Subgroups — C₇×#216 #66619

Order 336.

36 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
2	C₇×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₇×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₇×Q₁₆	—	3	1	no	maximal, Hall
5	C₃×C₄×C₇	—	2	1	no	—
6	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
7	C₇×Dic₃	—	2	1	no	—
8	C₇×Q₈	—	3	1	no	—
9	C₇×Q₈	D₃	1	1	yes	characteristic
10	C₇×C₈	—	3	1	no	—
11	#216	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₇	D₄	1	1	yes	characteristic
13	C₄×C₇	—	2	1	no	—
14	C₄×C₇	—	6	1	no	—
15	C₄×C₇	C₂×D₃	1	1	yes	characteristic
16	C₃×Q₈	C₂×C₇	1	1	yes	characteristic
17	Dic₆	C₂×C₇	1	1	yes	characteristic
18	C₃⋊C₈	C₂×C₇	1	1	yes	characteristic
19	C₃×C₇	Q₁₆	1	1	yes	characteristic, complemented, Hall
20	Q₁₆	—	3	1	no	Sylow
21	C₂×C₇	#67	1	1	yes	characteristic
22	C₃×C₄	—	2	1	no	—
23	C₃×C₄	C₂²×C₇	1	1	yes	characteristic
24	Dic₃	—	2	1	no	—
25	Q₈	—	3	1	no	—
26	Q₈	D₃×C₇	1	1	yes	characteristic
27	C₈	—	3	1	no	—
28	C₇	#216	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃	C₇×D₄	1	1	yes	characteristic
30	C₄	—	2	1	no	—
31	C₄	—	6	1	no	—
32	C₄	C₂×D₃×C₇	1	1	yes	characteristic
33	C₃	C₇×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₇×#67	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.