Subgroups — C₇×C₃⋊D₂₁₉ #22604157

Order 9198.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₁₉	—	3	4	no	maximal
3	C₃×C₇×C₇₃	D₃	1	4	yes	complemented
4	C₃⋊D₂₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₇₃	—	9	1	no	Hall
6	C₃²×C₇₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₇₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
8	D₂₁₉	—	3	4	no	—
9	C₃×C₇₃	D₃×C₇	1	4	yes	complemented
10	D₇₃	—	9	1	no	Hall
11	C₇×C₃⋊D₃	—	73	1	no	maximal, Hall
12	C₇₃	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
13	C₃²×C₇	D₇₃	1	1	yes	characteristic, complemented, Hall
14	D₃×C₇	—	219	4	no	—
15	C₃×C₇	D₂₁₉	1	4	yes	complemented
16	C₃⋊D₃	—	73	1	no	Hall
17	C₂×C₇	—	657	1	no	Hall
18	C₃²	C₇×D₇₃	1	1	yes	characteristic, complemented, Sylow
19	C₇	C₃⋊D₂₁₉	1	1	yes	characteristic, direct product factor, Sylow
20	D₃	—	219	4	no	—
21	C₃	C₇×D₂₁₉	1	4	yes	complemented
22	C₂	—	657	1	no	Sylow

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