Subgroups — C₂²×C₂₇×C₁₇₃ #72196462

Order 18684.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₇×C₁₇₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₉×C₁₇₃	C₃	1	1	yes	maximal, characteristic
3	C₂₇×C₁₇₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₉×C₁₇₃	C₂×C₃	1	3	yes	—
5	C₂²×C₃×C₁₇₃	C₉	1	1	yes	characteristic
6	C₉×C₁₇₃	C₂²×C₃	1	1	yes	characteristic
7	C₂×C₃×C₁₇₃	C₂×C₉	1	3	yes	—
8	C₂²×C₁₇₃	C₂₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₇₃	C₂²×C₉	1	1	yes	characteristic
10	C₂×C₁₇₃	C₂×C₂₇	1	3	yes	direct product factor
11	C₁₇₃	C₂²×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₂₇	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₂₇	C₂×C₁₇₃	1	3	yes	direct product factor
14	C₂²×C₉	C₃×C₁₇₃	1	1	yes	characteristic
15	C₂₇	C₂²×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₉	C₂×C₃×C₁₇₃	1	3	yes	—
17	C₂²×C₃	C₉×C₁₇₃	1	1	yes	characteristic
18	C₉	C₂²×C₃×C₁₇₃	1	1	yes	characteristic
19	C₂×C₃	C₂×C₉×C₁₇₃	1	3	yes	—
20	C₂²	C₂₇×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₂²×C₉×C₁₇₃	1	1	yes	characteristic
22	C₂	C₂×C₂₇×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.