Subgroups — #4493

Order 192.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#108	C₂	1	1	yes	maximal, characteristic
2	#819	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#368	—	3	1	no	maximal, Sylow
5	C₃×M₁₆	—	2	1	no	—
6	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
7	#208	—	2	1	no	—
8	C₃⋊C₁₆	C₄	1	2	yes	—
9	C₂×C₁₆	—	3	1	no	—
10	#108	—	3	1	no	—
11	#108	D₃	1	1	yes	characteristic
12	C₂×C₃×C₄	D₄	1	1	yes	characteristic
13	C₃×C₈	—	4	1	no	—
14	C₃×C₈	C₂×C₄	1	1	yes	characteristic
15	C₃×C₈	Q₈	1	1	yes	characteristic
16	C₃⋊C₈	—	4	1	no	—
17	M₁₆	—	2	1	no	—
18	M₁₆	—	6	1	no	—
19	C₂×C₈	C₂×D₃	1	1	yes	characteristic
20	C₁₆	—	3	2	no	—
21	C₂²×C₃	Q₁₆	1	1	yes	characteristic
22	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
23	C₃×C₄	D₈	1	1	yes	characteristic
24	C₂×C₄	#67	1	1	yes	characteristic
25	C₈	—	4	1	no	—
26	C₈	—	12	1	no	—
27	C₈	Dic₆	1	1	yes	characteristic
28	C₈	C₄×D₃	1	1	yes	characteristic
29	C₂×C₃	—	2	1	no	—
30	C₂×C₃	#107	1	1	yes	characteristic
31	C₂²	#216	1	1	yes	characteristic
32	C₄	Dic₃⋊C₄	1	1	yes	characteristic
33	C₄	#213	1	1	yes	characteristic
34	C₃	#368	1	1	yes	characteristic, complemented, Sylow
35	C₂	—	2	1	no	—
36	C₂	#807	1	1	yes	characteristic

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

N	H ≅ G/N	type
34. C₃	#368	semidirect

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