Subgroups — C₂×#1088 #6263

Order 216.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#272	C₂	1	1	yes	maximal, characteristic
2	#1088	C₂	1	2	yes	maximal, direct product factor
3	C₂×H(3,𝔽₃)	C₄	1	1	yes	characteristic, complemented
4	#272	C₄	1	1	yes	characteristic, complemented
5	#272	C₂²	1	1	yes	characteristic
6	C₂×C₃×D₃	—	6	2	no	—
7	H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₄	—	9	1	no	maximal
9	C₂×C₃²	—	2	2	no	—
10	C₃×D₃	—	6	2	no	—
11	C₃×D₃	—	6	2	no	—
12	C₂²×C₃	—	9	1	no	—
13	C₂×D₃	—	6	2	no	—
14	C₃×C₄	—	9	2	no	—
15	C₃²	—	2	2	no	—
16	C₂×C₄	—	9	1	no	Sylow
17	C₂×C₃	—	6	2	no	—
18	C₂×C₃	—	9	1	no	—
19	C₂×C₃	—	9	1	no	—
20	C₂×C₃	#157	1	1	yes	characteristic
21	D₃	—	6	2	no	—
22	D₃	—	6	2	no	—
23	C₂²	—	9	1	no	—
24	C₄	—	9	2	no	—
25	C₃	—	6	2	no	—
26	C₃	C₂×#157	1	1	yes	characteristic
27	C₂	—	9	1	no	—
28	C₂	—	9	1	no	—
29	C₂	#1088	1	1	yes	characteristic, direct product factor

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.