Subgroups — #366

Order 64.

23 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	#107	C₂	1	2	yes	maximal
3	C₂×C₈	C₂²	1	1	yes	characteristic
4	C₄⋊C₄	—	2	2	no	—
5	C₁₆	C₄	1	2	yes	complemented
6	C₂×C₄	—	4	2	no	—
7	C₂×C₄	D₄	1	1	yes	characteristic
8	C₈	C₂×C₄	1	1	yes	characteristic
9	C₈	Q₈	1	1	yes	characteristic
10	C₂²	D₈	1	1	yes	characteristic
11	C₄	—	8	2	no	—
12	C₄	C₄⋊C₄	1	1	yes	characteristic
13	C₄	Q₁₆	1	1	yes	characteristic
14	C₂	#107	1	1	yes	characteristic
15	C₂	D₁₆	1	1	yes	characteristic
16	C₂	Q₃₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₁₆	C₄	semidirect

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

subgroup	index
C₂×C₁₆	2
#107	2