Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1118 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 268 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.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782923 | 3 |
| C43⋊H(5,𝔽3) | 3 |
| C32×C32⋊(C43⋊C3) | 3 |
| #23782883 | 3 |
| #23782881 | 3 |
| #23782880 | 3 |
| #23782879 | 3 |
| C3×#16812507 | 3 |
| AΣL(1,𝔽27)×C43⋊C3 | 3 |
| C3×C43×AΣL(1,𝔽27) | 3 |
| #10624930 | 43 |