Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23782804 | C3 | semidirect |
| 3. C3×#16812499 | C3 | semidirect |
| 4. #23782719 | C3 | semidirect |
| 5. #23782716 | C3 | semidirect |
| 6. C43×#6868 | C3 | semidirect |
| 30. C3×C9×C43 | 3−1+2 | semidirect |
| 50. #6868 | C43⋊C3 | semidirect |
| 67. C43 | #10624790 | semidirect |
| 81. C3×C9 | #11923956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812513 | 3 |
| #23782804 | 3 |
| C3×#16812499 | 3 |
| #23782719 | 3 |
| #23782716 | 3 |
| C43×#6868 | 3 |
| #10624790 | 43 |