Subgroups — C₂×C₃×C₇×C₉ #67391

Order 378.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃²×C₇	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₉	C₃	1	3	yes	maximal, direct product factor
4	C₃²×C₇	C₂×C₃	1	1	yes	characteristic
5	C₇×C₉	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃×C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₇	C₉	1	3	yes	direct product factor
8	C₂×C₃×C₇	C₃²	1	1	yes	characteristic
9	C₃×C₉	C₂×C₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₇	C₂×C₉	1	3	yes	direct product factor
11	C₃×C₇	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃²	C₃×C₇	1	1	yes	characteristic
13	C₂×C₉	C₃×C₇	1	3	yes	direct product factor
14	C₂×C₇	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃²	C₂×C₃×C₇	1	1	yes	characteristic
16	C₉	C₂×C₃×C₇	1	3	yes	direct product factor
17	C₇	C₂×C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃	C₇×C₉	1	3	yes	direct product factor
19	C₂×C₃	C₃²×C₇	1	1	yes	characteristic
20	C₃	C₂×C₇×C₉	1	3	yes	direct product factor
21	C₃	C₂×C₃²×C₇	1	1	yes	characteristic
22	C₂	C₃×C₇×C₉	1	1	yes	characteristic, direct product factor, 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.