Subgroups — C₂²×C₃³×C₁₇₃ #72196464

Order 18684.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₁₇₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃²×C₁₇₃	C₃	1	13	yes	maximal, direct product factor
3	C₃³×C₁₇₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃²×C₁₇₃	C₂×C₃	1	39	yes	direct product factor
5	C₂²×C₃×C₁₇₃	C₃²	1	13	yes	direct product factor
6	C₃²×C₁₇₃	C₂²×C₃	1	13	yes	direct product factor
7	C₂×C₃×C₁₇₃	C₂×C₃²	1	39	yes	direct product factor
8	C₂²×C₁₇₃	C₃³	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₇₃	C₂²×C₃²	1	13	yes	direct product factor
10	C₂×C₁₇₃	C₂×C₃³	1	3	yes	direct product factor
11	C₁₇₃	C₂²×C₃³	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₃³	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃³	C₂×C₁₇₃	1	3	yes	direct product factor
14	C₂²×C₃²	C₃×C₁₇₃	1	13	yes	direct product factor
15	C₃³	C₂²×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃²	C₂×C₃×C₁₇₃	1	39	yes	direct product factor
17	C₂²×C₃	C₃²×C₁₇₃	1	13	yes	direct product factor
18	C₃²	C₂²×C₃×C₁₇₃	1	13	yes	direct product factor
19	C₂×C₃	C₂×C₃²×C₁₇₃	1	39	yes	direct product factor
20	C₂²	C₃³×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₂²×C₃²×C₁₇₃	1	13	yes	direct product factor
22	C₂	C₂×C₃³×C₁₇₃	1	3	yes	direct product factor

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.