Subgroups — C₃×#97 #840

Order 96.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈	C₂	1	2	yes	maximal
2	C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	#97	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₄	C₄	1	2	yes	—
5	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₃×C₈	C₄	1	4	yes	complemented
7	C₂×C₈	C₂×C₃	1	2	yes	—
8	C₄²	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
10	C₃×C₄	—	2	2	no	—
11	C₃×C₄	C₂×C₄	1	2	yes	—
12	C₂×C₄	C₃×C₄	1	2	yes	—
13	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
14	C₈	C₃×C₄	1	4	yes	complemented
15	C₂×C₃	C₄²	1	1	yes	characteristic
16	C₂×C₃	M₁₆	1	2	yes	—
17	C₂²	C₂×C₃×C₄	1	1	yes	characteristic
18	C₄	—	2	2	no	—
19	C₄	C₂×C₃×C₄	1	2	yes	—
20	C₃	#97	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	C₃×C₄²	1	1	yes	characteristic
22	C₂	C₃×M₁₆	1	2	yes	—

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.