Subgroups — C₃×C₇×#11761640 #36378956

Order 22596.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₂₆₉	C₂	1	1	yes	maximal, characteristic
2	C₇×#11761640	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₂₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×D₂₆₉	C₂×C₃	1	1	yes	characteristic
5	C₃×#11761640	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₂₆₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×D₂₆₉	C₂×C₇	1	1	yes	characteristic
8	#11761640	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₂₆₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
10	D₂₆₉	C₂×C₃×C₇	1	1	yes	characteristic
11	C₂₆₉	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₄×C₇	—	269	1	no	maximal, Hall
13	C₂×C₃×C₇	—	269	1	no	—
14	C₄×C₇	—	269	1	no	Hall
15	C₃×C₇	#11761640	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₇	—	269	1	no	—
17	C₃×C₄	—	269	1	no	Hall
18	C₇	C₃×#11761640	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	269	1	no	—
20	C₄	—	269	1	no	Sylow
21	C₃	C₇×#11761640	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	269	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.