Subgroups — D₃×#66502 #14520262

Order 1968.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#4223	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#66502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66502	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#66502	—	3	1	no	maximal, Hall
5	D₃×D₄₁	C₄	1	1	yes	characteristic
6	C₃⋊#4223	C₄	1	1	yes	characteristic
7	C₃×#4223	C₂²	1	1	yes	characteristic
8	C₂×#4223	—	3	1	no	—
9	#66502	—	3	1	no	—
10	#66502	D₃	1	1	yes	characteristic, direct product factor
11	D₁₂₃	C₈	1	1	yes	characteristic, complemented
12	C₃×D₄₁	C₂×C₄	1	1	yes	characteristic
13	D₃×C₄₁	C₈	1	1	yes	characteristic, complemented
14	C₂×D₄₁	—	3	1	no	—
15	#4223	—	3	1	no	—
16	#4223	C₂×D₃	1	1	yes	characteristic
17	C₃×C₄₁	C₂×C₈	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₁	—	3	1	no	—
19	D₄₁	—	3	1	no	—
20	D₄₁	C₄×D₃	1	1	yes	characteristic
21	D₃×C₈	—	41	1	no	maximal, Hall
22	C₄₁	D₃×C₈	1	1	yes	characteristic, complemented, Sylow
23	C₄×D₃	—	41	1	no	—
24	C₃×C₈	—	41	1	no	—
25	C₃⋊C₈	—	41	1	no	—
26	C₂×C₈	—	123	1	no	Sylow
27	C₂×D₃	—	41	1	no	—
28	C₃×C₄	—	41	1	no	—
29	Dic₃	—	41	1	no	—
30	C₂×C₄	—	123	1	no	—
31	C₈	—	41	1	no	—
32	C₈	—	123	1	no	—
33	C₂×C₃	—	41	1	no	—
34	D₃	—	41	1	no	—
35	D₃	#66502	1	1	yes	characteristic, direct product factor
36	C₂²	—	123	1	no	—
37	C₄	—	41	1	no	—
38	C₄	—	123	1	no	—
39	C₃	C₂×#66502	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	3	1	no	—
41	C₂	—	41	1	no	—
42	C₂	—	123	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₄₁	C₂×C₈
prime radical	D₃×D₄₁	C₄
cosocle	C₃×#4223	C₂²
LCS	G ▷ C₃×C₄₁
UCS	C₁

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.