Subgroups — C₈×C₄₉×C₆₇ #72203441

Order 26264.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₈×C₆₇	C₇	1	1	yes	maximal, characteristic
2	C₄×C₄₉×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₉×C₆₇	C₄	1	1	yes	characteristic
4	C₄₉×C₆₇	C₈	1	1	yes	characteristic, direct product factor, Hall
5	C₄×C₇×C₆₇	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₆₇	C₄×C₇	1	1	yes	characteristic
7	C₈×C₆₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₆₇	C₇×C₈	1	1	yes	characteristic
9	C₈×C₄₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₆₇	C₂×C₄₉	1	1	yes	characteristic
11	C₄×C₄₉	C₂×C₆₇	1	1	yes	characteristic
12	C₂×C₆₇	C₄×C₄₉	1	1	yes	characteristic
13	C₂×C₄₉	C₄×C₆₇	1	1	yes	characteristic
14	C₆₇	C₈×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₇×C₈	C₇×C₆₇	1	1	yes	characteristic
16	C₄₉	C₈×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₄×C₇	C₂×C₇×C₆₇	1	1	yes	characteristic
18	C₂×C₇	C₄×C₇×C₆₇	1	1	yes	characteristic
19	C₈	C₄₉×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₇×C₈×C₆₇	1	1	yes	characteristic
21	C₄	C₂×C₄₉×C₆₇	1	1	yes	characteristic
22	C₂	C₄×C₄₉×C₆₇	1	1	yes	characteristic

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.