Subgroups — C₃²×#16813208 #44565442

Order 32157.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16813208	C₃	1	12	yes	maximal, direct product factor
2	C₃³×C₃₉₇	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₃₉₇	C₉	1	9	yes	complemented
4	C₃²×C₃₉₇	C₃²	1	4	yes	—
5	#16813208	C₃²	1	9	yes	direct product factor
6	C₃×C₃₉₇	C₃×C₉	1	12	yes	complemented
7	C₃×C₃₉₇	C₃³	1	1	yes	characteristic
8	C₃₉₇	C₃²×C₉	1	1	yes	characteristic, complemented, Sylow
9	C₃²×C₉	—	397	1	no	maximal, Sylow
10	C₃³	C₃₉₇⋊C₃	1	1	yes	characteristic
11	C₃×C₉	—	397	12	no	—
12	C₃²	#16813208	1	9	yes	direct product factor
13	C₃²	C₃×C₃₉₇⋊C₃	1	4	yes	—
14	C₉	—	397	9	no	—
15	C₃	C₃×#16813208	1	12	yes	direct product factor
16	C₃	C₃²×C₃₉₇⋊C₃	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.