Subgroups — C₉×ΓL(1,𝔽₈) #4426

Order 189.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×ΓL(1,𝔽₈)	C₃	1	1	yes	maximal, characteristic
2	C₇×C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₃×C₉	—	7	1	no	maximal, Sylow
5	C₃×C₇	C₃²	1	1	yes	characteristic
6	ΓL(1,𝔽₈)	C₉	1	3	yes	direct product factor
7	C₃²	—	7	1	no	—
8	C₉	—	7	2	no	—
9	C₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
10	C₇	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
11	C₃	—	7	3	no	—
12	C₃	C₃×ΓL(1,𝔽₈)	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.