Subgroups — C₃³×C₄² #88865

Order 432.

420 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄	C₂	1	3	yes	maximal
2	C₃²×C₄²	C₃	1	13	yes	maximal, direct product factor
3	C₂²×C₃³	C₂²	1	1	yes	characteristic
4	C₃³×C₄	C₄	1	6	yes	direct product factor
5	C₂×C₃²×C₄	C₂×C₃	1	39	yes	—
6	C₂×C₃³	C₂×C₄	1	3	yes	—
7	C₃×C₄²	C₃²	1	13	yes	direct product factor
8	C₂²×C₃²	C₂²×C₃	1	13	yes	—
9	C₃²×C₄	C₃×C₄	1	78	yes	direct product factor
10	C₃³	C₄²	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₃×C₄	C₂×C₃²	1	39	yes	—
12	C₂×C₃²	C₂×C₃×C₄	1	39	yes	—
13	C₄²	C₃³	1	1	yes	characteristic, direct product factor, Sylow
14	C₂²×C₃	C₂²×C₃²	1	13	yes	—
15	C₃×C₄	C₃²×C₄	1	78	yes	direct product factor
16	C₃²	C₃×C₄²	1	13	yes	direct product factor
17	C₂×C₄	C₂×C₃³	1	3	yes	—
18	C₂×C₃	C₂×C₃²×C₄	1	39	yes	—
19	C₂²	C₂²×C₃³	1	1	yes	characteristic
20	C₄	C₃³×C₄	1	6	yes	direct product factor
21	C₃	C₃²×C₄²	1	13	yes	direct product factor
22	C₂	C₂×C₃³×C₄	1	3	yes	—

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
C₂×C₃³×C₄	2
C₃²×C₄²	3