Subgroups — C₂³×Dic₇₆₁ #37566935

Order 24352.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇₆₁	C₂	1	14	yes	maximal, direct product factor
2	C₂⁴×C₇₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₇₆₁	C₂²	1	28	yes	direct product factor
4	C₂³×C₇₆₁	C₄	1	8	yes	complemented
5	C₂³×C₇₆₁	C₂²	1	7	yes	—
6	C₂²×C₇₆₁	C₂×C₄	1	28	yes	complemented
7	C₂²×C₇₆₁	C₂³	1	7	yes	—
8	Dic₇₆₁	C₂³	1	8	yes	direct product factor
9	C₂×C₇₆₁	C₂²×C₄	1	14	yes	complemented
10	C₂×C₇₆₁	C₂⁴	1	1	yes	characteristic
11	C₇₆₁	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
12	C₂³×C₄	—	761	1	no	maximal, Sylow
13	C₂⁴	D₇₆₁	1	1	yes	characteristic
14	C₂²×C₄	—	761	14	no	—
15	C₂³	Dic₇₆₁	1	8	yes	direct product factor
16	C₂³	C₂×D₇₆₁	1	7	yes	—
17	C₂×C₄	—	761	28	no	—
18	C₂²	C₂×Dic₇₆₁	1	28	yes	direct product factor
19	C₂²	C₂²×D₇₆₁	1	7	yes	—
20	C₄	—	761	8	no	—
21	C₂	C₂²×Dic₇₆₁	1	14	yes	direct product factor
22	C₂	C₂³×D₇₆₁	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.