Subgroups — #67794

Order 384.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#494	C₂	1	1	yes	maximal, characteristic
2	#4463	C₂	1	2	yes	maximal
3	#1358	—	3	1	no	maximal, Sylow
4	C₂×C₃×Q₁₆	—	2	2	no	—
5	C₃×C₄⋊Q₈	C₄	1	2	yes	—
6	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
7	#812	—	2	2	no	—
8	#494	D₃	1	1	yes	characteristic
9	#364	—	3	2	no	—
10	C₂×C₃×Q₈	—	2	2	no	—
11	C₃×Q₁₆	—	4	2	no	—
12	C₃×Q₁₆	—	4	2	no	—
13	C₂×C₃×C₈	D₄	1	2	yes	—
14	C₃×C₄⋊C₄	—	4	2	no	—
15	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
16	C₃⋊C₁₆	—	4	2	no	—
17	C₂×Q₁₆	—	2	2	no	—
18	C₄⋊Q₈	Dic₃	1	2	yes	—
19	M₃₂	—	6	2	no	—
20	C₄×C₈	C₂×D₃	1	1	yes	characteristic
21	C₃×Q₈	—	4	4	no	—
22	C₂×C₃×C₄	—	2	1	no	—
23	C₂×C₃×C₄	—	4	2	no	—
24	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
25	C₃×C₈	D₈	1	2	yes	—
26	C₃×C₈	SD₁₆	1	2	yes	—
27	C₂×Q₈	—	2	2	no	—
28	Q₁₆	—	4	2	no	—
29	Q₁₆	—	4	2	no	—
30	C₂×C₈	#67	1	2	yes	—
31	C₄⋊C₄	—	4	2	no	—
32	C₄²	C₂×Dic₃	1	1	yes	characteristic
33	C₁₆	—	12	2	no	—
34	C₂²×C₃	#100	1	1	yes	characteristic
35	C₃×C₄	—	2	2	no	—
36	C₃×C₄	—	8	2	no	—
37	C₃×C₄	#102	1	2	yes	—
38	Q₈	—	4	4	no	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	—	4	2	no	—
41	C₂×C₄	#217	1	1	yes	characteristic
42	C₈	#213	1	2	yes	—
43	C₈	#214	1	2	yes	—
44	C₂×C₃	—	2	1	no	—
45	C₂×C₃	#331	1	1	yes	characteristic
46	C₂²	#833	1	1	yes	characteristic
47	C₄	—	2	2	no	—
48	C₄	—	8	2	no	—
49	C₄	#832	1	2	yes	—
50	C₃	#1358	1	1	yes	characteristic, complemented, Sylow
51	C₂	—	2	1	no	—
52	C₂	#4544	1	1	yes	characteristic

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

N	H ≅ G/N	type
50. C₃	#1358	semidirect

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