Subgroups — D₃×C₃₂ #4446

Order 192.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₂	—	3	1	no	maximal, Sylow
5	D₃×C₈	C₄	1	1	yes	characteristic
6	C₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₃⋊C₁₆	C₄	1	1	yes	characteristic
8	C₂×C₁₆	—	3	1	no	—
9	C₃₂	—	3	1	no	—
10	C₃₂	D₃	1	1	yes	characteristic, direct product factor
11	C₄×D₃	C₈	1	1	yes	characteristic
12	C₃×C₈	C₂×C₄	1	1	yes	characteristic
13	C₃⋊C₈	C₈	1	1	yes	characteristic
14	C₂×C₈	—	3	1	no	—
15	C₁₆	—	3	1	no	—
16	C₁₆	C₂×D₃	1	1	yes	characteristic
17	C₂×D₃	C₁₆	1	1	yes	characteristic
18	C₃×C₄	C₂×C₈	1	1	yes	characteristic
19	Dic₃	C₁₆	1	1	yes	characteristic
20	C₂×C₄	—	3	1	no	—
21	C₈	—	3	1	no	—
22	C₈	C₄×D₃	1	1	yes	characteristic
23	C₂×C₃	C₂×C₁₆	1	1	yes	characteristic
24	D₃	C₃₂	1	2	yes	direct product factor
25	C₂²	—	3	1	no	—
26	C₄	—	3	1	no	—
27	C₄	D₃×C₈	1	1	yes	characteristic
28	C₃	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	2	no	—
30	C₂	D₃×C₁₆	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.