Subgroups — #396⋊C₃ #4638

Order 192.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#95⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#396	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂²×A₄	—	4	1	no	maximal
4	C₂×C₄⋊C₄	—	3	1	no	—
5	C₂×C₂²⋊C₄	—	3	1	no	—
6	#95	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×A₄	—	4	2	no	—
8	C₂×A₄	—	4	1	no	—
9	C₂⁴	A₄	1	1	yes	characteristic
10	C₂²×C₄	—	3	1	no	—
11	C₂²×C₄	—	3	1	no	—
12	C₄⋊C₄	—	6	2	no	—
13	C₂²⋊C₄	—	6	2	no	—
14	C₂²×C₃	—	16	1	no	—
15	A₄	—	4	1	no	—
16	C₂³	—	6	1	no	—
17	C₂³	—	6	1	no	—
18	C₂³	SL(2,𝔽₃)	1	2	yes	—
19	C₂³	C₂×A₄	1	1	yes	characteristic
20	C₂×C₄	—	3	2	no	—
21	C₂×C₄	—	6	1	no	—
22	C₂×C₄	—	6	1	no	—
23	C₂×C₄	—	6	1	no	—
24	C₂×C₄	—	6	1	no	—
25	C₂×C₄	—	6	1	no	—
26	C₂×C₃	—	16	2	no	—
27	C₂×C₃	—	16	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	—	4	1	no	—
31	C₂²	—	6	2	no	—
32	C₂²	—	12	1	no	—
33	C₂²	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
34	C₄	—	6	2	no	—
35	C₄	—	12	1	no	—
36	C₃	—	16	1	no	Sylow
37	C₂	—	3	1	no	—
38	C₂	—	3	1	no	—
39	C₂	—	4	2	no	—
40	C₂	#126⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#126⋊C₃
commutator, cosocle, hypocenter	#95	C₂×C₃
Frattini, socle	C₂³	C₂×A₄
Fitting	#396	C₃
LCS	G ▷ #95
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.