Subgroups — C₄₇×C₃₄₃ #30633166

Order 16121.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×C₄₉	C₇	1	1	yes	maximal, characteristic
2	C₃₄₃	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
3	C₇×C₄₇	C₄₉	1	1	yes	characteristic
4	C₄₉	C₇×C₄₇	1	1	yes	characteristic
5	C₄₇	C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₇	C₄₇×C₄₉	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₃₄₃	C₄₇	direct (N × H)
5. C₄₇	C₃₄₃	direct (N × H)

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

subgroup	index
C₄₇×C₄₉	7
C₃₄₃	47