Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×AGL(2,𝔽3) |
| Fitting | C32×Q8 ⋊ GL(2,𝔽3) |
704 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
55 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×AGL(2,𝔽3), #41×AGL(2,𝔽3), SL(2,𝔽3)×AGL(2,𝔽3) |
| maximal normal subgroup of | SD16×AGL(2,𝔽3), #41×AGL(2,𝔽3), SL(2,𝔽3)×AGL(2,𝔽3) |
| maximal quotient of | C4⋊C4×AGL(2,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.