Finite Group DatabasebetaFinite Group Databasebeta| order | 16224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#72229062 |
| Fitting | C23×C132 ⋊ C3×C4 |
| Hall | C2×#72229039 ⋊ C3 |
| Hall | #92788 ⋊ C2×C22⋊C4 |
| Sylow | C132 ⋊ C2×C3×C22⋊C4 |
2112 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 2112 conjugacy classes of subgroups — too many to draw. Only its 196 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1352 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×#14523144, #72259753 |
| maximal normal subgroup of | C2×D4×#14523144, #72259753 |
Past the SmallGroups library coverage — no SmallGroups id.