Finite Group DatabasebetaFinite Group Databasebeta← C32×(C2×D3)⋊AGL(1,𝔽5) #72269739
Order 2160.
536 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|
| C2×C32×D3×D5 | 2 |
| C2×C32×ΓL(1,𝔽16) | 2 |
| C2×C33×AGL(1,𝔽5) | 2 |
| C32×C22⋊AGL(1,𝔽5) | 3 |
| C3×(C2×D3)⋊AGL(1,𝔽5) | 3 |
| C32×(C2×D3)⋊C4 | 5 |