Subgroups — C₉×C₁₆ #3659

Order 144.

15 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₆	C₃	1	1	yes	maximal, characteristic
3	C₄×C₉	C₄	1	1	yes	characteristic
4	C₃×C₈	C₂×C₃	1	1	yes	characteristic
5	C₂×C₉	C₈	1	1	yes	characteristic
6	C₁₆	C₉	1	1	yes	characteristic, direct product factor, Sylow
7	C₃×C₄	C₃×C₄	1	1	yes	characteristic
8	C₉	C₁₆	1	1	yes	characteristic, direct product factor, Sylow
9	C₈	C₂×C₉	1	1	yes	characteristic
10	C₂×C₃	C₃×C₈	1	1	yes	characteristic
11	C₄	C₄×C₉	1	1	yes	characteristic
12	C₃	C₃×C₁₆	1	1	yes	characteristic
13	C₂	C₈×C₉	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. C₁₆	C₉	direct (N × H)
8. C₉	C₁₆	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈×C₉	2
C₃×C₁₆	3