Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×((C3⋊S4)⋊C3)⋊C4 |
| derived | C22⋊H(3,𝔽3) ⋊ C2×C3×C4 |
592 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13164262, #72222983, #72222984 |
| maximal normal subgroup of | C3×#13164262, #72222983, #72222984 |
Past the SmallGroups library coverage — no SmallGroups id.