Subgroups — C₂²×#67 #1012

Order 96.

236 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, complemented
2	C₂³×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#67	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄	—	3	1	no	maximal, Sylow
6	C₂³×C₃	—	2	4	no	—
7	C₂³×C₃	C₂²	1	1	yes	characteristic
8	C₂³×C₃	C₂²	1	6	yes	complemented
9	C₂²×D₃	—	2	4	no	—
10	C₂²×D₃	C₂²	1	6	yes	complemented
11	#67	C₂²	1	16	yes	direct product factor
12	C₂×Dic₃	C₂²	1	6	yes	complemented
13	C₂⁴	—	3	1	no	—
14	C₂⁴	D₃	1	1	yes	characteristic, complemented
15	C₂×D₄	—	3	12	no	—
16	C₂²×C₄	—	3	1	no	—
17	C₂²×C₃	—	2	12	no	—
18	C₂²×C₃	D₄	1	4	yes	complemented
19	C₂²×C₃	C₂³	1	3	yes	—
20	C₂²×C₃	C₂³	1	4	yes	complemented
21	C₂×D₃	—	2	12	no	—
22	C₂×D₃	C₂³	1	4	yes	complemented
23	Dic₃	C₂³	1	4	yes	complemented
24	C₂³	—	2	4	no	—
25	C₂³	—	3	6	no	—
26	C₂³	—	6	4	no	—
27	C₂³	C₂×D₃	1	1	yes	characteristic
28	C₂³	C₂×D₃	1	6	yes	complemented
29	D₄	—	3	16	no	—
30	C₂×C₄	—	3	6	no	—
31	C₂×C₃	—	2	4	no	—
32	C₂×C₃	C₂×D₄	1	6	yes	complemented
33	C₂×C₃	C₂⁴	1	1	yes	characteristic
34	D₃	—	2	4	no	—
35	C₂²	—	2	12	no	—
36	C₂²	—	3	4	no	—
37	C₂²	—	6	12	no	—
38	C₂²	#67	1	4	yes	direct product factor
39	C₂²	C₂²×D₃	1	3	yes	—
40	C₂²	C₂²×D₃	1	4	yes	complemented
41	C₄	—	3	4	no	—
42	C₃	C₂²×D₄	1	1	yes	characteristic, complemented, Sylow
43	C₂	—	2	4	no	—
44	C₂	—	6	4	no	—
45	C₂	C₂×#67	1	6	yes	direct product factor
46	C₂	C₂³×D₃	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.