Subgroups — #3697

Order 144.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#611	C₂	1	2	yes	maximal, complemented
3	D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₉	C₂	1	2	yes	maximal, complemented
5	Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#235	—	3	1	no	maximal
7	C₂²×C₉	C₂²	1	1	yes	characteristic
8	C₂×D₉	C₂²	1	2	yes	—
9	C₄×C₉	C₂²	1	1	yes	characteristic
10	C₄×C₉	C₂²	1	1	yes	characteristic
11	Dic₉	C₂²	1	2	yes	—
12	C₂×C₃×C₄	D₃	1	1	yes	characteristic
13	#67	—	3	2	no	—
14	D₁₂	—	3	1	no	—
15	C₄×D₃	—	3	2	no	—
16	Dic₆	—	3	1	no	—
17	C₂×C₉	—	2	1	no	—
18	C₂×C₉	C₂³	1	1	yes	characteristic
19	D₉	—	2	2	no	—
20	#41	—	9	1	no	Sylow
21	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
22	C₂×D₃	—	3	2	no	—
23	C₃×C₄	C₂×D₃	1	1	yes	characteristic
24	C₃×C₄	C₂×D₃	1	1	yes	characteristic
25	Dic₃	—	3	2	no	—
26	C₉	#41	1	1	yes	characteristic, complemented, Sylow
27	Q₈	—	9	1	no	—
28	D₄	—	9	2	no	—
29	D₄	—	9	1	no	—
30	C₂×C₄	—	9	2	no	—
31	C₂×C₄	D₉	1	1	yes	characteristic, complemented
32	C₂×C₃	—	2	1	no	—
33	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
34	D₃	—	6	2	no	—
35	C₂²	—	9	2	no	—
36	C₂²	C₂×D₉	1	1	yes	characteristic
37	C₄	—	9	2	no	—
38	C₄	C₂×D₉	1	1	yes	characteristic
39	C₄	C₂×D₉	1	1	yes	characteristic
40	C₃	#235	1	1	yes	characteristic
41	C₂	—	2	1	no	—
42	C₂	—	18	2	no	—
43	C₂	C₂²×D₉	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.