Subgroups — #1423

Order 128.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂	C₂	1	1	yes	maximal, characteristic
2	#366	C₂	1	2	yes	maximal
3	C₂×C₁₆	C₂²	1	1	yes	characteristic
4	#107	—	2	2	no	—
5	C₃₂	C₄	1	2	yes	complemented
6	C₂×C₈	D₄	1	1	yes	characteristic
7	C₄⋊C₄	—	4	2	no	—
8	C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₁₆	Q₈	1	1	yes	characteristic
10	C₂×C₄	—	8	2	no	—
11	C₂×C₄	D₈	1	1	yes	characteristic
12	C₈	C₄⋊C₄	1	1	yes	characteristic
13	C₈	Q₁₆	1	1	yes	characteristic
14	C₂²	D₁₆	1	1	yes	characteristic
15	C₄	—	16	2	no	—
16	C₄	#107	1	1	yes	characteristic
17	C₄	Q₃₂	1	1	yes	characteristic
18	C₂	#366	1	1	yes	characteristic
19	C₂	D₃₂	1	1	yes	characteristic
20	C₂	Q₆₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₃₂	C₄	semidirect

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

subgroup	index
C₂×C₃₂	2
#366	2