Subgroups — C₂²×C₃⋊Dic₃ #3833

Order 144.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊Dic₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×Dic₃	—	3	4	no	maximal
4	C₂²×C₃²	C₄	1	4	yes	complemented
5	C₂²×C₃²	C₂²	1	3	yes	—
6	C₃⋊Dic₃	C₂²	1	4	yes	direct product factor
7	C₂³×C₃	D₃	1	4	yes	—
8	C₂×Dic₃	—	3	24	no	—
9	C₂×C₃²	C₂×C₄	1	6	yes	complemented
10	C₂×C₃²	C₂³	1	1	yes	characteristic
11	C₂²×C₄	—	9	1	no	Sylow
12	C₂²×C₃	Dic₃	1	16	yes	complemented
13	C₂²×C₃	C₂×D₃	1	12	yes	—
14	Dic₃	—	3	16	no	—
15	C₃²	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂³	C₃⋊D₃	1	1	yes	characteristic
17	C₂×C₄	—	9	6	no	—
18	C₂×C₃	C₂×Dic₃	1	24	yes	complemented
19	C₂×C₃	C₂²×D₃	1	4	yes	—
20	C₂²	C₃⋊Dic₃	1	4	yes	direct product factor
21	C₂²	C₂×C₃⋊D₃	1	3	yes	—
22	C₄	—	9	4	no	—
23	C₃	C₂²×Dic₃	1	4	yes	complemented
24	C₂	C₂×C₃⋊Dic₃	1	6	yes	direct product factor
25	C₂	C₂²×C₃⋊D₃	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.