Subgroups — C₇²×#10620323 #44567145

Order 32193.

60 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	C₇×#10620323	C₇	1	8	yes	maximal, direct product factor
3	C₇²×C₇₃	C₉	1	1	yes	characteristic, complemented, Hall
4	C₇×C₇₃⋊C₃	C₃×C₇	1	8	yes	—
5	#10620323	C₇²	1	1	yes	characteristic, direct product factor, Hall
6	C₇×C₇₃	C₇×C₉	1	8	yes	complemented
7	C₇²×C₉	—	73	1	no	maximal, Hall
8	C₇₃⋊C₃	C₃×C₇²	1	1	yes	characteristic
9	C₃×C₇²	—	73	1	no	—
10	C₇₃	C₇²×C₉	1	1	yes	characteristic, complemented, Sylow
11	C₇×C₉	—	73	8	no	—
12	C₇²	#10620323	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₇	—	73	8	no	—
14	C₉	—	73	1	no	Sylow
15	C₇	C₇×#10620323	1	8	yes	direct product factor
16	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.