Subgroups — D₃×C₆₄ #67431

Order 384.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₄	—	3	1	no	maximal, Sylow
5	D₃×C₁₆	C₄	1	1	yes	characteristic
6	C₃×C₃₂	C₂²	1	1	yes	characteristic
7	C₃⋊C₃₂	C₄	1	1	yes	characteristic
8	C₂×C₃₂	—	3	1	no	—
9	C₆₄	—	3	1	no	—
10	C₆₄	D₃	1	1	yes	characteristic, direct product factor
11	D₃×C₈	C₈	1	1	yes	characteristic
12	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₃⋊C₁₆	C₈	1	1	yes	characteristic
14	C₂×C₁₆	—	3	1	no	—
15	C₃₂	—	3	1	no	—
16	C₃₂	C₂×D₃	1	1	yes	characteristic
17	C₄×D₃	C₁₆	1	1	yes	characteristic
18	C₃×C₈	C₂×C₈	1	1	yes	characteristic
19	C₃⋊C₈	C₁₆	1	1	yes	characteristic
20	C₂×C₈	—	3	1	no	—
21	C₁₆	—	3	1	no	—
22	C₁₆	C₄×D₃	1	1	yes	characteristic
23	C₂×D₃	C₃₂	1	1	yes	characteristic
24	C₃×C₄	C₂×C₁₆	1	1	yes	characteristic
25	Dic₃	C₃₂	1	1	yes	characteristic
26	C₂×C₄	—	3	1	no	—
27	C₈	—	3	1	no	—
28	C₈	D₃×C₈	1	1	yes	characteristic
29	C₂×C₃	C₂×C₃₂	1	1	yes	characteristic
30	D₃	C₆₄	1	2	yes	direct product factor
31	C₂²	—	3	1	no	—
32	C₄	—	3	1	no	—
33	C₄	D₃×C₁₆	1	1	yes	characteristic
34	C₃	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
35	C₂	—	3	2	no	—
36	C₂	D₃×C₃₂	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.