Subgroups — #1454

Order 128.

89 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431	C₂	1	3	yes	maximal
2	#322	C₂	1	3	yes	maximal, complemented
3	C₈²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄²	C₂²	1	1	yes	characteristic
5	C₄⋊C₈	C₄	1	6	yes	—
6	C₂²⋊C₈	C₄	1	6	yes	—
7	C₄×C₈	C₂²	1	3	yes	—
8	C₄×C₈	C₂²	1	3	yes	—
9	C₂²×C₄	C₂×C₄	1	3	yes	—
10	C₂×C₈	C₂×C₄	1	6	yes	—
11	C₂×C₈	C₂×C₄	1	6	yes	—
12	C₄²	C₂×C₄	1	3	yes	—
13	C₄²	C₂³	1	1	yes	characteristic
14	C₂³	C₄²	1	1	yes	characteristic
15	C₂×C₄	—	2	6	no	—
16	C₂×C₄	C₄²	1	3	yes	—
17	C₂×C₄	C₂²×C₄	1	3	yes	—
18	C₈	—	2	6	no	—
19	C₈	—	2	6	no	—
20	C₂²	—	2	3	no	—
21	C₂²	C₂×C₄²	1	1	yes	characteristic
22	C₄	—	2	3	no	—
23	C₄	#131	1	6	yes	—
24	C₂	—	4	1	no	—
25	C₂	#405	1	3	yes	—

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

N	H ≅ G/N	type
2. #322	C₂	semidirect
3. C₈²	C₂	semidirect

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