Finite Group DatabasebetaFinite Group Databasebeta| order | 3136 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#13096364 |
| Fitting | C2×C72×D4 ⋊ C22 |
| Sylow | C72 ⋊ C22×D8 |
1030 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
202 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72214529, D3×#13096364 |
| maximal normal subgroup of | C2×#72214529 |
| maximal quotient of | D3×#13096364 |
Past the SmallGroups library coverage — no SmallGroups id.