Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×D3×AGL(1,ℤ/9) #14519300
Order 1944.
926 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C3×C9 | C23×C32 |
| Frattini | C3 | C2×C32×D32 |
| Fitting | C2×C32×3−1+2 | C22 |
| socle | C2×C33 | C2×C3×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C2×C3 | |
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 |
|---|---|
| C2×C3×C3⋊AGL(1,ℤ/9) | 2 |
| C2×C3×D3×3−1+2 | 2 |
| C2×C32×AGL(1,ℤ/9) | 2 |
| C3×D3×AGL(1,ℤ/9) | 2 |
| C2×C32×D32 | 3 |
| C22×C3×AGL(1,ℤ/9) | 3 |
| C2×D3×AGL(1,ℤ/9) | 3 |
| C2×C3×D3×D9 | 3 |