Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
716 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 274 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. #23782827 | C3 | semidirect |
| 3. #23782826 | C3 | semidirect |
| 4. #23782822 | C3 | semidirect |
| 5. #23782820 | C3 | semidirect |
| 7. #23782779 | C3 | semidirect |
| 8. C43×#6895 | C3 | semidirect |
| 16. #16812499 | C32 | semidirect |
| 17. (C43⋊C9)⋊C9 | C32 | semidirect |
| 18. (C43⋊C9)⋊C9 | C32 | semidirect |
| 19. (C43⋊C9)⋊C9 | C32 | semidirect |
| 22. C9×C43⋊C9 | C32 | semidirect |
| 24. C43×C9⋊C9 | C32 | semidirect |
| 33. C3×C43⋊C9 | 3−1+2 | semidirect |
| 61. #6895 | C43⋊C3 | semidirect |
| 80. C9⋊C9 | C3×C43⋊C3 | semidirect |
| 85. C43 | #10624885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923957 | 3 |
| #23782827 | 3 |
| #23782826 | 3 |
| #23782822 | 3 |
| #23782820 | 3 |
| #23782796 | 3 |
| #23782779 | 3 |
| C43×#6895 | 3 |
| #10624885 | 43 |