Subgroups — C₁₇×#10624551 #27136715

Order 12393.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉²×C₁₇	C₃	1	1	yes	maximal, characteristic
2	C₁₇×#6855	C₃	1	12	yes	maximal
3	C₃²×C₉×C₁₇	C₃²	1	9	yes	—
4	C₃²×C₉×C₁₇	C₃²	1	4	yes	—
5	C₉²×C₁₇	C₉	1	9	yes	complemented
6	#10624551	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃³×C₁₇	C₃³	1	1	yes	characteristic
8	C₃×C₉×C₁₇	—	3	12	no	—
9	C₃×C₉×C₁₇	—	3	36	no	—
10	C₃×C₉×C₁₇	C₃×C₉	1	12	yes	—
11	C₃×C₉²	C₃×C₁₇	1	1	yes	characteristic
12	#6855	C₃×C₁₇	1	12	yes	—
13	C₃²×C₁₇	C₃²×C₉	1	1	yes	characteristic
14	C₃²×C₁₇	#737	1	12	yes	—
15	C₉×C₁₇	—	3	12	no	—
16	C₉×C₁₇	—	9	9	no	—
17	C₃²×C₉	C₃²×C₁₇	1	9	yes	—
18	C₃²×C₉	C₃²×C₁₇	1	4	yes	—
19	C₉²	C₉×C₁₇	1	9	yes	complemented
20	C₃×C₁₇	#6887	1	4	yes	—
21	C₃×C₁₇	#6897	1	9	yes	—
22	C₃³	C₃³×C₁₇	1	1	yes	characteristic
23	C₃×C₉	—	3	12	no	—
24	C₃×C₉	—	3	36	no	—
25	C₃×C₉	C₃×C₉×C₁₇	1	12	yes	—
26	C₁₇	#10624551	1	1	yes	characteristic, direct product factor, Sylow
27	C₃²	C₃²×C₉×C₁₇	1	1	yes	characteristic
28	C₃²	C₁₇×#737	1	12	yes	—
29	C₉	—	3	12	no	—
30	C₉	—	9	9	no	—
31	C₃	C₁₇×#6887	1	4	yes	—
32	C₃	C₁₇×#6897	1	9	yes	—

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.