Subgroups — C₇×C₂²⋊(C₆₇⋊C₉) #30683085

Order 16884.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇×C₆₇	C₃	1	1	yes	maximal, characteristic
2	C₇×C₆₇⋊C₉	—	4	1	no	maximal, Hall
3	C₂×C₃×C₇×C₆₇	—	3	1	no	—
4	C₂²⋊(C₆₇⋊C₉)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₇×C₆₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇×C₆₇	A₄	1	1	yes	characteristic
7	C₂×C₇×C₆₇	—	3	1	no	—
8	C₂²×C₃×C₆₇	C₃×C₇	1	1	yes	characteristic
9	C₆₇⋊C₉	—	4	1	no	Hall
10	C₇×C₆₇	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₆₇	—	3	1	no	—
12	C₂²×C₆₇	C₇×C₉	1	1	yes	characteristic, complemented, Hall
13	C₇×C₂²⋊C₉	—	67	1	no	maximal, Hall
14	C₃×C₆₇	C₇×A₄	1	1	yes	characteristic
15	C₂×C₆₇	—	3	1	no	—
16	C₂²×C₃×C₇	C₆₇⋊C₃	1	1	yes	characteristic
17	C₆₇	C₇×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
18	C₇×C₉	—	268	1	no	Hall
19	C₂×C₃×C₇	—	3	1	no	—
20	C₂²⋊C₉	—	67	1	no	Hall
21	C₂²×C₇	C₆₇⋊C₉	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇	C₂²⋊(C₆₇⋊C₃)	1	1	yes	characteristic
23	C₂×C₇	—	3	1	no	—
24	C₂²×C₃	C₇×C₆₇⋊C₃	1	1	yes	characteristic
25	C₉	—	268	1	no	Sylow
26	C₇	C₂²⋊(C₆₇⋊C₉)	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂²	C₇×C₆₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₇×C₂²⋊(C₆₇⋊C₃)	1	1	yes	characteristic
30	C₂	—	3	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.