Subgroups — C₃×#1161 #66712

Order 336.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₈	C₂	1	3	yes	maximal, complemented
3	C₃×C₄×D₇	C₂	1	3	yes	maximal, complemented
4	#1161	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×D₇	C₂²	1	3	yes	—
6	C₃×C₄×C₇	C₂²	1	3	yes	—
7	C₃×Dic₇	C₂²	1	1	yes	characteristic
8	C₇×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
9	D₂₈	C₂×C₃	1	3	yes	complemented
10	C₄×D₇	C₂×C₃	1	3	yes	complemented
11	C₃×#41	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	C₂³	1	1	yes	characteristic
13	C₃×D₇	—	2	3	no	—
14	C₂×D₇	C₂²×C₃	1	3	yes	—
15	C₄×C₇	C₂²×C₃	1	3	yes	—
16	Dic₇	C₂²×C₃	1	1	yes	characteristic
17	C₃×Q₈	D₇	1	1	yes	characteristic, complemented
18	C₃×D₄	—	7	3	no	—
19	C₂×C₃×C₄	—	7	3	no	—
20	C₃×C₇	#41	1	1	yes	characteristic, complemented, Hall
21	#41	—	7	1	no	Sylow
22	C₂×C₇	C₂³×C₃	1	1	yes	characteristic
23	D₇	—	2	3	no	—
24	C₂²×C₃	—	7	3	no	—
25	C₃×C₄	—	7	1	no	—
26	C₃×C₄	C₂×D₇	1	3	yes	—
27	Q₈	C₃×D₇	1	1	yes	characteristic, complemented
28	D₄	—	7	3	no	—
29	C₂×C₄	—	7	3	no	—
30	C₇	C₃×#41	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	14	3	no	—
32	C₂×C₃	C₂²×D₇	1	1	yes	characteristic
33	C₂²	—	7	3	no	—
34	C₄	—	7	1	no	—
35	C₄	C₂×C₃×D₇	1	3	yes	—
36	C₃	#1161	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	14	3	no	—
38	C₂	C₂²×C₃×D₇	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.