Subgroups — #68057

Order 384.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4693	C₂	1	3	yes	maximal
2	#4680	C₂	1	3	yes	maximal, complemented
3	C₃×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
4	#1705	—	3	1	no	maximal, Sylow
5	C₂×#204	—	2	6	no	—
6	#874	C₂²	1	1	yes	characteristic
7	#869	C₂²	1	3	yes	—
8	C₃×C₄×C₈	C₂²	1	3	yes	—
9	#817	—	2	6	no	—
10	#498	—	3	3	no	—
11	#492	—	3	3	no	—
12	C₈²	D₃	1	1	yes	characteristic, complemented
13	C₂×D₁₂	—	2	3	no	—
14	C₂×Dic₆	—	2	3	no	—
15	C₂×C₃×C₈	D₄	1	6	yes	—
16	C₃×C₄²	C₂³	1	1	yes	characteristic
17	C₄⋊Dic₃	—	2	6	no	—
18	#204	—	4	12	no	—
19	C₂×SD₁₆	—	6	6	no	—
20	C₄⋊Q₈	—	3	3	no	—
21	#127	—	3	1	no	—
22	#106	—	6	6	no	—
23	C₄×C₈	C₂×D₃	1	3	yes	—
24	C₂²×D₃	—	4	1	no	—
25	C₂×C₃×C₄	C₂×D₄	1	3	yes	—
26	C₂×Dic₃	—	4	3	no	—
27	D₁₂	—	4	6	no	—
28	Dic₆	—	4	6	no	—
29	C₃×C₈	SD₁₆	1	12	yes	complemented
30	C₂×Q₈	—	6	3	no	—
31	C₂×D₄	—	6	3	no	—
32	SD₁₆	—	12	12	no	—
33	C₂×C₈	D₁₂	1	6	yes	—
34	C₄⋊C₄	—	6	6	no	—
35	C₄²	C₂²×D₃	1	1	yes	characteristic
36	C₂²×C₃	#127	1	1	yes	characteristic
37	C₂×D₃	—	8	3	no	—
38	C₃×C₄	C₂×SD₁₆	1	6	yes	—
39	Dic₃	—	8	3	no	—
40	C₂³	—	12	1	no	—
41	Q₈	—	12	6	no	—
42	D₄	—	12	6	no	—
43	C₂×C₄	—	12	3	no	—
44	C₂×C₄	C₂×D₁₂	1	3	yes	—
45	C₈	#204	1	12	yes	complemented
46	C₂×C₃	#492	1	3	yes	—
47	D₃	—	16	1	no	—
48	C₂²	—	24	3	no	—
49	C₂²	#874	1	1	yes	characteristic
50	C₄	—	24	3	no	—
51	C₄	C₂×#204	1	6	yes	—
52	C₃	#1705	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	48	1	no	—
54	C₂	#4693	1	3	yes	—

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.