Subgroups — C₄×C₉ #150

Order 36.

9 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄	C₃	1	1	yes	maximal, characteristic
3	C₉	C₄	1	1	yes	characteristic, direct product factor, Sylow
4	C₂×C₃	C₂×C₃	1	1	yes	characteristic
5	C₄	C₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	C₃×C₄	1	1	yes	characteristic
7	C₂	C₂×C₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, socle, prime radical, cosocle	C₂×C₃	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

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

N	H ≅ G/N	type
3. C₉	C₄	direct (N × H)
5. C₄	C₉	direct (N × H)

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

subgroup	index
C₂×C₉	2
C₃×C₄	3