Subgroups — #66636

Order 336.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₁	C₂	1	2	yes	maximal, complemented
3	C₂²⋊Dic₇	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₇	—	2	2	no	—
5	C₂²×C₃×C₇	C₄	1	2	yes	complemented
6	C₂²×C₃×C₇	C₂²	1	1	yes	characteristic
7	Dic₂₁	—	2	2	no	—
8	C₂³×C₇	D₃	1	1	yes	characteristic
9	C₂×Dic₇	—	3	2	no	—
10	#217	—	7	1	no	maximal, Hall
11	C₂×C₃×C₇	—	2	2	no	—
12	C₂×C₃×C₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₇	D₄	1	2	yes	—
14	C₂²×C₇	—	2	2	no	—
15	C₂²×C₇	Dic₃	1	2	yes	complemented
16	C₂²×C₇	C₂×D₃	1	1	yes	characteristic
17	Dic₇	—	6	2	no	—
18	C₂³×C₃	D₇	1	1	yes	characteristic
19	C₂×Dic₃	—	7	2	no	—
20	C₃×C₇	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
21	C₂²⋊C₄	—	21	1	no	Sylow
22	C₂×C₇	—	2	2	no	—
23	C₂×C₇	C₂×Dic₃	1	1	yes	characteristic
24	C₂×C₇	#67	1	2	yes	—
25	C₂²×C₃	—	2	2	no	—
26	C₂²×C₃	Dic₇	1	2	yes	complemented
27	C₂²×C₃	C₂×D₇	1	1	yes	characteristic
28	Dic₃	—	14	2	no	—
29	C₂³	D₂₁	1	1	yes	characteristic
30	C₂×C₄	—	21	2	no	—
31	C₇	#217	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃	—	2	2	no	—
33	C₂×C₃	C₂×Dic₇	1	1	yes	characteristic
34	C₂×C₃	C₂²⋊D₇	1	2	yes	—
35	C₂²	—	2	2	no	—
36	C₂²	Dic₂₁	1	2	yes	complemented
37	C₂²	C₂×D₂₁	1	1	yes	characteristic
38	C₄	—	42	2	no	—
39	C₃	C₂²⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	2	2	no	—
41	C₂	C₂×Dic₂₁	1	1	yes	characteristic
42	C₂	#4268	1	2	yes	—

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.