Subgroups — C₃×#338 #4585

Order 192.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×M₁₆	C₂	1	3	yes	maximal
2	#338	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
3	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
4	C₃×M₁₆	—	2	6	no	—
5	C₂×C₃×C₈	C₄	1	6	yes	—
6	C₂×M₁₆	C₂×C₃	1	3	yes	—
7	C₂³×C₃	Q₈	1	1	yes	characteristic
8	C₂×C₃×C₄	C₂×C₄	1	3	yes	—
9	C₂×C₃×C₄	D₄	1	3	yes	—
10	C₃×C₈	—	2	6	no	—
11	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
12	M₁₆	—	2	6	no	—
13	C₂×C₈	C₃×C₄	1	6	yes	—
14	C₂²×C₃	—	4	1	no	—
15	C₂²×C₃	C₄⋊C₄	1	3	yes	—
16	C₃×C₄	C₄²	1	1	yes	characteristic
17	C₃×C₄	C₂²⋊C₄	1	3	yes	—
18	C₂³	C₃×Q₈	1	1	yes	characteristic
19	C₂×C₄	C₂×C₃×C₄	1	3	yes	—
20	C₂×C₄	C₃×D₄	1	3	yes	—
21	C₈	—	2	6	no	—
22	C₂×C₃	—	2	3	no	—
23	C₂×C₃	#95	1	1	yes	characteristic
24	C₂²	—	4	1	no	—
25	C₂²	C₃×C₄⋊C₄	1	3	yes	—
26	C₄	C₃×C₄²	1	1	yes	characteristic
27	C₄	C₃×C₂²⋊C₄	1	3	yes	—
28	C₃	#338	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	2	3	no	—
30	C₂	C₃×#95	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #338	C₃	direct (N × H)
28. C₃	#338	direct (N × H)

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

subgroup	index
C₂×C₃×M₁₆	2
#338	3