Subgroups — #798

Order 96.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	M₃₂	—	3	1	no	maximal, Sylow
5	C₄×D₃	C₄	1	1	yes	characteristic
6	C₃×C₈	C₂²	1	1	yes	characteristic
7	C₃⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₈	—	3	1	no	—
9	C₁₆	—	3	1	no	—
10	C₁₆	D₃	1	1	yes	characteristic, complemented
11	C₂×D₃	C₈	1	1	yes	characteristic
12	C₃×C₄	C₂×C₄	1	1	yes	characteristic
13	Dic₃	C₈	1	1	yes	characteristic
14	C₂×C₄	—	3	1	no	—
15	C₈	—	3	1	no	—
16	C₈	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃	C₂×C₈	1	1	yes	characteristic
18	D₃	—	2	1	no	—
19	C₂²	—	3	1	no	—
20	C₄	—	3	1	no	—
21	C₄	C₄×D₃	1	1	yes	characteristic
22	C₃	M₃₂	1	1	yes	characteristic, complemented, Sylow
23	C₂	—	6	1	no	—
24	C₂	D₃×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.