Subgroups — C₇×C₃⋊(D₇₃⋊C₃) #22604129

Order 9198.

36 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	C₇×D₇₃⋊C₃	—	3	1	no	maximal
3	C₇×D₂₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₇×C₇₃⋊C₃	—	2	1	no	—
6	C₇×C₇₃⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₃⋊(D₇₃⋊C₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×D₇₃	—	3	1	no	Hall
9	C₃×C₇₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₇₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₂₁₉	C₃×C₇	1	1	yes	characteristic, complemented
12	D₇₃⋊C₃	—	3	1	no	—
13	C₃×C₇₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
14	C₇₃⋊C₃	—	2	1	no	—
15	C₇₃⋊C₃	D₃×C₇	1	1	yes	characteristic, complemented
16	D₇₃	—	3	1	no	Hall
17	C₃×D₃×C₇	—	73	1	no	maximal, Hall
18	C₇₃	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
19	C₃²×C₇	—	73	1	no	Hall
20	C₂×C₃×C₇	—	219	1	no	—
21	D₃×C₇	—	73	1	no	—
22	C₃×C₇	—	73	1	no	—
23	C₃×C₇	—	146	1	no	—
24	C₃×C₇	D₇₃⋊C₃	1	1	yes	characteristic, complemented
25	C₃×D₃	—	73	1	no	Hall
26	C₂×C₇	—	219	1	no	Hall
27	C₃²	—	73	1	no	Sylow
28	C₇	C₃⋊(D₇₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃	—	219	1	no	—
30	D₃	—	73	1	no	—
31	C₃	—	73	1	no	—
32	C₃	—	146	1	no	—
33	C₃	C₇×D₇₃⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	219	1	no	Sylow

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