Subgroups — C₂×C₄⋊(C₃⋊D₃) #3827

Order 144.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
2	C₂×C₃²×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃⋊D₃)	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₂	—	3	4	no	maximal
5	C₂²×C₃²	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊D₃	—	2	4	no	—
7	C₂×C₃⋊D₃	C₂²	1	4	yes	complemented
8	C₃²×C₄	C₂²	1	2	yes	complemented
9	C₂²×D₃	—	3	8	no	—
10	C₂×C₃×C₄	D₃	1	4	yes	complemented
11	D₁₂	—	3	16	no	—
12	C₂×C₃²	D₄	1	2	yes	complemented
13	C₂×C₃²	C₂³	1	1	yes	characteristic
14	C₃⋊D₃	—	2	4	no	—
15	C₂×D₄	—	9	1	no	Sylow
16	C₂²×C₃	C₂×D₃	1	4	yes	—
17	C₂×D₃	—	3	16	no	—
18	C₂×D₃	—	6	16	no	—
19	C₃×C₄	C₂×D₃	1	8	yes	complemented
20	C₃²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
21	C₂³	—	9	2	no	—
22	D₄	—	9	4	no	—
23	C₂×C₄	C₃⋊D₃	1	1	yes	characteristic, complemented
24	C₂×C₃	D₁₂	1	8	yes	complemented
25	C₂×C₃	C₂²×D₃	1	4	yes	—
26	D₃	—	6	16	no	—
27	C₂²	—	9	4	no	—
28	C₂²	—	18	4	no	—
29	C₂²	C₂×C₃⋊D₃	1	1	yes	characteristic
30	C₄	C₂×C₃⋊D₃	1	2	yes	complemented
31	C₃	C₂×D₁₂	1	4	yes	complemented
32	C₂	—	18	4	no	—
33	C₂	C₄⋊(C₃⋊D₃)	1	2	yes	direct product factor
34	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.