Subgroups — C₃₇×C₁₃₆₉ #61797872

Order 50653.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇²	C₃₇	1	1	yes	maximal, characteristic
2	C₁₃₆₉	C₃₇	1	37	yes	maximal, direct product factor
3	C₃₇	C₁₃₆₉	1	37	yes	direct product factor
4	C₃₇	C₃₇²	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₁₃₆₉	C₃₇	direct (N × H)
3. C₃₇	C₁₃₆₉	direct (N × H)

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

subgroup	index
C₃₇²	37
C₁₃₆₉	37