Subgroups — C₃²⋊(C₁₃⋊C₃) #66852

Order 351.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃⋊C₃	C₃	1	3	yes	maximal, complemented
3	C₃×C₁₃	—	3	1	no	—
4	C₃×C₁₃	C₃²	1	1	yes	characteristic
5	C₁₃⋊C₃	—	3	3	no	—
6	H(3,𝔽₃)	—	13	1	no	maximal, Sylow
7	C₁₃	H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
8	C₃²	—	13	3	no	—
9	C₃²	C₁₃⋊C₃	1	1	yes	characteristic, complemented
10	C₃	—	3	1	no	—
11	C₃	—	39	3	no	—
12	C₃	C₃×C₁₃⋊C₃	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.