Subgroups — D₁₇₂ #66810

Order 344.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₃	C₂	1	2	yes	maximal, complemented
2	C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃	C₂²	1	1	yes	characteristic
4	D₄₃	—	2	2	no	—
5	C₄₃	D₄	1	1	yes	characteristic, complemented, Sylow
6	D₄	—	43	1	no	maximal, Sylow
7	C₂²	—	43	2	no	—
8	C₄	D₄₃	1	1	yes	characteristic, complemented
9	C₂	—	86	2	no	—
10	C₂	C₂×D₄₃	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.