Subgroups — #504⋊C₃ #4645

Order 192.

29 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#131⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#504	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	#41⋊C₃	C₄	1	1	yes	characteristic
4	C₃×C₁₆	—	4	1	no	maximal
5	#131	C₂×C₃	1	1	yes	characteristic
6	M₃₂	—	3	1	no	—
7	C₂×C₁₆	—	3	1	no	—
8	SL(2,𝔽₃)	C₈	1	1	yes	characteristic
9	C₃×C₈	—	4	1	no	—
10	#41	C₃×C₄	1	1	yes	characteristic
11	M₁₆	—	3	1	no	—
12	C₂×C₈	—	3	1	no	—
13	C₁₆	—	3	1	no	—
14	C₁₆	A₄	1	1	yes	characteristic
15	C₃×C₄	—	4	1	no	—
16	Q₈	C₃×C₈	1	1	yes	characteristic
17	D₄	—	3	1	no	—
18	C₂×C₄	—	3	1	no	—
19	C₈	—	3	1	no	—
20	C₈	C₂×A₄	1	1	yes	characteristic
21	C₂×C₃	—	4	1	no	—
22	C₂²	—	3	1	no	—
23	C₄	—	3	1	no	—
24	C₄	C₄×A₄	1	1	yes	characteristic
25	C₃	—	4	1	no	Sylow
26	C₂	—	6	1	no	—
27	C₂	C₈×A₄	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #504	C₃	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.