Subgroups — C₂₇×C₁₂₀₁ #44569799

Order 32427.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₂₀₁	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₂₀₁	C₉	1	1	yes	characteristic
3	C₁₂₀₁	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
4	C₂₇	C₁₂₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₉	C₃×C₁₂₀₁	1	1	yes	characteristic
6	C₃	C₉×C₁₂₀₁	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. C₁₂₀₁	C₂₇	direct (N × H)
4. C₂₇	C₁₂₀₁	direct (N × H)

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

subgroup	index
C₉×C₁₂₀₁	3
C₂₇	1201