Subgroups — C₃³×C₄×C₁₈₁ #72197213

Order 19548.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₁₈₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×C₁₈₁	C₃	1	13	yes	maximal, direct product factor
3	C₃³×C₁₈₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃²×C₁₈₁	C₂×C₃	1	13	yes	—
5	C₃×C₄×C₁₈₁	C₃²	1	13	yes	direct product factor
6	C₃²×C₁₈₁	C₃×C₄	1	13	yes	direct product factor
7	C₂×C₃×C₁₈₁	C₂×C₃²	1	13	yes	—
8	C₄×C₁₈₁	C₃³	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₈₁	C₃²×C₄	1	13	yes	direct product factor
10	C₂×C₁₈₁	C₂×C₃³	1	1	yes	characteristic
11	C₁₈₁	C₃³×C₄	1	1	yes	characteristic, direct product factor, Sylow
12	C₃³×C₄	C₁₈₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃³	C₂×C₁₈₁	1	1	yes	characteristic
14	C₃²×C₄	C₃×C₁₈₁	1	13	yes	direct product factor
15	C₃³	C₄×C₁₈₁	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃²	C₂×C₃×C₁₈₁	1	13	yes	—
17	C₃×C₄	C₃²×C₁₈₁	1	13	yes	direct product factor
18	C₃²	C₃×C₄×C₁₈₁	1	13	yes	direct product factor
19	C₂×C₃	C₂×C₃²×C₁₈₁	1	13	yes	—
20	C₄	C₃³×C₁₈₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₃²×C₄×C₁₈₁	1	13	yes	direct product factor
22	C₂	C₂×C₃³×C₁₈₁	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.