Subgroups — C₂²×C₄×C₉ #3704

Order 144.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₉	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×C₄	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₉	C₄	1	4	yes	direct product factor
5	C₂²×C₉	C₂²	1	3	yes	—
6	C₄×C₉	C₂²	1	4	yes	direct product factor
7	C₂³×C₃	C₂×C₃	1	1	yes	characteristic
8	C₂×C₃×C₄	C₂×C₃	1	6	yes	—
9	C₂×C₉	C₂×C₄	1	6	yes	direct product factor
10	C₂×C₉	C₂³	1	1	yes	characteristic
11	C₂²×C₄	C₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₃	C₃×C₄	1	4	yes	—
13	C₂²×C₃	C₂²×C₃	1	3	yes	—
14	C₃×C₄	C₂²×C₃	1	4	yes	—
15	C₉	C₂²×C₄	1	1	yes	characteristic, direct product factor, Sylow
16	C₂³	C₂×C₉	1	1	yes	characteristic
17	C₂×C₄	C₂×C₉	1	6	yes	direct product factor
18	C₂×C₃	C₂×C₃×C₄	1	6	yes	—
19	C₂×C₃	C₂³×C₃	1	1	yes	characteristic
20	C₂²	C₄×C₉	1	4	yes	direct product factor
21	C₂²	C₂²×C₉	1	3	yes	—
22	C₄	C₂²×C₉	1	4	yes	direct product factor
23	C₃	C₂²×C₃×C₄	1	1	yes	characteristic
24	C₂	C₂×C₄×C₉	1	6	yes	direct product factor
25	C₂	C₂³×C₉	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.