Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q16×Dic134 |
| Sylow | C67 ⋊ Q8×Q16 |
336 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
959 conjugacy classes — view the full character table.
| maximal subgroup of | #30769520, #30769524, #30769548, … |
| maximal normal subgroup of | #30769520, #30769524, #30769548, … |
| maximal quotient of | #103×Dic134, Q16×Dic67⋊C4, Q16×C4⋊Dic67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17394);