Subgroups — C₃×D₇×C₇₃⋊C₃ #22604128

Order 9198.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₇₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₇×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₇×C₇₃⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₂×C₃×C₇₃⋊C₃	—	7	1	no	maximal, Hall
7	D₇×C₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇₃⋊C₃	D₇	1	1	yes	characteristic, direct product factor, Hall
9	C₇×C₇₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇₃	—	7	1	no	—
11	C₂×C₇₃⋊C₃	—	7	3	no	—
12	C₃×C₇₃	C₃×D₇	1	1	yes	characteristic, complemented
13	C₇₃⋊C₃	C₃×D₇	1	3	yes	direct product factor
14	C₂×C₇₃	—	7	1	no	Hall
15	C₃²×D₇	—	73	1	no	maximal, Hall
16	C₇₃	C₃²×D₇	1	1	yes	characteristic, complemented, Sylow
17	C₃²×C₇	—	73	1	no	Hall
18	C₃×D₇	—	73	3	no	—
19	C₃×D₇	C₇₃⋊C₃	1	1	yes	characteristic, direct product factor
20	C₃×C₇	—	73	3	no	—
21	C₃×C₇	C₂×C₇₃⋊C₃	1	1	yes	characteristic, complemented
22	C₂×C₃²	—	511	1	no	Hall
23	D₇	C₃×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃²	—	73	1	no	Sylow
25	C₇	C₂×C₃×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃	—	7	1	no	—
27	C₂×C₃	—	511	3	no	—
28	C₃	—	73	3	no	—
29	C₃	D₇×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	—	7	1	no	Sylow

Splittings G = N ⋊ H with N normal; H ≅ G/N.