Subgroups — C₃×D₃₂₈ #14520113

Order 1968.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₆₄	C₂	1	2	yes	maximal, complemented
2	C₃×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₂₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×D₄₁	—	2	2	no	—
5	C₃×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	D₁₆₄	C₂×C₃	1	2	yes	complemented
7	C₈×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₄₁	D₄	1	1	yes	characteristic
9	C₃×D₄₁	—	4	2	no	—
10	C₂×D₄₁	—	2	2	no	—
11	C₄×C₄₁	C₂²×C₃	1	1	yes	characteristic
12	C₃×C₄₁	D₈	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₁	C₃×D₄	1	1	yes	characteristic
14	D₄₁	—	4	2	no	—
15	C₃×D₈	—	41	1	no	maximal, Hall
16	C₄₁	C₃×D₈	1	1	yes	characteristic, complemented, Sylow
17	C₃×D₄	—	41	2	no	—
18	C₃×C₈	D₄₁	1	1	yes	characteristic, complemented
19	D₈	—	41	1	no	Sylow
20	C₂²×C₃	—	82	2	no	—
21	C₃×C₄	C₂×D₄₁	1	1	yes	characteristic
22	D₄	—	41	2	no	—
23	C₈	C₃×D₄₁	1	1	yes	characteristic, complemented
24	C₂×C₃	—	164	2	no	—
25	C₂×C₃	D₁₆₄	1	1	yes	characteristic
26	C₂²	—	82	2	no	—
27	C₄	C₂×C₃×D₄₁	1	1	yes	characteristic
28	C₃	D₃₂₈	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	164	2	no	—
30	C₂	C₃×D₁₆₄	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.