Subgroups — #4504

Order 192.

46 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	#818	C₂	1	2	yes	maximal
3	#366	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
5	C₄⋊Dic₃	—	2	2	no	—
6	C₃×C₁₆	C₄	1	2	yes	complemented
7	C₂×C₁₆	D₃	1	1	yes	characteristic
8	#107	—	3	2	no	—
9	C₂×C₃×C₄	D₄	1	1	yes	characteristic
10	C₂×Dic₃	—	4	2	no	—
11	C₃×C₈	C₂×C₄	1	1	yes	characteristic
12	C₃×C₈	Q₈	1	1	yes	characteristic
13	C₂×C₈	C₂×D₃	1	1	yes	characteristic
14	C₄⋊C₄	—	6	2	no	—
15	C₁₆	Dic₃	1	2	yes	complemented
16	C₂²×C₃	D₈	1	1	yes	characteristic
17	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
18	C₃×C₄	Q₁₆	1	1	yes	characteristic
19	Dic₃	—	8	2	no	—
20	C₂×C₄	—	12	2	no	—
21	C₂×C₄	D₁₂	1	1	yes	characteristic
22	C₈	Dic₆	1	1	yes	characteristic
23	C₈	C₂×Dic₃	1	1	yes	characteristic
24	C₂×C₃	#107	1	1	yes	characteristic
25	C₂×C₃	D₁₆	1	1	yes	characteristic
26	C₂×C₃	Q₃₂	1	1	yes	characteristic
27	C₂²	D₂₄	1	1	yes	characteristic
28	C₄	—	24	2	no	—
29	C₄	Dic₁₂	1	1	yes	characteristic
30	C₄	C₄⋊Dic₃	1	1	yes	characteristic
31	C₃	#366	1	1	yes	characteristic, complemented, Sylow
32	C₂	D₄₈	1	1	yes	characteristic
33	C₂	Dic₂₄	1	1	yes	characteristic
34	C₂	#818	1	1	yes	characteristic

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

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