Subgroups — #3716

Order 144.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#634	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#214	—	3	1	no	maximal
5	#204	—	3	1	no	maximal
6	C₂×C₃×D₃	—	2	1	no	—
7	C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₃⋊Dic₃	—	2	1	no	—
9	C₃×D₄	—	3	1	no	—
10	D₁₂	D₃	1	1	yes	characteristic
11	Dic₆	—	3	1	no	—
12	Dic₆	—	3	1	no	—
13	Dic₆	—	6	1	no	—
14	C₃×C₈	—	3	1	no	—
15	C₃⋊C₈	D₃	1	1	yes	characteristic, complemented
16	C₂×C₃²	D₄	1	1	yes	characteristic
17	C₃×D₃	—	4	1	no	—
18	SD₁₆	—	9	1	no	Sylow
19	C₂²×C₃	—	6	1	no	—
20	C₂×D₃	—	2	1	no	—
21	C₃×C₄	—	2	1	no	—
22	C₃×C₄	C₂×D₃	1	1	yes	characteristic
23	C₃×C₄	C₂×D₃	1	1	yes	characteristic
24	Dic₃	—	6	2	no	—
25	Dic₃	—	6	1	no	—
26	Dic₃	—	6	1	no	—
27	C₃²	SD₁₆	1	1	yes	characteristic, complemented, Sylow
28	Q₈	—	9	1	no	—
29	D₄	—	3	1	no	—
30	C₈	—	3	1	no	—
31	C₂×C₃	—	2	1	no	—
32	C₂×C₃	—	12	1	no	—
33	C₂×C₃	D₁₂	1	1	yes	characteristic
34	C₂×C₃	#67	1	1	yes	characteristic
35	D₃	—	4	1	no	—
36	C₂²	—	6	1	no	—
37	C₄	—	18	1	no	—
38	C₄	D₃²	1	1	yes	characteristic
39	C₃	—	2	1	no	—
40	C₃	#204	1	1	yes	characteristic, complemented
41	C₃	#214	1	1	yes	characteristic, complemented
42	C₂	—	12	1	no	—
43	C₂	#626	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.