Subgroups — C₂×AGL(1,𝔽₉) #3842

Order 144.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#157	C₂	1	1	yes	maximal, characteristic
2	AGL(1,𝔽₉)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊D₃	C₄	1	1	yes	characteristic
4	#157	C₄	1	1	yes	characteristic
5	#157	C₂²	1	1	yes	characteristic
6	C₂×C₃²	C₈	1	1	yes	characteristic, complemented
7	C₃⋊D₃	C₈	1	1	yes	characteristic, complemented
8	C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈	—	9	1	no	maximal, Sylow
10	C₂×D₃	—	12	1	no	—
11	C₃²	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₄	—	9	1	no	—
13	C₈	—	9	2	no	—
14	C₂×C₃	—	4	1	no	—
15	D₃	—	12	1	no	—
16	D₃	—	12	1	no	—
17	C₂²	—	9	1	no	—
18	C₄	—	9	1	no	—
19	C₄	—	9	1	no	—
20	C₃	—	4	1	no	—
21	C₂	—	9	1	no	—
22	C₂	—	9	1	no	—
23	C₂	AGL(1,𝔽₉)	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.