Subgroups — #3715

Order 144.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#215	—	3	1	no	maximal
5	#214	—	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×Q₈	—	3	1	no	—
10	C₃×D₄	—	3	1	no	—
11	D₁₂	D₃	1	1	yes	characteristic
12	Dic₆	D₃	1	1	yes	characteristic, complemented
13	C₃⋊C₈	—	3	1	no	—
14	C₃⋊C₈	—	3	1	no	—
15	C₃⋊C₈	—	6	1	no	—
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	—	6	1	no	—
23	C₃×C₄	C₂×D₃	1	1	yes	characteristic
24	C₃×C₄	C₂×D₃	1	1	yes	characteristic
25	Dic₃	—	2	1	no	—
26	C₃²	SD₁₆	1	1	yes	characteristic, complemented, Sylow
27	Q₈	—	3	1	no	—
28	D₄	—	3	1	no	—
29	C₈	—	9	1	no	—
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	—	12	1	no	—
32	C₂×C₃	#67	1	1	yes	characteristic
33	C₂×C₃	#67	1	1	yes	characteristic
34	D₃	—	4	1	no	—
35	C₂²	—	6	1	no	—
36	C₄	—	6	1	no	—
37	C₄	D₃²	1	1	yes	characteristic
38	C₃	—	2	1	no	—
39	C₃	#214	1	1	yes	characteristic, complemented
40	C₃	#215	1	1	yes	characteristic, complemented
41	C₂	—	12	1	no	—
42	C₂	#625	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.