Subgroups — C₂×C₄₉×C₆₇⋊C₃ #34089113

Order 19698.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₄₉×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₉×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₆₇⋊C₃	C₇	1	1	yes	maximal, characteristic
5	C₇×C₆₇⋊C₃	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₆₇	C₃×C₇	1	1	yes	characteristic
7	C₇×C₆₇	C₂×C₃×C₇	1	1	yes	characteristic
8	C₂×C₆₇⋊C₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₄₉	—	67	1	no	maximal, Hall
10	C₆₇⋊C₃	C₂×C₄₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₄₉	—	67	1	no	Hall
12	C₂×C₆₇	C₃×C₄₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₉	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₆₇	C₂×C₃×C₄₉	1	1	yes	characteristic, complemented, Sylow
15	C₄₉	C₂×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×C₇	—	67	1	no	—
17	C₃×C₇	—	67	1	no	—
18	C₂×C₇	C₇×C₆₇⋊C₃	1	1	yes	characteristic
19	C₇	C₂×C₇×C₆₇⋊C₃	1	1	yes	characteristic
20	C₂×C₃	—	67	1	no	Hall
21	C₃	—	67	1	no	Sylow
22	C₂	C₄₉×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

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.