Subgroups — #3714

Order 144.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#213	—	3	1	no	maximal
5	D₂₄	—	3	1	no	maximal
6	C₂×C₃⋊D₃	—	2	1	no	—
7	C₂×C₃×D₃	—	2	1	no	—
8	C₃²×C₄	C₂²	1	1	yes	characteristic
9	C₃×D₄	—	3	1	no	—
10	D₁₂	—	3	1	no	—
11	D₁₂	—	3	1	no	—
12	D₁₂	—	6	1	no	—
13	D₁₂	D₃	1	1	yes	characteristic, complemented
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	C₃×D₃	—	4	1	no	—
19	D₈	—	9	1	no	Sylow
20	C₂²×C₃	—	6	1	no	—
21	C₂×D₃	—	2	1	no	—
22	C₂×D₃	—	6	2	no	—
23	C₂×D₃	—	6	1	no	—
24	C₂×D₃	—	6	1	no	—
25	C₃×C₄	—	2	1	no	—
26	C₃×C₄	C₂×D₃	1	1	yes	characteristic
27	C₃×C₄	C₂×D₃	1	1	yes	characteristic
28	C₃²	D₈	1	1	yes	characteristic, complemented, Sylow
29	D₄	—	3	1	no	—
30	D₄	—	9	1	no	—
31	C₈	—	3	1	no	—
32	C₂×C₃	—	2	1	no	—
33	C₂×C₃	—	12	1	no	—
34	C₂×C₃	D₁₂	1	1	yes	characteristic
35	C₂×C₃	#67	1	1	yes	characteristic
36	D₃	—	4	1	no	—
37	D₃	—	12	2	no	—
38	D₃	—	12	1	no	—
39	D₃	—	12	1	no	—
40	C₂²	—	6	1	no	—
41	C₂²	—	18	1	no	—
42	C₄	D₃²	1	1	yes	characteristic
43	C₃	—	2	1	no	—
44	C₃	D₂₄	1	1	yes	characteristic, complemented
45	C₃	#213	1	1	yes	characteristic, complemented
46	C₂	—	12	1	no	—
47	C₂	—	36	1	no	—
48	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.