Subgroups — C₃⁴×C₉×C₃₇ #41004726

Order 26973.

10232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₃₇	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₉×C₃₇	C₃	1	120	yes	maximal, direct product factor
3	C₃⁴×C₃₇	C₉	1	81	yes	direct product factor
4	C₃⁴×C₃₇	C₃²	1	40	yes	—
5	C₃²×C₉×C₃₇	C₃²	1	1170	yes	direct product factor
6	C₃³×C₃₇	C₃×C₉	1	1080	yes	direct product factor
7	C₃³×C₃₇	C₃³	1	130	yes	—
8	C₃×C₉×C₃₇	C₃³	1	1080	yes	direct product factor
9	C₃⁴×C₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃²×C₃₇	C₃²×C₉	1	1170	yes	direct product factor
11	C₃²×C₃₇	C₃⁴	1	40	yes	—
12	C₉×C₃₇	C₃⁴	1	81	yes	direct product factor
13	C₃⁵	C₃×C₃₇	1	1	yes	characteristic
14	C₃³×C₉	C₃×C₃₇	1	120	yes	direct product factor
15	C₃×C₃₇	C₃³×C₉	1	120	yes	direct product factor
16	C₃×C₃₇	C₃⁵	1	1	yes	characteristic
17	C₃⁴	C₉×C₃₇	1	81	yes	direct product factor
18	C₃⁴	C₃²×C₃₇	1	40	yes	—
19	C₃²×C₉	C₃²×C₃₇	1	1170	yes	direct product factor
20	C₃₇	C₃⁴×C₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₃³	C₃×C₉×C₃₇	1	1080	yes	direct product factor
22	C₃³	C₃³×C₃₇	1	130	yes	—
23	C₃×C₉	C₃³×C₃₇	1	1080	yes	direct product factor
24	C₃²	C₃²×C₉×C₃₇	1	1170	yes	direct product factor
25	C₃²	C₃⁴×C₃₇	1	40	yes	—
26	C₉	C₃⁴×C₃₇	1	81	yes	direct product factor
27	C₃	C₃³×C₉×C₃₇	1	120	yes	direct product factor
28	C₃	C₃⁵×C₃₇	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.