Subgroups — C₂×#3771 #64217

Order 288.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#622	C₂	1	1	yes	maximal, characteristic
2	#3771	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊Dic₃	C₄	1	1	yes	characteristic
4	#622	C₄	1	1	yes	characteristic
5	#622	C₂²	1	1	yes	characteristic
6	C₂²×C₃²	C₈	1	1	yes	characteristic
7	C₃⋊Dic₃	C₈	1	1	yes	characteristic
8	C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₆	—	9	1	no	maximal, Sylow
10	C₂×Dic₃	—	12	1	no	—
11	C₂×C₃²	C₁₆	1	2	yes	complemented
12	C₂×C₃²	C₂×C₈	1	1	yes	characteristic
13	C₂×C₈	—	9	1	no	—
14	C₁₆	—	9	2	no	—
15	C₂²×C₃	—	4	1	no	—
16	Dic₃	—	12	1	no	—
17	Dic₃	—	12	1	no	—
18	C₃²	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₄	—	9	1	no	—
20	C₈	—	9	1	no	—
21	C₈	—	9	1	no	—
22	C₂×C₃	—	4	1	no	—
23	C₂×C₃	—	4	2	no	—
24	C₂²	AGL(1,𝔽₉)	1	1	yes	characteristic
25	C₄	—	9	1	no	—
26	C₄	—	9	1	no	—
27	C₃	—	4	1	no	—
28	C₂	#3771	1	2	yes	direct product factor
29	C₂	C₂×AGL(1,𝔽₉)	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.