Subgroups — C₇×C₇⋊#10587739 #41001657

Order 26852.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₁₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊#10587739	C₇	1	1	yes	maximal, characteristic, direct product factor
4	C₇×#10587739	—	7	1	no	maximal
5	C₇×D₁₃₇	—	2	3	no	—
6	C₇×D₁₃₇	D₇	1	1	yes	characteristic
7	C₇×D₁₃₇	C₂×C₇	1	1	yes	characteristic
8	C₇×C₁₃₇	—	2	3	no	—
9	C₇×C₁₃₇	Dic₇	1	1	yes	characteristic, complemented
10	C₇×C₁₃₇	C₄×C₇	1	1	yes	characteristic, complemented
11	#10587739	—	7	1	no	Hall
12	D₁₃₇	C₇×D₇	1	1	yes	characteristic
13	C₇×Dic₇	—	137	1	no	maximal, Hall
14	C₁₃₇	C₇×Dic₇	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₇²	—	137	1	no	—
16	C₇²	#10587739	1	1	yes	characteristic, complemented, Sylow
17	C₄×C₇	—	959	1	no	—
18	Dic₇	—	137	1	no	—
19	C₂×C₇	—	274	3	no	—
20	C₂×C₇	—	137	1	no	—
21	C₂×C₇	—	137	1	no	—
22	C₇	—	2	3	no	—
23	C₇	C₇×#10587739	1	1	yes	characteristic, complemented
24	C₇	C₇⋊#10587739	1	1	yes	characteristic, direct product factor
25	C₄	—	959	1	no	Sylow
26	C₂	—	137	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.