Subgroups — #37567009

Order 24353.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₇₁⋊C₇	C₇	1	1	yes	maximal, characteristic
2	C₄₉×C₇₁	C₇	1	1	yes	maximal, characteristic, complemented
3	C₇₁⋊C₄₉	C₇	1	6	yes	maximal, complemented
4	C₇×C₇₁	C₇²	1	1	yes	characteristic
5	C₇₁⋊C₇	—	7	1	no	—
6	7₋¹⁺²	—	71	1	no	maximal, Sylow
7	C₇₁	7₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
8	C₇²	—	71	1	no	—
9	C₄₉	—	71	6	no	—
10	C₄₉	C₇₁⋊C₇	1	1	yes	characteristic, complemented
11	C₇	—	497	1	no	—
12	C₇	C₇×C₇₁⋊C₇	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.