Subgroups — C₂₇×C₇₆₉ #35209307

Order 20763.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₇₆₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₇₆₉	C₉	1	1	yes	characteristic
3	C₇₆₉	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
4	C₂₇	C₇₆₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₉	C₃×C₇₆₉	1	1	yes	characteristic
6	C₃	C₉×C₇₆₉	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₇₆₉	C₂₇	direct (N × H)
4. C₂₇	C₇₆₉	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉×C₇₆₉	3
C₂₇	769