Subgroups — C₃⁴×#66524 #41008241

Order 26973.

10232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#66524	C₃	1	120	yes	maximal, direct product factor
2	C₃⁵×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃²×#66524	C₃²	1	1170	yes	direct product factor
4	C₃⁴×C₃₇	C₉	1	81	yes	complemented
5	C₃⁴×C₃₇	C₃²	1	40	yes	—
6	C₃³×C₃₇	C₃×C₉	1	1080	yes	complemented
7	C₃³×C₃₇	C₃³	1	130	yes	—
8	C₃×#66524	C₃³	1	1080	yes	direct product factor
9	C₃⁴×C₉	—	37	1	no	maximal, Sylow
10	C₃²×C₃₇	C₃²×C₉	1	1170	yes	complemented
11	C₃²×C₃₇	C₃⁴	1	40	yes	—
12	#66524	C₃⁴	1	81	yes	direct product factor
13	C₃⁵	C₃₇⋊C₃	1	1	yes	characteristic
14	C₃³×C₉	—	37	120	no	—
15	C₃×C₃₇	C₃³×C₉	1	120	yes	complemented
16	C₃×C₃₇	C₃⁵	1	1	yes	characteristic
17	C₃⁴	#66524	1	81	yes	direct product factor
18	C₃⁴	C₃×C₃₇⋊C₃	1	40	yes	—
19	C₃²×C₉	—	37	1170	no	—
20	C₃₇	C₃⁴×C₉	1	1	yes	characteristic, complemented, Sylow
21	C₃³	C₃×#66524	1	1080	yes	direct product factor
22	C₃³	C₃²×C₃₇⋊C₃	1	130	yes	—
23	C₃×C₉	—	37	1080	no	—
24	C₃²	C₃²×#66524	1	1170	yes	direct product factor
25	C₃²	C₃³×C₃₇⋊C₃	1	40	yes	—
26	C₉	—	37	81	no	—
27	C₃	C₃³×#66524	1	120	yes	direct product factor
28	C₃	C₃⁴×C₃₇⋊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.