Subgroups — #329

Order 64.

35 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#124	C₂	1	1	yes	maximal, characteristic
2	#97	C₂	1	2	yes	maximal, complemented
3	C₂×Q₈	C₄	1	1	yes	characteristic
4	C₂×D₄	C₄	1	1	yes	characteristic
5	C₂×C₈	—	2	2	no	—
6	C₂²⋊C₄	—	2	2	no	—
7	C₄²	C₂²	1	1	yes	characteristic
8	C₂³	—	2	1	no	—
9	Q₈	—	4	1	no	—
10	D₄	—	4	1	no	—
11	C₂×C₄	—	2	1	no	—
12	C₂×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄	D₄	1	2	yes	—
14	C₈	—	2	4	no	—
15	C₂²	—	4	1	no	—
16	C₂²	—	4	2	no	—
17	C₂²	C₂²⋊C₄	1	1	yes	characteristic
18	C₄	—	2	1	no	—
19	C₄	—	2	2	no	—
20	C₄	—	4	1	no	—
21	C₂	—	8	1	no	—
22	C₂	#100	1	1	yes	characteristic
23	C₂	#104	1	2	yes	—

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

N	H ≅ G/N	type
2. #97	C₂	semidirect

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

subgroup	index
#124	2
#97	2