Subgroups — C₃²×C₈×C₂₈₃ #72197939

Order 20376.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×C₂₈₃	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₄×C₂₈₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₂₈₃	C₄	1	1	yes	characteristic
4	C₃×C₄×C₂₈₃	C₂×C₃	1	4	yes	—
5	C₃²×C₂₈₃	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₈×C₂₈₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₂₈₃	C₃×C₄	1	4	yes	—
8	C₄×C₂₈₃	C₂×C₃²	1	1	yes	characteristic
9	C₃×C₂₈₃	C₃×C₈	1	4	yes	direct product factor
10	C₂×C₂₈₃	C₃²×C₄	1	1	yes	characteristic
11	C₂₈₃	C₃²×C₈	1	1	yes	characteristic, direct product factor, Sylow
12	C₃²×C₈	C₂₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₄	C₂×C₂₈₃	1	1	yes	characteristic
14	C₃×C₈	C₃×C₂₈₃	1	4	yes	direct product factor
15	C₂×C₃²	C₄×C₂₈₃	1	1	yes	characteristic
16	C₃×C₄	C₂×C₃×C₂₈₃	1	4	yes	—
17	C₃²	C₈×C₂₈₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₈	C₃²×C₂₈₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₃×C₄×C₂₈₃	1	4	yes	—
20	C₄	C₂×C₃²×C₂₈₃	1	1	yes	characteristic
21	C₃	C₃×C₈×C₂₈₃	1	4	yes	direct product factor
22	C₂	C₃²×C₄×C₂₈₃	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.