Subgroups — C₃×M₃₂ #853

Order 96.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₆	C₂	1	2	yes	maximal, complemented
3	M₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₄	C₄	1	1	yes	characteristic
5	C₃×C₈	C₄	1	1	yes	characteristic
6	C₃×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₈	C₂×C₃	1	1	yes	characteristic
8	C₁₆	C₂×C₃	1	2	yes	complemented
9	C₂²×C₃	C₈	1	1	yes	characteristic
10	C₃×C₄	C₈	1	1	yes	characteristic
11	C₃×C₄	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄	C₃×C₄	1	1	yes	characteristic
13	C₈	C₃×C₄	1	1	yes	characteristic
14	C₈	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃	—	2	1	no	—
16	C₂×C₃	C₂×C₈	1	1	yes	characteristic
17	C₂²	C₃×C₈	1	1	yes	characteristic
18	C₄	C₃×C₈	1	1	yes	characteristic
19	C₄	C₂×C₃×C₄	1	1	yes	characteristic
20	C₃	M₃₂	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	—	2	1	no	—
22	C₂	C₂×C₃×C₈	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.