Subgroups — C₃×#356 #4603

Order 192.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#101	C₂	1	2	yes	maximal
3	#356	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×Q₈	C₄	1	1	yes	characteristic
5	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
6	C₃×M₁₆	—	2	2	no	—
7	C₃×C₄⋊C₄	—	2	2	no	—
8	C₃×C₄²	C₄	1	1	yes	characteristic
9	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
10	#101	C₂×C₃	1	2	yes	—
11	C₃×Q₈	—	4	1	no	—
12	C₃×Q₈	—	4	1	no	—
13	C₂×C₃×C₄	—	2	1	no	—
14	C₂×C₃×C₄	—	2	1	no	—
15	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₄	D₄	1	2	yes	—
17	C₃×C₈	—	4	2	no	—
18	C₂×Q₈	C₃×C₄	1	1	yes	characteristic
19	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
20	M₁₆	—	2	2	no	—
21	C₄⋊C₄	—	2	2	no	—
22	C₄²	C₃×C₄	1	1	yes	characteristic
23	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₃×C₄	—	2	2	no	—
25	C₃×C₄	—	2	2	no	—
26	C₃×C₄	—	2	1	no	—
27	C₃×C₄	—	4	1	no	—
28	Q₈	—	4	1	no	—
29	Q₈	—	4	1	no	—
30	C₂×C₄	—	2	1	no	—
31	C₂×C₄	—	2	1	no	—
32	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
33	C₂×C₄	C₃×D₄	1	2	yes	—
34	C₈	—	4	2	no	—
35	C₂×C₃	—	2	1	no	—
36	C₂×C₃	#99	1	1	yes	characteristic
37	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
38	C₄	—	2	2	no	—
39	C₄	—	2	2	no	—
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₃	#356	1	1	yes	characteristic, direct product factor, Sylow
43	C₂	—	2	1	no	—
44	C₂	C₃×#99	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #356	C₃	direct (N × H)
42. C₃	#356	direct (N × H)

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