Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C22×#63694⋊C3 |
7003 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 7003 conjugacy classes of subgroups — too many to draw. Only its 318 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213207, C22×#72220152, A4×#63694⋊C3, … |
| maximal normal subgroup of | A4×#63694⋊C3 |
| maximal quotient of | #72253040, C22×#72220152 |
Past the SmallGroups library coverage — no SmallGroups id.