Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
518 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 76 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×#16812515 | C3 | semidirect |
| 3. C3×#16812514 | C3 | semidirect |
| 5. C3×C43×#733 | C3 | semidirect |
| 46. C3×C43⋊C3 | #733 | semidirect |
| 54. C3×#733 | C43⋊C3 | semidirect |
| 73. C43 | #10624733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C43⋊C3 | 3 |
| C3×#16812515 | 3 |
| C3×#16812514 | 3 |
| #23782795 | 3 |
| C3×C43×#733 | 3 |
| #10624733 | 43 |