Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊AGL(2,𝔽3) |
| Fitting | C2×C32×C4 ⋊ GL(2,𝔽3) |
1088 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×AGL(2,𝔽3), #72220196, #72220206, … |
| maximal normal subgroup of | C2×D4×AGL(2,𝔽3), #72220196, #72220206, … |
| maximal quotient of | #72220196, #72220424, #72220447, … |
Past the SmallGroups library coverage — no SmallGroups id.