Subgroups — C₄⋊(C₃⋊D₉) #6228

Order 216.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₉	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃⋊D₃)	—	3	1	no	maximal
4	D₃₆	—	3	3	no	maximal
5	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
6	C₃⋊D₉	—	2	2	no	—
7	C₂×C₃⋊D₃	—	3	2	no	—
8	C₃²×C₄	D₃	1	1	yes	characteristic
9	C₂×D₉	—	3	6	no	—
10	C₄×C₉	D₃	1	3	yes	complemented
11	C₃×C₉	D₄	1	1	yes	characteristic, complemented, Sylow
12	D₁₂	—	9	3	no	—
13	D₁₂	—	9	1	no	—
14	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
15	C₃⋊D₃	—	6	2	no	—
16	C₂×C₉	C₂×D₃	1	3	yes	—
17	D₉	—	6	6	no	—
18	C₂×D₃	—	9	6	no	—
19	C₂×D₃	—	9	2	no	—
20	C₃×C₄	D₉	1	3	yes	complemented
21	C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
22	C₃²	D₁₂	1	1	yes	characteristic
23	C₉	D₁₂	1	3	yes	complemented
24	D₄	—	27	1	no	Sylow
25	C₂×C₃	C₂×D₉	1	3	yes	—
26	C₂×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
27	D₃	—	18	6	no	—
28	D₃	—	18	2	no	—
29	C₂²	—	27	2	no	—
30	C₄	C₃⋊D₉	1	1	yes	characteristic, complemented
31	C₃	D₃₆	1	3	yes	complemented
32	C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
33	C₂	—	54	2	no	—
34	C₂	C₂×C₃⋊D₉	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.