Subgroups — #395⋊C₃ #4637

Order 192.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	#395	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₄×A₄	—	4	1	no	maximal
4	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic
5	C₂×C₄⋊C₄	—	3	1	no	—
6	#95	—	3	1	no	—
7	C₂×A₄	—	4	1	no	—
8	SL(2,𝔽₃)	—	8	2	no	—
9	C₂×Q₈	—	6	2	no	—
10	C₂²×C₄	—	3	1	no	—
11	C₂²×C₄	—	3	1	no	—
12	C₂²×C₄	A₄	1	1	yes	characteristic
13	C₄⋊C₄	—	6	2	no	—
14	A₄	—	4	1	no	—
15	C₃×C₄	—	16	1	no	—
16	C₂³	C₂×A₄	1	1	yes	characteristic
17	Q₈	—	2	2	no	—
18	Q₈	—	6	2	no	—
19	C₂×C₄	—	3	2	no	—
20	C₂×C₄	—	3	2	no	—
21	C₂×C₄	—	6	1	no	—
22	C₂×C₄	—	6	1	no	—
23	C₂×C₄	—	6	2	no	—
24	C₂×C₄	—	6	1	no	—
25	C₂×C₃	—	16	1	no	—
26	C₂²	—	3	1	no	—
27	C₂²	—	3	1	no	—
28	C₂²	#41⋊C₃	1	1	yes	characteristic
29	C₄	—	4	1	no	—
30	C₄	—	6	2	no	—
31	C₄	—	6	2	no	—
32	C₃	—	16	1	no	Sylow
33	C₂	—	3	1	no	—
34	C₂	—	3	1	no	—
35	C₂	#120⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#120⋊C₃
commutator, cosocle, hypocenter	C₂²×Q₈	C₂×C₃
Frattini, socle	C₂³	C₂×A₄
Fitting	#395	C₃
prime radical	C₂²⋊SL(2,𝔽₃)	C₂
LCS	G ▷ C₂²×Q₈
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #395	C₃	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.