Subgroups — C₇×#14581472 #32913708

Order 18396.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#10620321⋊C₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×#64408	C₃	1	1	yes	maximal, characteristic
3	C₇×#10620321	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×D₇₃	C₂×C₃	1	1	yes	characteristic
5	#14581472	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×#64408	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₇₃	C₃×C₄	1	1	yes	characteristic
8	#10620321⋊C₂	C₂×C₇	1	1	yes	characteristic
9	C₇×D₇₃	C₂×C₉	1	1	yes	characteristic
10	C₃×#64408	C₃×C₇	1	1	yes	characteristic
11	#10620321	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₇₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×D₇₃	C₂×C₃×C₇	1	1	yes	characteristic
14	#64408	C₇×C₉	1	1	yes	characteristic, complemented, Hall
15	C₄×C₇×C₉	—	73	1	no	maximal, Hall
16	C₃×C₇₃	C₃×C₄×C₇	1	1	yes	characteristic
17	D₇₃	C₂×C₇×C₉	1	1	yes	characteristic
18	C₂×C₇×C₉	—	73	1	no	—
19	C₃×C₄×C₇	—	219	1	no	—
20	C₇₃	C₄×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
21	C₇×C₉	—	73	1	no	Hall
22	C₂×C₃×C₇	—	219	1	no	—
23	C₄×C₉	—	73	1	no	Hall
24	C₄×C₇	—	219	1	no	Hall
25	C₃×C₇	#64408⋊C₃	1	1	yes	characteristic
26	C₂×C₉	—	73	1	no	—
27	C₂×C₇	—	219	1	no	—
28	C₃×C₄	—	219	1	no	—
29	C₉	—	73	1	no	Sylow
30	C₇	#14581472	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	219	1	no	—
32	C₄	—	219	1	no	Sylow
33	C₃	C₇×#64408⋊C₃	1	1	yes	characteristic
34	C₂	—	219	1	no	—

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.