Subgroups — C₂×#638 #3834

Order 144.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#638	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#67	—	3	4	no	maximal
6	C₂²×C₃²	—	2	2	no	—
7	C₂²×C₃²	C₂²	1	1	yes	characteristic
8	C₂²×C₃²	C₂²	1	2	yes	complemented
9	C₂×C₃⋊D₃	—	2	2	no	—
10	C₂×C₃⋊D₃	C₂²	1	2	yes	complemented
11	C₃⋊Dic₃	C₂²	1	2	yes	complemented
12	C₂³×C₃	D₃	1	4	yes	complemented
13	C₂²×D₃	—	3	4	no	—
14	#67	—	3	16	no	—
15	C₂×Dic₃	—	3	4	no	—
16	C₂×C₃²	—	2	2	no	—
17	C₂×C₃²	D₄	1	2	yes	complemented
18	C₂×C₃²	C₂³	1	1	yes	characteristic
19	C₃⋊D₃	—	2	2	no	—
20	C₂×D₄	—	9	1	no	Sylow
21	C₂²×C₃	—	2	8	no	—
22	C₂²×C₃	C₂×D₃	1	4	yes	—
23	C₂²×C₃	C₂×D₃	1	8	yes	complemented
24	C₂×D₃	—	3	8	no	—
25	C₂×D₃	—	6	8	no	—
26	Dic₃	—	3	8	no	—
27	C₃²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
28	C₂³	—	9	1	no	—
29	C₂³	C₃⋊D₃	1	1	yes	characteristic, complemented
30	D₄	—	9	4	no	—
31	C₂×C₄	—	9	1	no	—
32	C₂×C₃	—	2	8	no	—
33	C₂×C₃	#67	1	8	yes	complemented
34	C₂×C₃	C₂²×D₃	1	4	yes	—
35	D₃	—	6	8	no	—
36	C₂²	—	2	2	no	—
37	C₂²	—	9	2	no	—
38	C₂²	—	18	2	no	—
39	C₂²	C₂×C₃⋊D₃	1	1	yes	characteristic
40	C₂²	C₂×C₃⋊D₃	1	2	yes	complemented
41	C₄	—	9	2	no	—
42	C₃	C₂×#67	1	4	yes	complemented
43	C₂	—	2	2	no	—
44	C₂	—	18	2	no	—
45	C₂	#638	1	2	yes	direct product factor
46	C₂	C₂²×C₃⋊D₃	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.