Subgroups — C₃×C₂₃×#3866 #23779288

Order 10212.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×D₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3866	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₃×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂₃×D₃₇	C₂×C₃	1	1	yes	characteristic
5	C₂₃×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#3866	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₄×C₂₃	—	37	1	no	maximal, Hall
8	C₃×D₃₇	C₂×C₂₃	1	1	yes	characteristic
9	#3866	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₂₃	—	37	1	no	—
11	C₃×C₃₇	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
12	C₄×C₂₃	—	37	1	no	Hall
13	D₃₇	C₂×C₃×C₂₃	1	1	yes	characteristic
14	C₃×C₂₃	#3866	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₂₃	—	37	1	no	—
16	C₃₇	C₃×C₄×C₂₃	1	1	yes	characteristic, complemented, Sylow
17	C₂₃	C₃×#3866	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	37	1	no	Hall
19	C₂×C₃	—	37	1	no	—
20	C₄	—	37	1	no	Sylow
21	C₃	C₂₃×#3866	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	37	1	no	—

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