Subgroups — C₄×C₃⋊Dic₃ #3749

Order 144.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊Dic₃	C₂	1	2	yes	maximal
3	C₄×Dic₃	—	3	4	no	maximal
4	C₂²×C₃²	C₂²	1	1	yes	characteristic
5	C₃²×C₄	C₄	1	2	yes	complemented
6	C₃⋊Dic₃	C₄	1	4	yes	direct product factor
7	C₂×C₃×C₄	D₃	1	4	yes	—
8	C₂×Dic₃	—	3	8	no	—
9	C₂×C₃²	C₂×C₄	1	2	yes	—
10	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
11	C₄²	—	9	1	no	Sylow
12	C₂²×C₃	C₂×D₃	1	4	yes	—
13	C₃×C₄	Dic₃	1	8	yes	complemented
14	Dic₃	—	3	16	no	—
15	C₃²	C₄²	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₄	—	9	2	no	—
17	C₂×C₄	C₃⋊D₃	1	1	yes	characteristic
18	C₂×C₃	C₄×D₃	1	8	yes	—
19	C₂×C₃	C₂×Dic₃	1	4	yes	—
20	C₂²	C₂×C₃⋊D₃	1	1	yes	characteristic
21	C₄	—	9	4	no	—
22	C₄	C₃⋊Dic₃	1	2	yes	direct product factor
23	C₃	C₄×Dic₃	1	4	yes	complemented
24	C₂	C₄×C₃⋊D₃	1	2	yes	—
25	C₂	C₂×C₃⋊Dic₃	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.