Subgroups — C₉₇×#66526 #44568136

Order 32301.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉₇×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃₇×C₉₇	C₉	1	1	yes	characteristic, complemented, Hall
3	C₉×C₉₇	—	37	1	no	maximal, Hall
4	#66526	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₉₇	—	37	1	no	—
6	C₃₇⋊C₃	C₃×C₉₇	1	1	yes	characteristic
7	C₉₇	#66526	1	1	yes	characteristic, direct product factor, Sylow
8	C₃₇	C₉×C₉₇	1	1	yes	characteristic, complemented, Sylow
9	C₉	—	37	1	no	Sylow
10	C₃	—	37	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.