Finite Group DatabasebetaFinite Group Databasebeta| order | 16224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×#14523146 |
| Fitting | D4×C132 ⋊ C3×C4 |
| Hall | D4×#10621729 ⋊ C3 |
| Hall | #92788 ⋊ C4×D4 |
| Sylow | C132 ⋊ C3×C4×D4 |
700 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#72210302, #72259573, #72259776 |
| maximal normal subgroup of | D4×#72210302, #72259573, #72259776 |
Past the SmallGroups library coverage — no SmallGroups id.