Subgroups — D₃×#66493 #14520171

Order 1968.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×Dic₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#66493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#66493	—	3	1	no	maximal, Hall
5	C₂×D₃×C₄₁	C₄	1	1	yes	characteristic
6	Dic₁₂₃	C₄	1	1	yes	characteristic
7	C₃×Dic₄₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₄₁	—	3	1	no	—
9	#66493	—	3	1	no	—
10	#66493	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₄₁	C₂×C₄	1	1	yes	characteristic
12	D₃×C₄₁	C₈	1	2	yes	complemented
13	C₂²×C₄₁	—	3	1	no	—
14	Dic₄₁	—	3	1	no	—
15	Dic₄₁	C₂×D₃	1	1	yes	characteristic
16	C₃×C₄₁	C₂×C₈	1	1	yes	characteristic, complemented, Hall
17	C₂×C₄₁	—	3	2	no	—
18	C₂×C₄₁	C₄×D₃	1	1	yes	characteristic
19	D₃×C₈	—	41	1	no	maximal, Hall
20	C₄₁	D₃×C₈	1	1	yes	characteristic, complemented, Sylow
21	C₄×D₃	—	41	1	no	—
22	C₃×C₈	—	41	1	no	—
23	C₃⋊C₈	—	41	1	no	—
24	C₂×C₈	—	123	1	no	Sylow
25	C₂×D₃	#4223	1	1	yes	characteristic
26	C₃×C₄	—	41	1	no	—
27	Dic₃	—	41	1	no	—
28	C₂×C₄	—	123	1	no	—
29	C₈	—	41	1	no	—
30	C₈	—	123	1	no	—
31	C₂×C₃	C₂×#4223	1	1	yes	characteristic
32	D₃	#66493	1	2	yes	direct product factor
33	C₂²	—	3	1	no	—
34	C₄	—	41	1	no	—
35	C₄	—	123	1	no	—
36	C₃	C₂×#66493	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	3	2	no	—
38	C₂	D₃×#4223	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#4223
commutator, hypocenter	C₃×C₄₁	C₂×C₈
Fitting, socle	C₂×C₃×C₄₁	C₂×C₄
prime radical	C₂×D₃×C₄₁	C₄
cosocle	C₃×Dic₄₁	C₂²
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₂

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.