Subgroups — C₆₇×#5997 #27190082

Order 13132.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₇×C₆₇	—	14	4	no	—
4	C₇×C₆₇	—	2	4	no	—
5	C₄×C₆₇	—	49	1	no	maximal, Hall
6	#5997	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₆₇	—	49	1	no	—
8	C₇⋊D₇	C₂×C₆₇	1	1	yes	characteristic
9	C₆₇	#5997	1	1	yes	characteristic, direct product factor, Sylow
10	C₇²	C₄×C₆₇	1	1	yes	characteristic, complemented, Sylow
11	D₇	—	14	4	no	—
12	C₇	—	2	4	no	—
13	C₄	—	49	1	no	Sylow
14	C₂	—	49	1	no	—

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.