Subgroups — #12902⋊C₃ #11709191

Order 768.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1747⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#12902	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	A₄×C₁₆	—	4	1	no	maximal
4	#338⋊C₃	C₄	1	1	yes	characteristic
5	#2153	—	3	1	no	—
6	#2151	—	3	1	no	—
7	#1747	C₂×C₃	1	1	yes	characteristic
8	C₈×A₄	—	4	1	no	—
9	C₂×M₃₂	—	3	1	no	—
10	C₂²×C₁₆	A₄	1	1	yes	characteristic
11	#405	—	3	1	no	—
12	#364	—	6	2	no	—
13	C₄⋊C₁₆	—	6	2	no	—
14	#338	C₃×C₄	1	1	yes	characteristic
15	H(3,ℤ/4)	—	3	1	no	—
16	C₄×A₄	—	4	1	no	—
17	C₃×C₁₆	—	16	1	no	—
18	C₂×M₁₆	—	3	1	no	—
19	C₂²×C₈	C₂×A₄	1	1	yes	characteristic
20	#117	—	3	1	no	—
21	M₃₂	—	6	2	no	—
22	C₂×C₁₆	—	6	1	no	—
23	C₂×C₁₆	—	6	1	no	—
24	#97	—	3	2	no	—
25	C₄×C₈	—	3	2	no	—
26	C₂×A₄	—	4	1	no	—
27	C₃×C₈	—	16	1	no	—
28	C₂²×C₄	C₄×A₄	1	1	yes	characteristic
29	M₁₆	—	6	2	no	—
30	C₂×C₈	—	3	1	no	—
31	C₂×C₈	—	3	1	no	—
32	C₂×C₈	—	3	2	no	—
33	C₄⋊C₄	—	6	1	no	—
34	C₂²⋊C₄	—	6	1	no	—
35	C₄²	—	3	2	no	—
36	C₁₆	—	4	1	no	—
37	C₁₆	—	12	1	no	—
38	A₄	—	4	1	no	—
39	C₃×C₄	—	16	1	no	—
40	C₂³	#131⋊C₃	1	1	yes	characteristic
41	C₂×C₄	—	3	1	no	—
42	C₂×C₄	—	3	1	no	—
43	C₂×C₄	—	6	2	no	—
44	C₈	—	3	1	no	—
45	C₈	—	6	2	no	—
46	C₈	#127⋊C₃	1	1	yes	characteristic
47	C₂×C₃	—	16	1	no	—
48	C₂²	—	3	1	no	—
49	C₂²	—	4	1	no	—
50	C₄	—	3	1	no	—
51	C₄	—	12	2	no	—
52	C₄	#384⋊C₃	1	1	yes	characteristic
53	C₃	—	16	1	no	Sylow
54	C₂	—	6	1	no	—
55	C₂	#1843⋊C₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #12902	C₃	semidirect

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