Subgroups — #3717

Order 144.

48 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
2	C₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#215	—	3	1	no	maximal
5	#204	—	3	1	no	maximal
6	C₂×C₃⋊D₃	—	2	1	no	—
7	C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₃×Dic₃	—	2	1	no	—
9	C₃×Q₈	—	3	1	no	—
10	D₁₂	—	3	1	no	—
11	D₁₂	—	3	1	no	—
12	D₁₂	—	6	1	no	—
13	Dic₆	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	SD₁₆	—	9	1	no	Sylow
19	C₂×D₃	—	6	2	no	—
20	C₂×D₃	—	6	1	no	—
21	C₂×D₃	—	6	1	no	—
22	C₃×C₄	—	2	1	no	—
23	C₃×C₄	—	6	1	no	—
24	C₃×C₄	C₂×D₃	1	1	yes	characteristic
25	C₃×C₄	C₂×D₃	1	1	yes	characteristic
26	Dic₃	—	2	1	no	—
27	C₃²	SD₁₆	1	1	yes	characteristic, complemented, Sylow
28	Q₈	—	3	1	no	—
29	D₄	—	9	1	no	—
30	C₈	—	3	1	no	—
31	C₂×C₃	—	2	1	no	—
32	C₂×C₃	D₁₂	1	1	yes	characteristic
33	C₂×C₃	#67	1	1	yes	characteristic
34	D₃	—	12	2	no	—
35	D₃	—	12	1	no	—
36	D₃	—	12	1	no	—
37	C₂²	—	18	1	no	—
38	C₄	—	6	1	no	—
39	C₄	D₃²	1	1	yes	characteristic
40	C₃	—	2	1	no	—
41	C₃	#204	1	1	yes	characteristic, complemented
42	C₃	#215	1	1	yes	characteristic, complemented
43	C₂	—	36	1	no	—
44	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.