Finite Group DatabasebetaFinite Group Databasebeta← C3×AΣL(1,𝔽27)×C31⋊C3 #36382877
Order 22599.
2672 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 2672 conjugacy classes of subgroups — too many to draw. Only its 292 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 |
|---|---|
| C34×C31⋊C3 | 3 |
| C3×3−1+2×C31⋊C3 | 3 |
| C3×H(3,𝔽3)×C31⋊C3 | 3 |
| C3×#14578895 | 3 |
| C3×#14578894 | 3 |
| C3×#14578893 | 3 |
| AΣL(1,𝔽27)×C31⋊C3 | 3 |
| C3×C31×AΣL(1,𝔽27) | 3 |
| C32×AΣL(1,𝔽27) | 31 |