Subgroups — C₇×#18012536 #46798103

Order 33740.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₂₀₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₂₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×#11757210	—	5	1	no	maximal, Hall
4	#18012536	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₂₄₁	—	5	1	no	—
6	D₁₂₀₅	C₂×C₇	1	1	yes	characteristic
7	C₇×C₂₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
8	C₅×C₂₄₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
9	#11757210	—	5	1	no	Hall
10	D₂₄₁	—	5	1	no	—
11	C₂₄₁	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
12	C₇×AGL(1,𝔽₅)	—	241	1	no	maximal, Hall
13	C₇×D₅	—	241	1	no	—
14	C₅×C₇	#11757210	1	1	yes	characteristic, complemented, Hall
15	C₄×C₇	—	1205	1	no	Hall
16	AGL(1,𝔽₅)	—	241	1	no	Hall
17	C₂×C₇	—	1205	1	no	—
18	D₅	—	241	1	no	—
19	C₇	#18012536	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	C₇×#11757210	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	1205	1	no	Sylow
22	C₂	—	1205	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.