Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
894 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 86 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×(C22⋊C9)⋊C2 | 2 |
| C3×D4×C22⋊C9 | 2 |
| C3×#63694 | 2 |
| C3×C4⋊((C22⋊C9)⋊C2) | 2 |
| C3×C4×(C22⋊C9)⋊C2 | 2 |
| C3×D4×#67 | 3 |
| D4×(C22⋊C9)⋊C2 | 3 |
| C3×D4×D9 | 4 |