Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
644 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 262 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 |
|---|---|---|
| 1. #23782834 | C3 | semidirect |
| 2. #23782829 | C3 | semidirect |
| 3. #23782818 | C3 | semidirect |
| 4. #23782817 | C3 | semidirect |
| 5. #23782812 | C3 | semidirect |
| 7. #23782792 | C3 | semidirect |
| 8. 3−1+2×C43⋊C9 | C3 | semidirect |
| 15. #16812500 | C32 | semidirect |
| 16. #16812499 | C32 | semidirect |
| 17. (C43⋊C9)⋊C9 | C32 | semidirect |
| 18. (C43⋊C9)⋊C9 | C32 | semidirect |
| 19. (C43⋊C9)⋊C9 | C32 | semidirect |
| 32. C9×C43⋊C9 | C32 | semidirect |
| 128. C43 | #10624906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782834 | 3 |
| #23782829 | 3 |
| #23782818 | 3 |
| #23782817 | 3 |
| #23782812 | 3 |
| #23782798 | 3 |
| #23782792 | 3 |
| 3−1+2×C43⋊C9 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C43×#6891 | 3 |
| #10624906 | 43 |