Subgroups — M₆₄ #370

Order 64.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃₂	C₂	1	2	yes	maximal, complemented
3	C₂×C₈	C₄	1	1	yes	characteristic
4	C₁₆	C₄	1	1	yes	characteristic
5	C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₄	C₈	1	1	yes	characteristic
7	C₈	C₈	1	1	yes	characteristic
8	C₈	C₂×C₄	1	1	yes	characteristic
9	C₂²	C₁₆	1	1	yes	characteristic
10	C₄	C₁₆	1	1	yes	characteristic
11	C₄	C₂×C₈	1	1	yes	characteristic
12	C₂	—	2	1	no	—
13	C₂	C₂×C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₃₂	C₂	semidirect

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

subgroup	index
C₂×C₁₆	2
C₃₂	2