Subgroups — C₃²×#16813210 #44565463

Order 32157.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16813210	C₃	1	12	yes	maximal, direct product factor
2	C₃²×C₃₉₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₃₉₇	C₉	1	1	yes	characteristic, complemented
4	C₃×C₃₉₇⋊C₃	C₉	1	8	yes	complemented
5	C₃×C₃₉₇⋊C₃	C₃²	1	4	yes	—
6	#16813210	C₃²	1	9	yes	direct product factor
7	C₃×C₃₉₇	C₃×C₉	1	4	yes	complemented
8	C₃₉₇⋊C₃	C₃×C₉	1	8	yes	complemented
9	C₃₉₇⋊C₃	C₃³	1	1	yes	characteristic
10	C₃₉₇	C₃²×C₉	1	1	yes	characteristic, complemented, Sylow
11	C₃²×C₉	—	397	1	no	maximal, Sylow
12	C₃³	—	397	1	no	—
13	C₃×C₉	—	397	12	no	—
14	C₃²	—	397	4	no	—
15	C₃²	—	397	8	no	—
16	C₃²	#16813210	1	1	yes	characteristic, direct product factor
17	C₉	—	397	9	no	—
18	C₃	—	397	8	no	—
19	C₃	—	397	1	no	—
20	C₃	C₃×#16813210	1	4	yes	direct product factor

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.