Subgroups — C₃²⋊#16813210 #44565455

Order 32157.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16813210	C₃	1	3	yes	maximal, complemented
2	C₃²×C₃₉₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₃₉₇	C₉	1	1	yes	characteristic, complemented
4	C₃×C₃₉₇⋊C₃	—	3	1	no	—
5	C₃×C₃₉₇⋊C₃	—	3	2	no	—
6	C₃×C₃₉₇⋊C₃	C₉	1	2	yes	complemented
7	C₃×C₃₉₇⋊C₃	C₃²	1	1	yes	characteristic
8	#16813210	—	3	3	no	—
9	C₃×C₃₉₇	—	3	1	no	—
10	C₃×C₃₉₇	C₃×C₉	1	1	yes	characteristic
11	C₃₉₇⋊C₃	—	3	2	no	—
12	C₃₉₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃₉₇⋊C₃	3₋¹⁺²	1	2	yes	—
14	C₃₉₇	C₃²⋊C₉	1	1	yes	characteristic, complemented, Sylow
15	C₃²⋊C₉	—	397	1	no	maximal, Sylow
16	C₃³	—	397	1	no	—
17	C₃×C₉	—	397	3	no	—
18	C₃²	—	397	1	no	—
19	C₃²	—	397	2	no	—
20	C₃²	—	1191	1	no	—
21	C₃²	—	1191	2	no	—
22	C₃²	#16813210	1	1	yes	characteristic, complemented
23	C₉	—	1191	3	no	—
24	C₃	—	3	1	no	—
25	C₃	—	397	1	no	—
26	C₃	—	397	2	no	—
27	C₃	—	1191	2	no	—
28	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.