Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
855 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 855 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|
| C22×C3×AΣL(1,𝔽27) | 2 |
| C2×D3×AΣL(1,𝔽27) | 2 |
| C22×C33×D3 | 3 |
| C22×D3×3−1+2 | 3 |
| C22×D3×H(3,𝔽3) | 3 |
| C23×AΣL(1,𝔽27) | 3 |