Subgroups — #3797

Order 144.

84 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	2	yes	maximal, complemented
3	#627	C₂	1	2	yes	maximal, complemented
4	#624	C₂	1	2	yes	maximal
5	D₃×Q₈	—	3	2	no	maximal
6	C₂×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₃⋊Dic₃	C₂²	1	1	yes	characteristic
9	C₃×Dic₃	C₂²	1	4	yes	—
10	C₃×Q₈	—	3	2	no	—
11	C₄×D₃	—	3	2	no	—
12	C₄×D₃	—	3	4	no	—
13	C₄×D₃	—	6	1	no	—
14	Dic₆	—	3	4	no	—
15	Dic₆	D₃	1	2	yes	complemented
16	C₂×C₃²	C₂³	1	1	yes	characteristic
17	C₃⋊D₃	Q₈	1	2	yes	complemented
18	C₂×Q₈	—	9	1	no	Sylow
19	C₂×D₃	—	3	2	no	—
20	C₂×D₃	—	6	1	no	—
21	C₃×C₄	—	2	1	no	—
22	C₃×C₄	—	3	4	no	—
23	C₃×C₄	C₂×D₃	1	2	yes	—
24	Dic₃	—	3	2	no	—
25	Dic₃	—	6	1	no	—
26	Dic₃	C₂×D₃	1	4	yes	—
27	C₃²	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
28	Q₈	—	3	2	no	—
29	Q₈	—	9	2	no	—
30	C₂×C₄	—	9	2	no	—
31	C₂×C₄	—	9	1	no	—
32	C₂×C₃	—	2	1	no	—
33	C₂×C₃	C₂²×D₃	1	2	yes	—
34	D₃	—	3	4	no	—
35	D₃	—	6	2	no	—
36	C₂²	—	9	1	no	—
37	C₄	—	3	4	no	—
38	C₄	—	9	1	no	—
39	C₄	D₃²	1	1	yes	characteristic
40	C₃	—	2	1	no	—
41	C₃	D₃×Q₈	1	2	yes	complemented
42	C₂	—	9	2	no	—
43	C₂	C₂×D₃²	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.