Subgroups — C₄₉×C₂₂₇ #26013255

Order 11123.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₂₇	C₇	1	1	yes	maximal, characteristic
2	C₂₂₇	C₄₉	1	1	yes	characteristic, direct product factor, Sylow
3	C₄₉	C₂₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₇	C₇×C₂₂₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₂₂₇	C₄₉	direct (N × H)
3. C₄₉	C₂₂₇	direct (N × H)

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

subgroup	index
C₇×C₂₂₇	7
C₄₉	227