Subgroups — C₃×#214 #3738

Order 144.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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