Subgroups — C₂×#216 #943

Order 96.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₆	C₂	1	1	yes	maximal, characteristic
3	#216	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆	—	3	1	no	maximal, Sylow
6	C₃×Q₈	—	2	1	no	—
7	C₃×Q₈	C₂²	1	2	yes	—
8	C₂×C₃×C₄	—	2	1	no	—
9	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂×Dic₃	—	2	1	no	—
11	Dic₆	—	2	1	no	—
12	Dic₆	C₂²	1	2	yes	—
13	C₃⋊C₈	C₂²	1	2	yes	—
14	C₂×Q₈	—	3	1	no	—
15	C₂×Q₈	D₃	1	1	yes	characteristic
16	Q₁₆	—	3	4	no	—
17	C₂×C₈	—	3	1	no	—
18	C₂²×C₃	D₄	1	1	yes	characteristic
19	C₃×C₄	—	2	2	no	—
20	C₃×C₄	D₄	1	1	yes	characteristic
21	C₃×C₄	C₂³	1	1	yes	characteristic
22	Dic₃	—	2	2	no	—
23	Q₈	—	2	1	no	—
24	Q₈	—	3	2	no	—
25	Q₈	—	6	1	no	—
26	Q₈	C₂×D₃	1	2	yes	—
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	6	1	no	—
29	C₂×C₄	C₂×D₃	1	1	yes	characteristic
30	C₈	—	3	2	no	—
31	C₂×C₃	Q₁₆	1	2	yes	complemented
32	C₂×C₃	C₂×D₄	1	1	yes	characteristic
33	C₂²	#67	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	6	2	no	—
36	C₄	#67	1	1	yes	characteristic
37	C₄	C₂²×D₃	1	1	yes	characteristic
38	C₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₂	#216	1	2	yes	direct product factor
40	C₂	C₂×#67	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.