Subgroups — D₃×#15667865 #30685204

Order 17082.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15667865	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₃×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#15667865	—	3	1	no	maximal
4	C₃×C₁₃×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
5	#15667865	—	2	1	no	—
6	#15667865	D₃	1	1	yes	characteristic, direct product factor
7	C₂×C₁₃×C₇₃	—	3	1	no	Hall
8	D₃×C₇₃⋊C₃	—	13	1	no	maximal, Hall
9	C₁₃×C₇₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇₃⋊C₃	—	13	1	no	Hall
11	D₃×C₇₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented
12	C₂×C₇₃⋊C₃	—	39	1	no	—
13	D₃×C₁₃⋊C₃	—	73	1	no	maximal, Hall
14	C₃×C₇₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₇₃⋊C₃	—	13	1	no	—
16	C₇₃⋊C₃	—	26	1	no	—
17	C₂×C₇₃	—	3	1	no	Hall
18	C₃×C₁₃⋊C₃	—	73	1	no	Hall
19	D₃×C₁₃	C₇₃⋊C₃	1	1	yes	characteristic, complemented
20	C₂×C₁₃⋊C₃	—	219	1	no	—
21	C₇₃	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₃	C₂×C₇₃⋊C₃	1	1	yes	characteristic, complemented
23	C₁₃⋊C₃	—	73	1	no	—
24	C₁₃⋊C₃	—	146	1	no	—
25	C₂×C₁₃	—	3	1	no	Hall
26	C₃×D₃	—	949	1	no	Hall
27	C₁₃	D₃×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₃²	—	949	1	no	Sylow
29	C₂×C₃	—	2847	1	no	—
30	D₃	#15667865	1	1	yes	characteristic, direct product factor
31	C₃	—	1898	1	no	—
32	C₃	—	949	1	no	—
33	C₃	C₂×#15667865	1	1	yes	characteristic, complemented
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₇₃	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₇₃
UCS	C₁

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.