Subgroups — C₇×C₃⋊C₃₂ #10620421

Order 672.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₇×C₃₂	—	3	1	no	maximal, Hall
3	C₃×C₇×C₈	C₄	1	1	yes	characteristic
4	C₇×C₁₆	D₃	1	1	yes	characteristic
5	C₃⋊C₃₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₄×C₇	C₈	1	1	yes	characteristic
7	C₇×C₈	Dic₃	1	1	yes	characteristic
8	C₃×C₁₆	C₂×C₇	1	1	yes	characteristic
9	C₂×C₃×C₇	C₁₆	1	1	yes	characteristic
10	C₃₂	—	3	1	no	Sylow
11	C₄×C₇	C₃⋊C₈	1	1	yes	characteristic
12	C₃×C₈	C₄×C₇	1	1	yes	characteristic
13	C₃×C₇	C₃₂	1	1	yes	characteristic, complemented, Hall
14	C₁₆	D₃×C₇	1	1	yes	characteristic
15	C₂×C₇	C₃⋊C₁₆	1	1	yes	characteristic
16	C₃×C₄	C₇×C₈	1	1	yes	characteristic
17	C₈	C₇×Dic₃	1	1	yes	characteristic
18	C₇	C₃⋊C₃₂	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₇×C₁₆	1	1	yes	characteristic
20	C₄	C₇×C₃⋊C₈	1	1	yes	characteristic
21	C₃	C₇×C₃₂	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₇×C₃⋊C₁₆	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.