Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
698 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 292 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. #23782848 | C3 | semidirect |
| 3. #23782844 | C3 | semidirect |
| 4. #23782828 | C3 | semidirect |
| 5. #23782816 | C3 | semidirect |
| 6. #23782810 | C3 | semidirect |
| 8. #23782782 | C3 | semidirect |
| 9. #23782782 | C3 | semidirect |
| 10. C3×C43×C9⋊C9 | C3 | semidirect |
| 48. C3×C9×C43 | 3−1+2 | semidirect |
| 77. C3×C9⋊C9 | C43⋊C3 | semidirect |
| 107. C43 | #10624887 | semidirect |
| 120. C3×C9 | #11923956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| #23782848 | 3 |
| #23782844 | 3 |
| #23782828 | 3 |
| #23782816 | 3 |
| #23782810 | 3 |
| #23782803 | 3 |
| #23782782 | 3 |
| C3×C43×C9⋊C9 | 3 |
| #10624887 | 43 |