Subgroups — D₃×Q₁₆ #917

Order 96.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×Q₈	C₂	1	2	yes	maximal
2	C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#216	C₂	1	2	yes	maximal, complemented
4	Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆	—	3	1	no	maximal, Sylow
7	C₃×Q₈	C₂²	1	2	yes	—
8	C₄×D₃	—	2	2	no	—
9	C₄×D₃	C₂²	1	1	yes	characteristic
10	Dic₆	—	2	2	no	—
11	Dic₆	C₂²	1	2	yes	—
12	C₃×C₈	C₂²	1	1	yes	characteristic
13	C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×Q₈	—	3	2	no	—
15	Q₁₆	—	3	2	no	—
16	Q₁₆	—	3	1	no	—
17	Q₁₆	D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₈	—	3	1	no	—
19	C₂×D₃	D₄	1	1	yes	characteristic
20	C₃×C₄	—	2	2	no	—
21	C₃×C₄	C₂³	1	1	yes	characteristic
22	Dic₃	—	2	2	no	—
23	Dic₃	D₄	1	1	yes	characteristic
24	Q₈	—	3	2	no	—
25	Q₈	—	6	2	no	—
26	Q₈	C₂×D₃	1	2	yes	—
27	C₂×C₄	—	3	1	no	—
28	C₂×C₄	—	6	2	no	—
29	C₈	—	3	1	no	—
30	C₈	C₂×D₃	1	1	yes	characteristic
31	C₂×C₃	C₂×D₄	1	1	yes	characteristic
32	D₃	Q₁₆	1	2	yes	direct product factor
33	C₂²	—	3	1	no	—
34	C₄	—	2	2	no	—
35	C₄	—	3	1	no	—
36	C₄	—	6	2	no	—
37	C₄	C₂²×D₃	1	1	yes	characteristic
38	C₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₂	—	3	2	no	—
40	C₂	D₃×D₄	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.