Subgroups — C₇×#17987164 #44567147

Order 32193.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₇₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#17987164	C₇	1	1	yes	maximal, characteristic, direct product factor
3	C₇×#10620323	—	7	1	no	maximal
4	C₇²×C₇₃	C₉	1	1	yes	characteristic, complemented, Hall
5	C₇×C₇₃⋊C₃	—	3	2	no	—
6	C₇×C₇₃⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
7	C₇×C₇₃⋊C₃	C₃×C₇	1	1	yes	characteristic
8	#10620323	—	7	1	no	Hall
9	C₇×C₇₃	—	3	2	no	—
10	C₇×C₇₃	C₇⋊C₉	1	1	yes	characteristic, complemented
11	C₇×C₇₃	C₇×C₉	1	1	yes	characteristic, complemented
12	C₇×C₇⋊C₉	—	73	1	no	maximal, Hall
13	C₇₃⋊C₃	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₃×C₇²	—	73	1	no	—
15	C₇₃	C₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
16	C₇×C₉	—	511	1	no	—
17	C₇⋊C₉	—	73	1	no	—
18	C₇²	#10620323	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₇	—	73	1	no	—
20	C₃×C₇	—	73	1	no	—
21	C₃×C₇	—	219	2	no	—
22	C₉	—	511	1	no	Sylow
23	C₇	—	3	2	no	—
24	C₇	C₇×#10620323	1	1	yes	characteristic, complemented
25	C₇	#17987164	1	1	yes	characteristic, direct product factor
26	C₃	—	73	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.