Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
312 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×#16812505 | C3 | semidirect |
| 3. #23782728 | C3 | semidirect |
| 4. C3×C43×C27⋊C3 | C3 | semidirect |
| 17. #16812505 | C32 | semidirect |
| 22. C3×C27×C43 | C32 | semidirect |
| 62. C3×C27⋊C3 | C43⋊C3 | semidirect |
| 86. C3×C27 | C3×C43⋊C3 | semidirect |
| 87. C43 | #10624702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| C3×#16812505 | 3 |
| #23782728 | 3 |
| C3×C43×C27⋊C3 | 3 |
| #10624702 | 43 |