Subgroups — C₃×#216 #3740

Order 144.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×Q₁₆	—	3	1	no	maximal
5	#216	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₄	—	2	1	no	—
7	C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₃×Dic₃	—	2	1	no	—
9	C₃×Q₈	—	2	1	no	—
10	C₃×Q₈	—	3	1	no	—
11	C₃×Q₈	D₃	1	1	yes	characteristic
12	C₃×Q₈	C₂×C₃	1	1	yes	characteristic
13	Dic₆	C₂×C₃	1	1	yes	characteristic
14	C₃×C₈	—	3	1	no	—
15	C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
16	C₂×C₃²	D₄	1	1	yes	characteristic
17	Q₁₆	—	3	1	no	Sylow
18	C₃×C₄	—	2	2	no	—
19	C₃×C₄	—	2	1	no	—
20	C₃×C₄	—	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	C₂²×C₃	1	1	yes	characteristic
25	Dic₃	—	2	1	no	—
26	C₃²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
27	Q₈	—	3	1	no	—
28	Q₈	C₃×D₃	1	1	yes	characteristic
29	C₈	—	3	1	no	—
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	#67	1	1	yes	characteristic
32	C₂×C₃	C₃×D₄	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	6	1	no	—
35	C₄	C₂×C₃×D₃	1	1	yes	characteristic
36	C₃	—	2	1	no	—
37	C₃	#216	1	1	yes	characteristic, direct product factor
38	C₃	C₃×Q₁₆	1	1	yes	characteristic, complemented
39	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.