Subgroups — C₇×#157×C₆₇ #30683237

Order 16884.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₃×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇×C₆₇	—	6	2	no	—
4	#157×C₆₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄×C₇×C₆₇	—	9	1	no	maximal, Hall
6	C₃×C₇×C₆₇	—	2	2	no	—
7	C₃⋊D₃×C₆₇	C₂×C₇	1	1	yes	characteristic
8	C₂×C₇×C₆₇	—	9	1	no	—
9	C₃²×C₆₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₆₇	#157	1	1	yes	characteristic, direct product factor, Hall
11	D₃×C₆₇	—	6	2	no	—
12	C₄×C₆₇	—	9	1	no	Hall
13	C₇×#157	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₆₇	—	2	2	no	—
15	C₂×C₆₇	—	9	1	no	—
16	C₇×C₃⋊D₃	C₂×C₆₇	1	1	yes	characteristic
17	C₆₇	C₇×#157	1	1	yes	characteristic, direct product factor, Sylow
18	C₃²×C₇	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
19	D₃×C₇	—	6	2	no	—
20	#157	C₇×C₆₇	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₇	—	9	1	no	Hall
22	C₃×C₇	—	2	2	no	—
23	C₃⋊D₃	C₂×C₇×C₆₇	1	1	yes	characteristic
24	C₂×C₇	—	9	1	no	—
25	C₃²	C₄×C₇×C₆₇	1	1	yes	characteristic, complemented, Sylow
26	C₇	#157×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	9	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	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.