Subgroups — C₃×#1309 #67869

Order 384.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#423	C₂	1	3	yes	maximal
2	#1309	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
3	C₂×C₃×M₁₆	C₄	1	6	yes	—
4	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
5	C₃×C₄⋊C₈	—	2	6	no	—
6	#423	C₂×C₃	1	3	yes	—
7	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
8	C₃×M₁₆	—	4	6	no	—
9	C₂×C₃×C₈	—	2	6	no	—
10	C₃×C₄²	D₄	1	3	yes	—
11	C₃×C₄²	Q₈	1	1	yes	characteristic
12	C₂×M₁₆	C₃×C₄	1	6	yes	—
13	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
14	C₄⋊C₈	—	2	6	no	—
15	C₂³×C₃	C₄²	1	1	yes	characteristic
16	C₂×C₃×C₄	—	2	3	no	—
17	C₂×C₃×C₄	—	2	3	no	—
18	C₂×C₃×C₄	C₂²⋊C₄	1	3	yes	—
19	C₂×C₃×C₄	C₄⋊C₄	1	3	yes	—
20	C₃×C₈	—	4	6	no	—
21	C₂²×C₄	C₂×C₃×C₄	1	3	yes	—
22	M₁₆	—	4	6	no	—
23	C₂×C₈	—	2	6	no	—
24	C₄²	C₃×D₄	1	3	yes	—
25	C₄²	C₃×Q₈	1	1	yes	characteristic
26	C₂²×C₃	—	2	3	no	—
27	C₂²×C₃	#95	1	1	yes	characteristic
28	C₃×C₄	—	2	3	no	—
29	C₃×C₄	#100	1	3	yes	—
30	C₃×C₄	#101	1	3	yes	—
31	C₂³	C₃×C₄²	1	1	yes	characteristic
32	C₂×C₄	—	2	3	no	—
33	C₂×C₄	—	2	3	no	—
34	C₂×C₄	C₃×C₂²⋊C₄	1	3	yes	—
35	C₂×C₄	C₃×C₄⋊C₄	1	3	yes	—
36	C₈	—	4	6	no	—
37	C₂×C₃	—	4	1	no	—
38	C₂×C₃	#343	1	3	yes	—
39	C₂²	—	2	3	no	—
40	C₂²	C₃×#95	1	1	yes	characteristic
41	C₄	—	2	3	no	—
42	C₄	C₃×#100	1	3	yes	—
43	C₄	C₃×#101	1	3	yes	—
44	C₃	#1309	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	4	1	no	—
46	C₂	C₃×#343	1	3	yes	—

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

N	H ≅ G/N	type
2. #1309	C₃	direct (N × H)
44. C₃	#1309	direct (N × H)

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

subgroup	index
C₃×#423	2
#1309	3