Subgroups — #44565456

Order 32157.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16813210	C₃	1	3	yes	maximal
2	C₉×C₃₉₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₃₉₇⋊C₃	C₃²	1	1	yes	characteristic
4	#16813210	—	3	3	no	—
5	C₉×C₃₉₇	C₉	1	1	yes	characteristic, complemented
6	#16813208	C₉	1	2	yes	complemented
7	C₃×C₃₉₇	C₃×C₉	1	1	yes	characteristic
8	C₃₉₇⋊C₃	3₋¹⁺²	1	3	yes	—
9	C₃₉₇	C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
10	C₉⋊C₉	—	397	1	no	maximal, Sylow
11	C₃×C₉	—	397	1	no	—
12	C₃×C₉	—	397	3	no	—
13	C₃²	—	397	1	no	—
14	C₉	—	397	2	no	—
15	C₉	—	1191	3	no	—
16	C₉	#16813210	1	1	yes	characteristic, complemented
17	C₃	—	397	3	no	—
18	C₃	C₃×#16813210	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.