Subgroups — C₇×Dic₅₄ #13094132

Order 1512.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₂₇	C₂	1	2	yes	maximal
3	C₇×Dic₁₈	—	3	1	no	maximal
4	C₂×C₇×C₂₇	C₂²	1	1	yes	characteristic
5	C₄×C₇×C₉	D₃	1	1	yes	characteristic
6	C₇×Dic₉	—	3	2	no	—
7	Dic₅₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₂₇	Q₈	1	1	yes	characteristic, complemented, Hall
9	C₇×Dic₆	—	9	1	no	—
10	C₂×C₇×C₉	C₂×D₃	1	1	yes	characteristic
11	C₄×C₂₇	C₂×C₇	1	1	yes	characteristic
12	Dic₂₇	C₂×C₇	1	2	yes	—
13	C₃×C₄×C₇	D₉	1	1	yes	characteristic
14	C₇×Dic₃	—	9	2	no	—
15	Dic₁₈	—	3	1	no	—
16	C₇×C₉	Dic₆	1	1	yes	characteristic
17	C₇×Q₈	—	27	1	no	Hall
18	C₂×C₂₇	C₂²×C₇	1	1	yes	characteristic
19	C₂×C₃×C₇	C₂×D₉	1	1	yes	characteristic
20	C₄×C₉	D₃×C₇	1	1	yes	characteristic
21	Dic₉	—	3	2	no	—
22	C₄×C₇	—	27	2	no	—
23	C₄×C₇	D₂₇	1	1	yes	characteristic
24	C₂₇	C₇×Q₈	1	1	yes	characteristic, complemented, Sylow
25	Dic₆	—	9	1	no	—
26	C₃×C₇	Dic₁₈	1	1	yes	characteristic
27	C₂×C₉	C₂×D₃×C₇	1	1	yes	characteristic
28	C₂×C₇	C₂×D₂₇	1	1	yes	characteristic
29	C₃×C₄	C₇×D₉	1	1	yes	characteristic
30	Dic₃	—	9	2	no	—
31	C₉	C₇×Dic₆	1	1	yes	characteristic
32	Q₈	—	27	1	no	Sylow
33	C₇	Dic₅₄	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₃	C₂×C₇×D₉	1	1	yes	characteristic
35	C₄	—	27	2	no	—
36	C₄	C₇×D₂₇	1	1	yes	characteristic
37	C₃	C₇×Dic₁₈	1	1	yes	characteristic
38	C₂	C₂×C₇×D₂₇	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.