Subgroups — C₁₆×H(3,𝔽₃) #88388

Order 432.

55 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₆	C₃	1	4	yes	maximal, complemented
3	C₄×H(3,𝔽₃)	C₄	1	1	yes	characteristic
4	C₃²×C₈	C₂×C₃	1	4	yes	—
5	C₂×H(3,𝔽₃)	C₈	1	1	yes	characteristic
6	C₃×C₁₆	—	3	4	no	—
7	C₃×C₁₆	C₃²	1	1	yes	characteristic
8	C₃²×C₄	C₃×C₄	1	4	yes	—
9	H(3,𝔽₃)	C₁₆	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₈	—	3	4	no	—
11	C₃×C₈	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃²	C₃×C₈	1	4	yes	—
13	C₁₆	H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
14	C₃×C₄	—	3	4	no	—
15	C₃×C₄	C₃²×C₄	1	1	yes	characteristic
16	C₃²	C₃×C₁₆	1	4	yes	complemented
17	C₈	C₂×H(3,𝔽₃)	1	1	yes	characteristic
18	C₂×C₃	—	3	4	no	—
19	C₂×C₃	C₃²×C₈	1	1	yes	characteristic
20	C₄	C₄×H(3,𝔽₃)	1	1	yes	characteristic
21	C₃	—	3	4	no	—
22	C₃	C₃²×C₁₆	1	1	yes	characteristic
23	C₂	C₈×H(3,𝔽₃)	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.

subgroup	index
C₈×H(3,𝔽₃)	2
C₃²×C₁₆	3