D₃×SL(2,𝔽₃)⋊C₈ #11920559

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₃×S₄
commutator, hypocenter	C₃×SL(2,𝔽₃)	C₂×C₈
Fitting	C₃×C₄×Q₈	C₂×D₃
socle	C₂²×C₃	C₂×SL(2,ℤ/4)
prime radical	C₂×D₃×SL(2,𝔽₃)	C₄
cosocle	C₃×C₄×SL(2,𝔽₃)	C₂²
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₄

317 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 317 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 192

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154570);