Subgroups — C₃×SL(2,ℤ/4) #3780

Order 144.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×A₄	C₂	1	1	yes	maximal, characteristic
2	SL(2,ℤ/4)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₂²⋊C₄	—	3	1	no	maximal
4	C₃×A₄	C₄	1	1	yes	characteristic, complemented
5	C₃×Dic₃	—	4	1	no	maximal
6	C₂³×C₃	D₃	1	1	yes	characteristic
7	C₂×A₄	—	2	1	no	—
8	C₂×A₄	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×C₄	—	3	1	no	—
10	C₂×C₃×C₄	—	3	1	no	—
11	C₂×C₃²	—	4	1	no	—
12	C₂²⋊C₄	—	3	1	no	Sylow
13	C₂²×C₃	—	3	1	no	—
14	C₂²×C₃	—	3	1	no	—
15	C₂²×C₃	Dic₃	1	1	yes	characteristic, complemented
16	A₄	—	2	1	no	—
17	A₄	C₃×C₄	1	1	yes	characteristic, complemented
18	C₃×C₄	—	6	1	no	—
19	C₃×C₄	—	6	1	no	—
20	Dic₃	—	4	1	no	—
21	C₃²	—	4	1	no	Sylow
22	C₂³	C₃×D₃	1	1	yes	characteristic
23	C₂×C₄	—	3	1	no	—
24	C₂×C₄	—	3	1	no	—
25	C₂×C₃	—	3	1	no	—
26	C₂×C₃	—	3	1	no	—
27	C₂×C₃	—	4	1	no	—
28	C₂×C₃	—	8	1	no	—
29	C₂×C₃	S₄	1	1	yes	characteristic
30	C₂²	—	3	1	no	—
31	C₂²	—	3	1	no	—
32	C₂²	C₃×Dic₃	1	1	yes	characteristic, complemented
33	C₄	—	6	1	no	—
34	C₄	—	6	1	no	—
35	C₃	—	4	1	no	—
36	C₃	—	8	1	no	—
37	C₃	SL(2,ℤ/4)	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—
39	C₂	—	3	1	no	—
40	C₂	C₃×S₄	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.