Subgroups — C₃₇×#10624551 #41004340

Order 26973.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic
2	C₃₇×#6855	C₃	1	12	yes	maximal
3	C₃²×C₉×C₃₇	C₃²	1	9	yes	—
4	C₃²×C₉×C₃₇	C₃²	1	4	yes	—
5	C₉²×C₃₇	C₉	1	9	yes	complemented
6	C₃³×C₃₇	C₃³	1	1	yes	characteristic
7	C₃×C₉×C₃₇	—	3	12	no	—
8	C₃×C₉×C₃₇	—	3	36	no	—
9	C₃×C₉×C₃₇	C₃×C₉	1	12	yes	—
10	#10624551	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
12	C₃²×C₃₇	#737	1	12	yes	—
13	C₉×C₃₇	—	3	12	no	—
14	C₉×C₃₇	—	9	9	no	—
15	C₃×C₉²	C₃×C₃₇	1	1	yes	characteristic
16	#6855	C₃×C₃₇	1	12	yes	—
17	C₃×C₃₇	#6887	1	4	yes	—
18	C₃×C₃₇	#6897	1	9	yes	—
19	C₃²×C₉	C₃²×C₃₇	1	9	yes	—
20	C₃²×C₉	C₃²×C₃₇	1	4	yes	—
21	C₉²	C₉×C₃₇	1	9	yes	complemented
22	C₃₇	#10624551	1	1	yes	characteristic, direct product factor, Sylow
23	C₃³	C₃³×C₃₇	1	1	yes	characteristic
24	C₃×C₉	—	3	12	no	—
25	C₃×C₉	—	3	36	no	—
26	C₃×C₉	C₃×C₉×C₃₇	1	12	yes	—
27	C₃²	C₃²×C₉×C₃₇	1	1	yes	characteristic
28	C₃²	C₃₇×#737	1	12	yes	—
29	C₉	—	3	12	no	—
30	C₉	—	9	9	no	—
31	C₃	C₃₇×#6887	1	4	yes	—
32	C₃	C₃₇×#6897	1	9	yes	—

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.