3 | semidirect |
| 5. #23782731 | C3 | semidirect |
| 6. #23782727 | C3 | semidirect |
| 7. #23782726 | C3 | semidirect |
| 8. #23782717 | C3 | semidirect |
| 9. C43×#6873 | C3 | semidirect |
| 73. #6873 | C43⋊C3 | semidirect |
| 104. C43 | #10624725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782874 | 3 |
| #23782858 | 3 |
| #23782857 | 3 |
| C3×#16812504 | 3 |
| #23782731 | 3 |
| #23782727 | 3 |
| #23782726 | 3 |
| #23782717 | 3 |
| C43×#6873 | 3 |
| #10624725 | 43 |