Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
684 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 162 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×(C3⋊D3)⋊C3 | 2 |
| C3×D4×H(3,𝔽3) | 2 |
| C3×#638⋊C3 | 2 |
| C3×C4⋊((C3⋊D3)⋊C3) | 2 |
| C3×C4×(C3⋊D3)⋊C3 | 2 |
| C3×D4×C3⋊D3 | 3 |
| C32×D3×D4 | 3 |
| D4×(C3⋊D3)⋊C3 | 3 |