Subgroups — C₃×#504 #5378

Order 192.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#131	C₂	1	1	yes	maximal, characteristic
2	C₃×M₃₂	C₂	1	3	yes	maximal, complemented
3	C₂×C₃×C₁₆	C₂	1	3	yes	maximal, complemented
4	#504	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×#41	C₄	1	1	yes	characteristic
6	C₃×M₁₆	C₄	1	3	yes	—
7	C₂×C₃×C₈	C₂²	1	3	yes	—
8	C₃×C₁₆	C₂²	1	3	yes	—
9	C₃×C₁₆	C₂²	1	1	yes	characteristic
10	#131	C₂×C₃	1	1	yes	characteristic
11	M₃₂	C₂×C₃	1	3	yes	complemented
12	C₂×C₁₆	C₂×C₃	1	3	yes	complemented
13	C₃×Q₈	C₈	1	1	yes	characteristic
14	C₃×D₄	C₈	1	3	yes	—
15	C₂×C₃×C₄	C₂×C₄	1	3	yes	—
16	C₃×C₈	C₂×C₄	1	3	yes	—
17	C₃×C₈	C₂³	1	1	yes	characteristic
18	#41	C₃×C₄	1	1	yes	characteristic
19	M₁₆	C₃×C₄	1	3	yes	—
20	C₂×C₈	C₂²×C₃	1	3	yes	—
21	C₁₆	C₂²×C₃	1	1	yes	characteristic
22	C₁₆	C₂²×C₃	1	3	yes	—
23	C₂²×C₃	C₂×C₈	1	3	yes	—
24	C₃×C₄	C₂×C₈	1	3	yes	—
25	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
26	Q₈	C₃×C₈	1	1	yes	characteristic
27	D₄	C₃×C₈	1	3	yes	—
28	C₂×C₄	C₂×C₃×C₄	1	3	yes	—
29	C₈	C₂×C₃×C₄	1	3	yes	—
30	C₈	C₂³×C₃	1	1	yes	characteristic
31	C₂×C₃	—	2	3	no	—
32	C₂×C₃	C₂²×C₈	1	1	yes	characteristic
33	C₂²	C₂×C₃×C₈	1	3	yes	—
34	C₄	C₂×C₃×C₈	1	3	yes	—
35	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
36	C₃	#504	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	2	3	no	—
38	C₂	C₂²×C₃×C₈	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.