Subgroups — #13133499

Order 1701.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
2	#10588038	C₃	1	3	yes	maximal, complemented
3	#6879	—	7	1	no	maximal, Sylow
4	C₃×C₇×C₉	—	3	1	no	—
5	C₃×C₇×C₉	C₃²	1	1	yes	characteristic
6	C₇⋊H(3,𝔽₃)	—	3	3	no	—
7	#732	—	7	3	no	—
8	C₉²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
9	C₃²×C₇	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃×ΓL(1,𝔽₈)	—	9	3	no	—
11	C₇×C₉	—	3	3	no	—
12	C₇×C₉	—	3	1	no	—
13	H(3,𝔽₃)	—	21	3	no	—
14	C₃×C₉	—	3	1	no	—
15	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₃×C₇	—	3	1	no	—
17	C₃×C₇	#732	1	1	yes	characteristic
18	ΓL(1,𝔽₈)	—	27	3	no	—
19	C₃²	—	63	3	no	—
20	C₃²	C₇⋊H(3,𝔽₃)	1	1	yes	characteristic
21	C₉	—	3	3	no	—
22	C₉	—	3	1	no	—
23	C₇	#6879	1	1	yes	characteristic, complemented, Sylow
24	C₃	—	3	1	no	—
25	C₃	—	189	3	no	—
26	C₃	#10588038	1	1	yes	characteristic

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.