Subgroups — #5388

Order 192.

67 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#226	C₂	1	1	yes	maximal, characteristic
2	C₄×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
3	#859	C₂	1	1	yes	maximal, characteristic
4	#441	—	3	1	no	maximal, Sylow
5	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
6	#226	C₄	1	2	yes	complemented
7	Dic₃⋊C₄	—	4	1	no	maximal
8	C₂×Q₁₆	—	3	1	no	—
9	C₄×Q₈	—	3	1	no	—
10	C₄×Q₈	D₃	1	1	yes	characteristic
11	#106	—	3	1	no	—
12	#103	—	3	1	no	—
13	#103	—	3	1	no	—
14	#97	—	3	1	no	—
15	C₂×C₃×C₄	—	4	1	no	—
16	C₂×Dic₃	—	4	1	no	—
17	C₂×Dic₃	—	4	1	no	—
18	SL(2,𝔽₃)	C₂×C₄	1	1	yes	characteristic
19	C₂×Q₈	—	3	1	no	—
20	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
21	Q₁₆	—	3	2	no	—
22	Q₁₆	—	3	2	no	—
23	C₂×C₈	—	3	1	no	—
24	C₂×C₈	—	3	1	no	—
25	C₄⋊C₄	—	3	1	no	—
26	C₄⋊C₄	—	3	1	no	—
27	C₄⋊C₄	—	6	1	no	—
28	C₄²	—	3	1	no	—
29	C₄²	—	6	1	no	—
30	C₂²×C₃	—	4	1	no	—
31	C₃×C₄	—	8	1	no	—
32	Dic₃	—	4	2	no	—
33	Dic₃	—	8	1	no	—
34	Q₈	—	3	1	no	—
35	Q₈	—	3	2	no	—
36	Q₈	—	6	1	no	—
37	Q₈	C₄×D₃	1	1	yes	characteristic
38	C₂×C₄	—	3	1	no	—
39	C₂×C₄	—	3	1	no	—
40	C₂×C₄	—	6	1	no	—
41	C₂×C₄	—	6	1	no	—
42	C₂×C₄	S₄	1	1	yes	characteristic
43	C₈	—	3	2	no	—
44	C₈	—	6	1	no	—
45	C₂×C₃	—	4	1	no	—
46	C₂×C₃	—	4	1	no	—
47	C₂×C₃	—	4	1	no	—
48	C₂²	C₂×S₄	1	1	yes	characteristic
49	C₄	—	2	1	no	—
50	C₄	—	3	1	no	—
51	C₄	—	3	1	no	—
52	C₄	—	6	2	no	—
53	C₄	—	6	1	no	—
54	C₄	—	12	1	no	—
55	C₃	—	4	1	no	Sylow
56	C₂	C₄×S₄	1	1	yes	characteristic
57	C₂	#983	1	1	yes	characteristic
58	C₂	#984	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. #226	C₄	semidirect

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