Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
316 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 67 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. C3×(C43⋊C9)⋊C9 | C3 | semidirect |
| 4. #23782725 | C3 | semidirect |
| 5. #23782725 | C3 | semidirect |
| 6. #23782725 | C3 | semidirect |
| 7. #23782722 | C3 | semidirect |
| 8. #23782722 | C3 | semidirect |
| 9. #23782722 | C3 | semidirect |
| 13. C43×#6895 | C3 | semidirect |
| 104. #6895 | C43⋊C3 | semidirect |
| 151. C43 | #10624780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| #23782822 | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| #23782725 | 3 |
| #23782722 | 3 |
| #23782719 | 3 |
| C43×#6895 | 3 |
| #10624780 | 43 |