Subgroups — #4499

Order 192.

32 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	C₃⋊C₃₂	C₂	1	2	yes	maximal, complemented
3	M₆₄	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₈	C₄	1	1	yes	characteristic
5	C₃×C₁₆	C₄	1	1	yes	characteristic
6	C₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₆	D₃	1	1	yes	characteristic
8	C₃₂	—	3	2	no	—
9	C₂×C₃×C₄	C₈	1	1	yes	characteristic
10	C₃×C₈	C₈	1	1	yes	characteristic
11	C₃×C₈	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈	Dic₃	1	1	yes	characteristic
13	C₁₆	Dic₃	1	1	yes	characteristic
14	C₁₆	C₂×D₃	1	1	yes	characteristic
15	C₂²×C₃	C₁₆	1	1	yes	characteristic
16	C₃×C₄	C₁₆	1	1	yes	characteristic
17	C₃×C₄	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄	C₃⋊C₈	1	1	yes	characteristic
19	C₈	C₃⋊C₈	1	1	yes	characteristic
20	C₈	C₂×Dic₃	1	1	yes	characteristic
21	C₂×C₃	—	2	1	no	—
22	C₂×C₃	C₂×C₁₆	1	1	yes	characteristic
23	C₂²	C₃⋊C₁₆	1	1	yes	characteristic
24	C₄	C₃⋊C₁₆	1	1	yes	characteristic
25	C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
26	C₃	M₆₄	1	1	yes	characteristic, complemented, Sylow
27	C₂	—	2	1	no	—
28	C₂	C₂×C₃⋊C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₃⋊C₃₂	C₂	semidirect
26. C₃	M₆₄	semidirect

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