Subgroups — #1726⋊C₃ #68021

Order 384.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#376⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#1726	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₈×A₄	—	4	1	no	maximal
4	#95⋊C₃	C₄	1	1	yes	characteristic
5	C₂×#97	—	3	1	no	—
6	C₂×C₄×C₈	—	3	1	no	—
7	#376	C₂×C₃	1	1	yes	characteristic
8	C₄×A₄	—	4	1	no	—
9	C₂²×C₈	—	3	1	no	—
10	C₂²×C₈	A₄	1	1	yes	characteristic
11	C₂×C₄²	—	3	1	no	—
12	#97	—	3	4	no	—
13	C₄×C₈	—	3	2	no	—
14	C₄×C₈	—	3	2	no	—
15	#95	—	3	1	no	—
16	#95	C₃×C₄	1	1	yes	characteristic
17	C₂×A₄	—	4	1	no	—
18	C₃×C₈	—	16	1	no	—
19	C₂²×C₄	—	3	1	no	—
20	C₂²×C₄	—	3	1	no	—
21	C₂²×C₄	C₂×A₄	1	1	yes	characteristic
22	C₂×C₈	—	3	2	no	—
23	C₂×C₈	—	3	4	no	—
24	C₂×C₈	—	3	1	no	—
25	C₂×C₈	—	3	1	no	—
26	C₄²	—	3	2	no	—
27	C₄²	—	3	2	no	—
28	A₄	—	4	1	no	—
29	C₃×C₄	—	16	1	no	—
30	C₂³	C₄×A₄	1	1	yes	characteristic
31	C₂×C₄	—	3	1	no	—
32	C₂×C₄	—	3	1	no	—
33	C₂×C₄	—	3	2	no	—
34	C₂×C₄	—	3	2	no	—
35	C₂×C₄	—	6	2	no	—
36	C₂×C₄	—	6	1	no	—
37	C₂×C₄	—	6	1	no	—
38	C₈	—	3	4	no	—
39	C₈	—	3	1	no	—
40	C₈	C₄²⋊C₃	1	1	yes	characteristic
41	C₂×C₃	—	16	1	no	—
42	C₂²	—	3	1	no	—
43	C₂²	—	3	1	no	—
44	C₂²	#131⋊C₃	1	1	yes	characteristic
45	C₄	—	3	1	no	—
46	C₄	—	6	2	no	—
47	C₄	—	6	2	no	—
48	C₄	C₂×C₄²⋊C₃	1	1	yes	characteristic
49	C₃	—	16	1	no	Sylow
50	C₂	—	3	1	no	—
51	C₂	—	3	1	no	—
52	C₂	C₄×C₄²⋊C₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #1726	C₃	semidirect

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