Subgroups — #4489

Order 192.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#107	C₂	1	1	yes	maximal, characteristic
2	#818	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#366	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₃×C₄⋊C₄	—	2	1	no	—
7	C₄⋊Dic₃	—	2	1	no	—
8	C₃⋊C₁₆	C₄	1	2	yes	complemented
9	C₂×C₁₆	—	3	1	no	—
10	#107	—	3	1	no	—
11	#107	D₃	1	1	yes	characteristic
12	C₂×C₃×C₄	—	4	1	no	—
13	C₂×C₃×C₄	D₄	1	1	yes	characteristic
14	C₂×Dic₃	—	4	1	no	—
15	C₃×C₈	C₂×C₄	1	1	yes	characteristic
16	C₃×C₈	Q₈	1	1	yes	characteristic
17	C₂×C₈	C₂×D₃	1	1	yes	characteristic
18	C₄⋊C₄	—	2	1	no	—
19	C₄⋊C₄	—	6	1	no	—
20	C₁₆	—	3	2	no	—
21	C₂²×C₃	D₈	1	1	yes	characteristic
22	C₃×C₄	—	8	1	no	—
23	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
24	C₃×C₄	Q₁₆	1	1	yes	characteristic
25	Dic₃	—	8	1	no	—
26	C₂×C₄	—	4	1	no	—
27	C₂×C₄	—	12	1	no	—
28	C₂×C₄	#67	1	1	yes	characteristic
29	C₈	Dic₆	1	1	yes	characteristic
30	C₈	C₄×D₃	1	1	yes	characteristic
31	C₂×C₃	#107	1	1	yes	characteristic
32	C₂×C₃	D₁₆	1	1	yes	characteristic
33	C₂×C₃	Q₃₂	1	1	yes	characteristic
34	C₂²	#213	1	1	yes	characteristic
35	C₄	—	8	1	no	—
36	C₄	—	24	1	no	—
37	C₄	Dic₃⋊C₄	1	1	yes	characteristic
38	C₄	#216	1	1	yes	characteristic
39	C₃	#366	1	1	yes	characteristic, complemented, Sylow
40	C₂	#807	1	1	yes	characteristic
41	C₂	#826	1	1	yes	characteristic
42	C₂	#829	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. C₃⋊C₁₆	C₄	semidirect
39. C₃	#366	semidirect

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