Subgroups — C₃⁴×#66526 #41008657

Order 26973.

10232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#66526	C₃	1	120	yes	maximal, direct product factor
2	C₃⁴×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×#66526	C₃²	1	1170	yes	direct product factor
4	C₃³×C₃₇⋊C₃	C₉	1	80	yes	complemented
5	C₃³×C₃₇⋊C₃	C₃²	1	40	yes	—
6	C₃⁴×C₃₇	C₉	1	1	yes	characteristic, complemented
7	C₃³×C₃₇	C₃×C₉	1	40	yes	complemented
8	C₃²×C₃₇⋊C₃	C₃×C₉	1	1040	yes	complemented
9	C₃²×C₃₇⋊C₃	C₃³	1	130	yes	—
10	C₃×#66526	C₃³	1	1080	yes	direct product factor
11	C₃⁴×C₉	—	37	1	no	maximal, Sylow
12	C₃²×C₃₇	C₃²×C₉	1	130	yes	complemented
13	C₃×C₃₇⋊C₃	C₃²×C₉	1	1040	yes	complemented
14	C₃×C₃₇⋊C₃	C₃⁴	1	40	yes	—
15	#66526	C₃⁴	1	81	yes	direct product factor
16	C₃⁵	—	37	1	no	—
17	C₃³×C₉	—	37	120	no	—
18	C₃×C₃₇	C₃³×C₉	1	40	yes	complemented
19	C₃₇⋊C₃	C₃³×C₉	1	80	yes	complemented
20	C₃₇⋊C₃	C₃⁵	1	1	yes	characteristic
21	C₃⁴	—	37	40	no	—
22	C₃⁴	—	37	80	no	—
23	C₃⁴	#66526	1	1	yes	characteristic, direct product factor
24	C₃²×C₉	—	37	1170	no	—
25	C₃₇	C₃⁴×C₉	1	1	yes	characteristic, complemented, Sylow
26	C₃³	—	37	1040	no	—
27	C₃³	—	37	130	no	—
28	C₃³	C₃×#66526	1	40	yes	direct product factor
29	C₃×C₉	—	37	1080	no	—
30	C₃²	—	37	40	no	—
31	C₃²	—	37	1040	no	—
32	C₃²	C₃²×#66526	1	130	yes	direct product factor
33	C₉	—	37	81	no	—
34	C₃	—	37	1	no	—
35	C₃	—	37	80	no	—
36	C₃	C₃³×#66526	1	40	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.