Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
132 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 37 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. C3×#16812505 | C3 | semidirect |
| 3. C32⋊(C43⋊C27) | C3 | semidirect |
| 4. C43×C32⋊C27 | C3 | semidirect |
| 50. C32⋊C27 | C43⋊C3 | semidirect |
| 67. C43 | #10624453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812505 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| C32⋊(C43⋊C27) | 3 |
| C43×C32⋊C27 | 3 |
| #10624453 | 43 |