Subgroups — C₂×#733⋊C₂ #66388

Order 324.

65 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#733	C₂	1	1	yes	maximal, characteristic, complemented
2	#733⋊C₂	C₂	1	2	yes	maximal, direct product factor
3	C₂×AGL(1,ℤ/9)	—	3	3	no	maximal
4	C₂×C₃×D₉	—	3	1	no	maximal
5	#733	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×3₋¹⁺²	D₃	1	3	yes	—
7	C₂×C₃×C₉	D₃	1	1	yes	characteristic
8	AGL(1,ℤ/9)	—	3	6	no	—
9	C₃×D₉	—	3	2	no	—
10	C₂×C₃×D₃	—	9	1	no	—
11	C₂×D₉	—	3	1	no	—
12	C₂×D₉	—	3	3	no	—
13	3₋¹⁺²	C₂×D₃	1	3	yes	—
14	C₃×C₉	C₂×D₃	1	1	yes	characteristic
15	C₂×C₃²	C₃⋊D₃	1	1	yes	characteristic
16	C₃×D₃	—	9	2	no	—
17	C₂×C₉	—	3	1	no	—
18	C₂×C₉	—	3	3	no	—
19	D₉	—	3	2	no	—
20	D₉	—	3	6	no	—
21	C₂²×C₃	—	27	1	no	—
22	C₂×D₃	—	9	1	no	—
23	C₃²	C₂×C₃⋊D₃	1	1	yes	characteristic
24	C₉	—	3	1	no	—
25	C₉	—	3	3	no	—
26	C₂×C₃	—	3	1	no	—
27	C₂×C₃	—	27	2	no	—
28	C₂×C₃	#272	1	1	yes	characteristic
29	D₃	—	9	2	no	—
30	C₂²	—	27	1	no	Sylow
31	C₃	—	3	1	no	—
32	C₃	C₂×#272	1	1	yes	characteristic
33	C₂	—	27	2	no	—
34	C₂	#733⋊C₂	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#733⋊C₂
commutator, cosocle, hypocenter	#733	C₂²
Frattini	C₃²	C₂×C₃⋊D₃
Fitting	C₂×#733	C₂
socle	C₂×C₃	#272
LCS	G ▷ #733
UCS	C₁ ◁ C₂

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.