Subgroups — C₇×Dic₁₈ #92603

Order 504.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₉	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₉	C₂	1	2	yes	maximal
3	C₇×Dic₆	—	3	1	no	maximal
4	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₇	D₃	1	1	yes	characteristic
6	C₇×Dic₃	—	3	2	no	—
7	Dic₁₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₉	Q₈	1	1	yes	characteristic, complemented, Hall
9	C₇×Q₈	—	9	1	no	Hall
10	C₂×C₃×C₇	C₂×D₃	1	1	yes	characteristic
11	C₄×C₉	C₂×C₇	1	1	yes	characteristic
12	Dic₉	C₂×C₇	1	2	yes	—
13	C₄×C₇	—	9	2	no	—
14	C₄×C₇	D₉	1	1	yes	characteristic
15	Dic₆	—	3	1	no	—
16	C₃×C₇	Dic₆	1	1	yes	characteristic
17	C₂×C₉	C₂²×C₇	1	1	yes	characteristic
18	C₂×C₇	C₂×D₉	1	1	yes	characteristic
19	C₃×C₄	D₃×C₇	1	1	yes	characteristic
20	Dic₃	—	3	2	no	—
21	C₉	C₇×Q₈	1	1	yes	characteristic, complemented, Sylow
22	Q₈	—	9	1	no	Sylow
23	C₇	Dic₁₈	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃	C₂×D₃×C₇	1	1	yes	characteristic
25	C₄	—	9	2	no	—
26	C₄	C₇×D₉	1	1	yes	characteristic
27	C₃	C₇×Dic₆	1	1	yes	characteristic
28	C₂	C₂×C₇×D₉	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.