Subgroups — #3752

Order 144.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₃)⋊C₄	—	3	4	no	maximal
5	C₂²×C₃²	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊D₃	—	2	1	no	—
7	C₂×C₃⋊D₃	—	2	1	no	—
8	C₂×C₃⋊D₃	C₄	1	2	yes	complemented
9	C₃²×C₄	—	2	1	no	—
10	C₃⋊Dic₃	—	2	1	no	—
11	C₂²×D₃	—	3	4	no	—
12	C₂×C₃×C₄	D₃	1	4	yes	complemented
13	C₂×Dic₃	—	3	4	no	—
14	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃²	D₄	1	1	yes	characteristic
16	C₂×C₃²	D₄	1	1	yes	characteristic
17	C₃⋊D₃	—	2	2	no	—
18	C₂²⋊C₄	—	9	1	no	Sylow
19	C₂²×C₃	C₂×D₃	1	4	yes	—
20	C₂×D₃	—	3	8	no	—
21	C₂×D₃	—	6	4	no	—
22	C₂×D₃	—	6	4	no	—
23	C₃×C₄	—	2	4	no	—
24	Dic₃	—	6	4	no	—
25	C₃²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	9	1	no	—
27	C₂×C₄	—	9	1	no	—
28	C₂×C₄	C₃⋊D₃	1	1	yes	characteristic, complemented
29	C₂×C₃	C₄×D₃	1	4	yes	—
30	C₂×C₃	D₁₂	1	4	yes	—
31	C₂×C₃	#67	1	4	yes	—
32	D₃	—	6	8	no	—
33	C₂²	—	9	2	no	—
34	C₂²	—	18	1	no	—
35	C₂²	—	18	1	no	—
36	C₂²	C₂×C₃⋊D₃	1	1	yes	characteristic
37	C₄	—	2	1	no	—
38	C₄	—	18	1	no	—
39	C₃	(C₂×D₃)⋊C₄	1	4	yes	complemented
40	C₂	—	18	2	no	—
41	C₂	C₄×C₃⋊D₃	1	1	yes	characteristic
42	C₂	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
43	C₂	#638	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.