Subgroups — C₇×SL(2,ℤ/4) #66648

Order 336.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×A₄	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂²⋊C₄	—	3	1	no	maximal, Hall
3	C₇×A₄	C₄	1	1	yes	characteristic, complemented
4	C₇×Dic₃	—	4	1	no	maximal
5	C₂³×C₇	D₃	1	1	yes	characteristic
6	C₂×C₄×C₇	—	3	1	no	—
7	C₂×C₄×C₇	—	3	1	no	—
8	SL(2,ℤ/4)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇	—	4	1	no	—
10	C₂²×C₇	—	3	1	no	—
11	C₂²×C₇	—	3	1	no	—
12	C₂²×C₇	Dic₃	1	1	yes	characteristic, complemented
13	C₄×C₇	—	6	1	no	—
14	C₄×C₇	—	6	1	no	—
15	C₂×A₄	C₂×C₇	1	1	yes	characteristic
16	C₃×C₇	—	4	1	no	Hall
17	C₂²⋊C₄	—	3	1	no	Sylow
18	C₂×C₇	—	3	1	no	—
19	C₂×C₇	—	3	1	no	—
20	C₂×C₇	S₄	1	1	yes	characteristic
21	A₄	C₄×C₇	1	1	yes	characteristic, complemented
22	Dic₃	—	4	1	no	—
23	C₂³	D₃×C₇	1	1	yes	characteristic
24	C₂×C₄	—	3	1	no	—
25	C₂×C₄	—	3	1	no	—
26	C₇	SL(2,ℤ/4)	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	4	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	C₇×Dic₃	1	1	yes	characteristic, complemented
31	C₄	—	6	1	no	—
32	C₄	—	6	1	no	—
33	C₃	—	4	1	no	Sylow
34	C₂	—	3	1	no	—
35	C₂	—	3	1	no	—
36	C₂	C₇×S₄	1	1	yes	characteristic

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

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