Finite Group DatabasebetaFinite Group Databasebeta← C3×H(3,𝔽3)×AGL(1,ℤ/9) #72243813
Order 4374.
6028 conjugacy classes of subgroups; only the 734 normal subgroups are shown.
This group has 6028 conjugacy classes of subgroups — too many to draw. Only its 734 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)×3−1+2 | 2 |
| C33×AGL(1,ℤ/9) | 3 |
| C32×D3×H(3,𝔽3) | 3 |
| H(3,𝔽3)×AGL(1,ℤ/9) | 3 |
| C3×D9⋊H(3,𝔽3) | 3 |
| C3×D9×H(3,𝔽3) | 3 |