Subgroups — C₂²×#14523721 #22554698

Order 8436.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14523721	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₉×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#14523721	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₉×C₃₇	C₂×C₃	1	3	yes	complemented
5	C₁₉×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₃₇⋊C₃	—	19	1	no	maximal, Hall
7	C₂²×C₁₉⋊C₃	—	37	1	no	maximal, Hall
8	C₂×C₃₇⋊C₃	—	19	3	no	—
9	C₂²×C₃₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₉⋊C₃	—	37	3	no	—
11	C₃₇⋊C₃	—	19	1	no	Hall
12	C₂²×C₁₉	C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃₇	C₂×C₁₉⋊C₃	1	3	yes	complemented
14	C₁₉⋊C₃	—	37	1	no	Hall
15	C₂×C₁₉	C₂×C₃₇⋊C₃	1	3	yes	complemented
16	C₃₇	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₁₉	C₂²×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₃	—	703	1	no	Hall
19	C₂×C₃	—	703	3	no	—
20	C₂²	#14523721	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	703	1	no	Sylow
22	C₂	C₂×#14523721	1	3	yes	direct product factor

Splittings G = N ⋊ H with N normal; H ≅ G/N.