Subgroups — D₃×C₂₃×C₁₆₉ #37552215

Order 23322.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₂₃×C₁₆₉	—	3	1	no	maximal, Hall
3	C₂₃×C₁₆₉	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₁₃×C₂₃	C₁₃	1	1	yes	maximal, characteristic
5	D₃×C₁₆₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₂₃	C₂×C₁₃	1	1	yes	characteristic
7	C₂×C₁₃×C₂₃	—	3	1	no	—
8	C₃×C₁₆₉	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₆₉	—	3	1	no	Hall
10	C₁₃×C₂₃	D₃×C₁₃	1	1	yes	characteristic
11	C₁₆₉	D₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
12	D₃×C₂₃	C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
13	D₃×C₁₃	C₁₃×C₂₃	1	1	yes	characteristic
14	C₃×C₂₃	C₂×C₁₆₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₂₃	—	3	1	no	Hall
16	C₃×C₁₃	C₂×C₁₃×C₂₃	1	1	yes	characteristic
17	C₂×C₁₃	—	3	1	no	—
18	C₂₃	D₃×C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₃	D₃×C₁₃×C₂₃	1	1	yes	characteristic
20	D₃	C₂₃×C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₂₃×C₁₆₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3	1	no	Sylow

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.