Subgroups — C₂×#217 #952

Order 96.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃	C₂	1	2	yes	maximal, complemented
3	#217	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₂²⋊C₄	—	3	1	no	maximal, Sylow
5	C₂³×C₃	—	2	4	no	—
6	C₂³×C₃	C₄	1	4	yes	complemented
7	C₂³×C₃	C₂²	1	2	yes	—
8	C₂³×C₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₃	—	2	4	no	—
10	C₂×Dic₃	C₂²	1	4	yes	complemented
11	C₂⁴	D₃	1	1	yes	characteristic
12	C₂²×C₄	—	3	2	no	—
13	C₂²⋊C₄	—	3	4	no	—
14	C₂²×C₃	—	2	8	no	—
15	C₂²×C₃	—	2	4	no	—
16	C₂²×C₃	C₂×C₄	1	2	yes	—
17	C₂²×C₃	C₂×C₄	1	4	yes	complemented
18	C₂²×C₃	D₄	1	4	yes	—
19	C₂²×C₃	C₂³	1	1	yes	characteristic
20	Dic₃	—	2	4	no	—
21	C₂³	—	2	4	no	—
22	C₂³	Dic₃	1	4	yes	complemented
23	C₂³	C₂×D₃	1	2	yes	—
24	C₂³	C₂×D₃	1	1	yes	characteristic
25	C₂×C₄	—	3	4	no	—
26	C₂×C₄	—	6	4	no	—
27	C₂×C₃	—	2	4	no	—
28	C₂×C₃	C₂²⋊C₄	1	4	yes	complemented
29	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₃	C₂×D₄	1	2	yes	—
31	C₂²	—	2	8	no	—
32	C₂²	—	2	4	no	—
33	C₂²	C₂×Dic₃	1	2	yes	—
34	C₂²	C₂×Dic₃	1	4	yes	complemented
35	C₂²	#67	1	4	yes	—
36	C₂²	C₂²×D₃	1	1	yes	characteristic
37	C₄	—	6	4	no	—
38	C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
39	C₂	—	2	4	no	—
40	C₂	#217	1	4	yes	direct product factor
41	C₂	C₂²×Dic₃	1	1	yes	characteristic
42	C₂	C₂×#67	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.