Subgroups — #4506

Order 192.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	#819	C₂	1	2	yes	maximal
3	#368	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
5	#208	—	2	2	no	—
6	C₃×C₁₆	C₄	1	2	yes	—
7	C₂×C₁₆	D₃	1	1	yes	characteristic
8	#108	—	3	2	no	—
9	C₂×C₃×C₄	D₄	1	1	yes	characteristic
10	C₃×C₈	C₂×C₄	1	1	yes	characteristic
11	C₃×C₈	Q₈	1	1	yes	characteristic
12	C₃⋊C₈	—	4	2	no	—
13	M₁₆	—	6	2	no	—
14	C₂×C₈	C₂×D₃	1	1	yes	characteristic
15	C₁₆	Dic₃	1	2	yes	—
16	C₂²×C₃	Q₁₆	1	1	yes	characteristic
17	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
18	C₃×C₄	D₈	1	1	yes	characteristic
19	C₂×C₄	D₁₂	1	1	yes	characteristic
20	C₈	—	12	2	no	—
21	C₈	Dic₆	1	1	yes	characteristic
22	C₈	C₂×Dic₃	1	1	yes	characteristic
23	C₂×C₃	—	2	1	no	—
24	C₂×C₃	#107	1	1	yes	characteristic
25	C₂²	Dic₁₂	1	1	yes	characteristic
26	C₄	D₂₄	1	1	yes	characteristic
27	C₄	C₄⋊Dic₃	1	1	yes	characteristic
28	C₃	#368	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	2	1	no	—
30	C₂	#818	1	1	yes	characteristic

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

N	H ≅ G/N	type
28. C₃	#368	semidirect

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