Subgroups — C₃×#365 #4612

Order 192.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×#108	C₂	1	1	yes	maximal, characteristic
3	C₃×#106	C₂	1	1	yes	maximal, characteristic
4	#365	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×M₁₆	—	2	1	no	—
6	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
7	C₃×C₄⋊C₄	—	2	1	no	—
8	C₃×C₁₆	C₄	1	2	yes	complemented
9	M₃₂	C₂×C₃	1	1	yes	characteristic
10	#108	C₂×C₃	1	1	yes	characteristic
11	#106	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃×C₄	—	4	1	no	—
13	C₂×C₃×C₄	D₄	1	1	yes	characteristic
14	C₃×C₈	—	4	1	no	—
15	C₃×C₈	C₂×C₄	1	1	yes	characteristic
16	C₃×C₈	Q₈	1	1	yes	characteristic
17	M₁₆	—	2	1	no	—
18	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
19	C₄⋊C₄	—	2	1	no	—
20	C₁₆	C₃×C₄	1	2	yes	complemented
21	C₂²×C₃	SD₁₆	1	1	yes	characteristic
22	C₃×C₄	—	8	1	no	—
23	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
24	C₃×C₄	SD₁₆	1	1	yes	characteristic
25	C₂×C₄	—	4	1	no	—
26	C₂×C₄	C₃×D₄	1	1	yes	characteristic
27	C₈	—	4	1	no	—
28	C₈	C₂×C₃×C₄	1	1	yes	characteristic
29	C₈	C₃×Q₈	1	1	yes	characteristic
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	#106	1	1	yes	characteristic
32	C₂²	C₃×SD₁₆	1	1	yes	characteristic
33	C₄	—	8	1	no	—
34	C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
35	C₄	C₃×SD₁₆	1	1	yes	characteristic
36	C₃	#365	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	2	1	no	—
38	C₂	C₃×#106	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.