Subgroups — #1747⋊C₃ #68023

Order 384.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#338⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#1747	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₈×A₄	—	4	1	no	maximal
4	#405	—	3	1	no	—
5	#338	C₂×C₃	1	1	yes	characteristic
6	H(3,ℤ/4)	—	3	1	no	—
7	C₄×A₄	—	4	1	no	—
8	C₂×M₁₆	—	3	1	no	—
9	C₂²×C₈	A₄	1	1	yes	characteristic
10	#117	—	3	1	no	—
11	#97	—	3	2	no	—
12	C₄×C₈	—	3	2	no	—
13	C₂×A₄	—	4	1	no	—
14	C₃×C₈	—	16	1	no	—
15	C₂²×C₄	C₂×A₄	1	1	yes	characteristic
16	M₁₆	—	6	2	no	—
17	C₂×C₈	—	3	1	no	—
18	C₂×C₈	—	3	1	no	—
19	C₂×C₈	—	3	2	no	—
20	C₄⋊C₄	—	6	1	no	—
21	C₂²⋊C₄	—	6	1	no	—
22	C₄²	—	3	2	no	—
23	A₄	—	4	1	no	—
24	C₃×C₄	—	16	1	no	—
25	C₂³	#41⋊C₃	1	1	yes	characteristic
26	C₂×C₄	—	3	1	no	—
27	C₂×C₄	—	3	1	no	—
28	C₂×C₄	—	6	2	no	—
29	C₈	—	3	1	no	—
30	C₈	—	6	2	no	—
31	C₈	C₄²⋊C₃	1	1	yes	characteristic
32	C₂×C₃	—	16	1	no	—
33	C₂²	—	3	1	no	—
34	C₂²	—	4	1	no	—
35	C₄	—	3	1	no	—
36	C₄	—	12	2	no	—
37	C₄	C₂×C₄²⋊C₃	1	1	yes	characteristic
38	C₃	—	16	1	no	Sylow
39	C₂	—	6	1	no	—
40	C₂	#376⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	C₄²⋊C₃
commutator, cosocle, hypocenter	#338	C₂×C₃
Frattini	C₂²×C₄	C₂×A₄
Fitting	#1747	C₃
socle	C₂	#376⋊C₃
prime radical	#338⋊C₃	C₂
LCS	G ▷ #338
UCS	C₁ ◁ C₈

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

N	H ≅ G/N	type
2. #1747	C₃	semidirect

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