Subgroups — #3719

Order 144.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#634	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	#216	—	3	1	no	maximal
5	Dic₁₂	—	3	1	no	maximal
6	C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₃⋊Dic₃	—	2	1	no	—
8	C₃×Dic₃	—	2	1	no	—
9	C₃×Q₈	—	3	1	no	—
10	Dic₆	—	3	1	no	—
11	Dic₆	—	3	1	no	—
12	Dic₆	—	6	1	no	—
13	Dic₆	D₃	1	1	yes	characteristic
14	C₃×C₈	—	3	1	no	—
15	C₃⋊C₈	D₃	1	1	yes	characteristic
16	C₂×C₃²	D₄	1	1	yes	characteristic
17	Q₁₆	—	9	1	no	Sylow
18	C₃×C₄	—	2	1	no	—
19	C₃×C₄	—	6	1	no	—
20	C₃×C₄	C₂×D₃	1	1	yes	characteristic
21	C₃×C₄	C₂×D₃	1	1	yes	characteristic
22	Dic₃	—	2	1	no	—
23	Dic₃	—	6	2	no	—
24	Dic₃	—	6	1	no	—
25	Dic₃	—	6	1	no	—
26	C₃²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
27	Q₈	—	3	1	no	—
28	Q₈	—	9	1	no	—
29	C₈	—	3	1	no	—
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	D₁₂	1	1	yes	characteristic
32	C₂×C₃	#67	1	1	yes	characteristic
33	C₄	—	6	1	no	—
34	C₄	—	18	1	no	—
35	C₄	D₃²	1	1	yes	characteristic
36	C₃	—	2	1	no	—
37	C₃	Dic₁₂	1	1	yes	characteristic, complemented
38	C₃	#216	1	1	yes	characteristic, complemented
39	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.