Subgroups — C₂×#5997 #87660

Order 392.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	#5997	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇²	C₄	1	1	yes	characteristic, complemented
4	C₇⋊D₇	C₄	1	1	yes	characteristic, complemented
5	C₇⋊D₇	C₂²	1	1	yes	characteristic
6	C₇²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
7	C₂×D₇	—	14	4	no	—
8	C₂×C₇	—	2	4	no	—
9	D₇	—	14	4	no	—
10	D₇	—	14	4	no	—
11	C₂×C₄	—	49	1	no	maximal, Sylow
12	C₇	—	2	4	no	—
13	C₂²	—	49	1	no	—
14	C₄	—	49	2	no	—
15	C₂	—	49	1	no	—
16	C₂	—	49	1	no	—
17	C₂	#5997	1	1	yes	characteristic, direct product factor

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.