Subgroups — C₂×#4179 #66381

Order 324.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#732	C₂	1	1	yes	maximal, characteristic, complemented
2	#4179	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₃⋊D₃)⋊C₃	—	3	1	no	maximal
5	#732	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×H(3,𝔽₃)	—	2	1	no	—
7	C₂×H(3,𝔽₃)	D₃	1	1	yes	characteristic
8	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃⋊D₉	C₂×C₃	1	2	yes	complemented
10	(C₃⋊D₃)⋊C₃	—	3	2	no	—
11	C₂×C₃⋊D₃	—	3	1	no	—
12	C₂×C₃×D₃	—	9	1	no	—
13	C₂×D₉	—	9	1	no	—
14	H(3,𝔽₃)	—	2	1	no	—
15	H(3,𝔽₃)	C₂×D₃	1	1	yes	characteristic
16	C₃×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
17	C₂×C₃²	—	3	1	no	—
18	C₂×C₃²	—	6	1	no	—
19	C₂×C₃²	C₃×D₃	1	1	yes	characteristic
20	C₃⋊D₃	—	3	2	no	—
21	C₃×D₃	—	9	2	no	—
22	C₂×C₉	—	3	1	no	—
23	D₉	—	9	2	no	—
24	C₂²×C₃	—	27	1	no	—
25	C₂×D₃	—	9	1	no	—
26	C₂×D₃	—	27	1	no	—
27	C₃²	—	3	1	no	—
28	C₃²	—	6	1	no	—
29	C₃²	C₂×C₃×D₃	1	1	yes	characteristic
30	C₉	—	3	1	no	—
31	C₂×C₃	—	3	1	no	—
32	C₂×C₃	—	9	1	no	—
33	C₂×C₃	—	18	1	no	—
34	C₂×C₃	—	27	2	no	—
35	C₂×C₃	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
36	D₃	—	9	2	no	—
37	D₃	—	27	2	no	—
38	C₂²	—	27	1	no	Sylow
39	C₃	—	3	1	no	—
40	C₃	—	9	1	no	—
41	C₃	—	18	1	no	—
42	C₃	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
43	C₂	—	27	2	no	—
44	C₂	#4179	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#4179
commutator, cosocle, hypocenter	C₃×C₉	C₂²×C₃
Frattini	C₃²	C₂×C₃×D₃
Fitting	C₂×#732	C₂
socle	C₂×C₃	(C₃⋊D₃)⋊C₃
LCS	G ▷ C₃×C₉
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.