Subgroups — C₁₃×C₃⋊D₃ #6625

Order 234.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₃	—	3	4	no	maximal
3	C₃×C₁₃	D₃	1	4	yes	complemented
4	C₂×C₁₃	—	9	1	no	Hall
5	C₃⋊D₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
7	C₃²	C₂×C₁₃	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	3	4	no	—
9	C₃	D₃×C₁₃	1	4	yes	complemented
10	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₃

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.