Subgroups — H(3,ℤ/4) #337

Order 64.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆	C₂	1	1	yes	maximal, characteristic
2	#117	C₂	1	2	yes	maximal
3	C₂²×C₄	C₂²	1	1	yes	characteristic
4	M₁₆	—	2	2	no	—
5	C₂×C₈	C₄	1	2	yes	complemented
6	C₄⋊C₄	—	2	2	no	—
7	C₂²⋊C₄	—	2	2	no	—
8	C₄²	C₄	1	4	yes	complemented
9	C₂³	D₄	1	1	yes	characteristic
10	C₂×C₄	—	2	4	no	—
11	C₂×C₄	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄	C₂×C₄	1	2	yes	—
13	C₂×C₄	D₄	1	2	yes	—
14	C₂×C₄	Q₈	1	1	yes	characteristic
15	C₈	—	2	2	no	—
16	C₂²	—	4	1	no	—
17	C₂²	C₂²⋊C₄	1	2	yes	—
18	C₂²	C₄⋊C₄	1	1	yes	characteristic
19	C₄	—	4	4	no	—
20	C₄	C₄²	1	1	yes	characteristic
21	C₄	C₂²⋊C₄	1	1	yes	characteristic
22	C₄	C₄⋊C₄	1	2	yes	—
23	C₂	—	2	2	no	—
24	C₂	—	2	1	no	—
25	C₂	#95	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₂×C₈	C₄	semidirect
8. C₄²	C₄	semidirect

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

subgroup	index
C₂×M₁₆	2
#117	2