Subgroups — C₂×#67 #241

Order 48.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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