Subgroups — C₃²×#11923883 #23780905

Order 10404.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₃×#11923883	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇⋊D₁₇	C₂×C₃	1	4	yes	—
5	#11923883	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₇²	C₃×C₄	1	4	yes	complemented
7	C₃²×#595	—	17	18	no	maximal
8	C₁₇⋊D₁₇	C₂×C₃²	1	1	yes	characteristic
9	C₃²×D₁₇	—	17	18	no	—
10	C₁₇²	C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₃×#595	—	17	72	no	—
12	C₃²×C₁₇	#595	1	18	yes	complemented
13	C₃×D₁₇	—	17	72	no	—
14	#595	—	17	18	no	—
15	C₃×C₁₇	C₃×#595	1	72	yes	complemented
16	C₃²×C₄	—	289	1	no	Hall
17	D₁₇	—	17	18	no	—
18	C₂×C₃²	—	289	1	no	—
19	C₁₇	C₃²×#595	1	18	yes	complemented
20	C₃×C₄	—	289	4	no	—
21	C₃²	#11923883	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₃	—	289	4	no	—
23	C₄	—	289	1	no	Sylow
24	C₃	C₃×#11923883	1	4	yes	direct product factor
25	C₂	—	289	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.