Subgroups — #1313

Order 128.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#346	C₂	1	1	yes	maximal, characteristic
2	#346	C₂	1	1	yes	maximal, characteristic
3	#322	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆	C₄	1	2	yes	—
5	C₂×C₁₆	C₄	1	2	yes	—
6	C₄×C₈	C₄	1	2	yes	—
7	C₄×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₈	—	2	2	no	—
9	C₂×C₈	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈	C₂×C₄	1	1	yes	characteristic
11	C₄²	C₂×C₄	1	1	yes	characteristic
12	C₁₆	—	2	2	no	—
13	C₁₆	C₈	1	4	yes	complemented
14	C₂×C₄	C₄²	1	1	yes	characteristic
15	C₂×C₄	M₁₆	1	2	yes	—
16	C₈	—	4	2	no	—
17	C₈	C₂×C₈	1	2	yes	—
18	C₈	M₁₆	1	2	yes	—
19	C₂²	#97	1	1	yes	characteristic
20	C₄	—	2	2	no	—
21	C₄	C₄×C₈	1	1	yes	characteristic
22	C₄	#97	1	1	yes	characteristic
23	C₂	#322	1	1	yes	characteristic
24	C₂	#347	1	2	yes	—

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

N	H ≅ G/N	type
13. C₁₆	C₈	semidirect

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

subgroup	index
#346	2
#322	2