Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1196 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1196 conjugacy classes of subgroups — too many to draw. Only its 271 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 |
|---|---|
| C3×3−1+2×C43⋊C3 | 3 |
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| #23782883 | 3 |
| #23782882 | 3 |
| #23782881 | 3 |
| #23782880 | 3 |
| #23782879 | 3 |
| AΣL(1,𝔽27)×C43⋊C3 | 3 |
| C43×#6909 | 3 |
| C3×#6909 | 43 |