Subgroups — #3798

Order 144.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×D₃	C₂	1	2	yes	maximal, complemented
3	#627	C₂	1	1	yes	maximal, characteristic, complemented
4	#626	C₂	1	2	yes	maximal, complemented
5	#625	C₂	1	1	yes	maximal, characteristic, complemented
6	#235	—	3	2	no	maximal
7	C₂×C₃⋊D₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×D₃	C₂²	1	2	yes	—
9	C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₃⋊Dic₃	C₂²	1	1	yes	characteristic
11	C₃×Dic₃	C₂²	1	2	yes	—
12	C₂×C₃×C₄	—	3	2	no	—
13	#67	—	3	2	no	—
14	#67	—	3	2	no	—
15	D₁₂	—	3	2	no	—
16	C₄×D₃	—	3	2	no	—
17	C₄×D₃	—	6	1	no	—
18	C₄×D₃	D₃	1	2	yes	complemented
19	Dic₆	—	3	2	no	—
20	C₂×C₃²	C₂³	1	1	yes	characteristic
21	C₃⋊D₃	—	2	1	no	—
22	C₃×D₃	—	2	2	no	—
23	#41	—	9	1	no	Sylow
24	C₂²×C₃	—	3	2	no	—
25	C₂×D₃	—	3	2	no	—
26	C₂×D₃	—	6	1	no	—
27	C₂×D₃	C₂×D₃	1	2	yes	—
28	C₃×C₄	—	2	1	no	—
29	C₃×C₄	—	3	2	no	—
30	C₃×C₄	C₂×D₃	1	2	yes	—
31	Dic₃	—	3	2	no	—
32	Dic₃	—	6	1	no	—
33	Dic₃	C₂×D₃	1	2	yes	—
34	C₃²	#41	1	1	yes	characteristic, complemented, Sylow
35	Q₈	—	9	1	no	—
36	D₄	—	9	2	no	—
37	D₄	—	9	1	no	—
38	C₂×C₄	—	3	2	no	—
39	C₂×C₄	—	9	1	no	—
40	C₂×C₃	—	2	1	no	—
41	C₂×C₃	—	6	2	no	—
42	C₂×C₃	C₂²×D₃	1	2	yes	—
43	D₃	—	2	2	no	—
44	D₃	—	6	2	no	—
45	D₃	—	6	2	no	—
46	C₂²	—	3	2	no	—
47	C₂²	—	9	1	no	—
48	C₄	—	3	2	no	—
49	C₄	—	9	1	no	—
50	C₄	D₃²	1	1	yes	characteristic
51	C₃	—	2	1	no	—
52	C₃	#235	1	2	yes	complemented
53	C₂	—	6	2	no	—
54	C₂	—	18	1	no	—
55	C₂	C₂×D₃²	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.