Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
926 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 274 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×H(3,𝔽3)×C43⋊C3 | 3 |
| #23782805 | 3 |
| #23782804 | 3 |
| #23782803 | 3 |
| #23782802 | 3 |
| #23782801 | 3 |
| #23782800 | 3 |
| #23782799 | 3 |
| #23782797 | 3 |
| #23782796 | 3 |
| #23782795 | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| C43×C9⋊H(3,𝔽3) | 3 |
| #10624883 | 43 |