Subgroups — C₄⋊(C₃⋊Dic₃) #3751

Order 144.

78 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	—	2	2	no	—
7	C₂×C₃×C₄	D₃	1	4	yes	—
8	C₂×Dic₃	—	3	8	no	—
9	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
10	C₂×C₃²	D₄	1	1	yes	characteristic
11	C₂×C₃²	Q₈	1	1	yes	characteristic
12	C₄⋊C₄	—	9	1	no	Sylow
13	C₂²×C₃	C₂×D₃	1	4	yes	—
14	C₃×C₄	Dic₃	1	8	yes	complemented
15	Dic₃	—	6	8	no	—
16	C₃²	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₄	—	9	2	no	—
18	C₂×C₄	C₃⋊D₃	1	1	yes	characteristic
19	C₂×C₃	Dic₆	1	4	yes	—
20	C₂×C₃	D₁₂	1	4	yes	—
21	C₂×C₃	C₂×Dic₃	1	4	yes	—
22	C₂²	C₂×C₃⋊D₃	1	1	yes	characteristic
23	C₄	—	18	2	no	—
24	C₄	C₃⋊Dic₃	1	2	yes	complemented
25	C₃	C₄⋊Dic₃	1	4	yes	complemented
26	C₂	#634	1	1	yes	characteristic
27	C₂	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
28	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.