Subgroups — D₃×C₉×C₃₇ #14522005

Order 1998.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₃×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₃₇	—	3	1	no	maximal
4	C₃²×C₃₇	C₂×C₃	1	1	yes	characteristic
5	C₉×C₃₇	—	2	1	no	—
6	C₉×C₃₇	D₃	1	1	yes	characteristic, direct product factor
7	C₂×C₃×C₃₇	—	3	1	no	—
8	D₃×C₃₇	C₉	1	1	yes	characteristic, direct product factor
9	C₃×C₃₇	—	2	1	no	—
10	C₃×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented
11	C₃×C₃₇	C₃×D₃	1	1	yes	characteristic
12	C₂×C₃₇	—	3	1	no	Hall
13	D₃×C₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃₇	D₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₉	C₂×C₃₇	1	1	yes	characteristic, complemented, Sylow
16	C₃×D₃	C₃×C₃₇	1	1	yes	characteristic
17	C₂×C₉	—	3	1	no	—
18	C₃²	C₂×C₃×C₃₇	1	1	yes	characteristic
19	C₉	—	2	1	no	—
20	C₉	D₃×C₃₇	1	1	yes	characteristic, direct product factor
21	C₂×C₃	—	3	1	no	—
22	D₃	C₉×C₃₇	1	1	yes	characteristic, direct product factor
23	C₃	—	2	1	no	—
24	C₃	C₂×C₉×C₃₇	1	1	yes	characteristic, complemented
25	C₃	C₃×D₃×C₃₇	1	1	yes	characteristic
26	C₂	—	3	1	no	Sylow

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.