Subgroups — C₇×C₂₃×#6157 #46802421

Order 34132.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₃×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₃×#6157	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂₃×D₅₃	C₂×C₇	1	1	yes	characteristic
5	C₇×#6157	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂₃×C₅₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×D₅₃	C₂×C₂₃	1	1	yes	characteristic
8	C₄×C₇×C₂₃	—	53	1	no	maximal, Hall
9	C₇×C₅₃	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₂₃	—	53	1	no	—
11	#6157	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₂₃	#6157	1	1	yes	characteristic, direct product factor, Hall
13	D₅₃	C₂×C₇×C₂₃	1	1	yes	characteristic
14	C₄×C₂₃	—	53	1	no	Hall
15	C₅₃	C₄×C₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₃	—	53	1	no	—
17	C₄×C₇	—	53	1	no	Hall
18	C₂₃	C₇×#6157	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇	—	53	1	no	—
20	C₇	C₂₃×#6157	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	53	1	no	Sylow
22	C₂	—	53	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.