Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
5964 conjugacy classes of subgroups; only the 1163 normal subgroups are shown.
This group has 5964 conjugacy classes of subgroups — too many to draw. Only its 1163 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×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C22×C4×C3⋊(C3⋊D3) | 2 |
| C2×C33×C4⋊C4 | 2 |
| C2×#88859 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #11723934 | 2 |
| C2×#64102 | 3 |