Subgroups — #16924461

Order 4352.

696 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537417	C₂	1	1	yes	maximal, characteristic
2	C₄×#10587612	C₂	1	1	yes	maximal, characteristic
3	#14526670	C₂	1	4	yes	maximal
4	C₁₇×#2283	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587612	—	2	1	no	—
6	#11762866	—	2	1	no	—
7	#11762866	—	2	1	no	—
8	#11762862	—	2	1	no	—
9	#11762862	—	2	1	no	—
10	#11762833	C₄	1	2	yes	complemented
11	#11762773	C₂²	1	2	yes	—
12	C₄×#63223	C₄	1	2	yes	complemented
13	C₄×C₄⋊Dic₁₇	—	2	1	no	—
14	C₄×C₄⋊Dic₁₇	C₄	1	2	yes	complemented
15	C₄×C₂²⋊Dic₁₇	—	2	1	no	—
16	C₄×C₂²⋊Dic₁₇	C₂²	1	2	yes	—
17	#11762655	C₄	1	2	yes	complemented
18	C₄²×Dic₁₇	—	2	1	no	—
19	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
20	C₁₇×#383	C₄	1	2	yes	complemented
21	C₁₇×#382	C₄	1	2	yes	complemented
22	C₁₇×#381	—	2	1	no	—
23	C₁₇×#380	—	2	1	no	—
24	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
25	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
26	C₁₇×#376	—	2	1	no	—
27	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
31	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
32	C₂×C₄²×C₁₇	—	2	2	no	—
33	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
45	C₂×C₂²⋊Dic₁₇	—	2	2	no	—
46	#10587612	—	2	8	no	—
47	C₂×C₄⋊Dic₁₇	—	2	2	no	—
48	C₂×C₄×Dic₁₇	—	2	2	no	—
49	C₂×C₄×Dic₁₇	—	2	2	no	—
50	C₂×C₄×Dic₁₇	—	2	2	no	—
51	C₂×#63223	C₂×C₄	1	4	yes	—
52	C₁₇×#95	—	2	2	no	—
53	C₁₇×#95	—	2	2	no	—
54	C₁₇×#95	—	2	2	no	—
55	C₁₇×#95	C₂×C₄	1	4	yes	—
56	#10587502	—	2	2	no	—
57	#10587502	C₂×C₄	1	4	yes	—
58	C₂²⋊#3622	—	2	2	no	—
59	C₂²⋊#3622	—	2	2	no	—
60	C₄⋊#3622	—	2	2	no	—
61	C₄⋊#3622	—	2	2	no	—
62	#10587474	—	2	2	no	—
63	C₄×#3622	—	2	2	no	—
64	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₇	—	2	4	no	—
66	C₂²×C₄×C₁₇	—	2	4	no	—
67	C₂²×C₄×C₁₇	—	4	2	no	—
68	C₂²×C₄×C₁₇	—	4	2	no	—
69	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
87	C₂²×Dic₁₇	—	2	4	no	—
88	C₄⋊C₄×C₁₇	—	4	4	no	—
89	C₂²⋊C₄×C₁₇	—	4	4	no	—
90	C₄²×C₁₇	—	4	4	no	—
91	C₄²×C₁₇	C₄²	1	1	yes	characteristic
92	C₄²×C₁₇	C₄²	1	1	yes	characteristic
93	C₄²×C₁₇	C₄²	1	1	yes	characteristic
94	C₄²×C₁₇	C₄²	1	1	yes	characteristic
95	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
107	C₂²⋊Dic₁₇	—	2	8	no	—
108	C₄⋊Dic₁₇	—	2	8	no	—
109	C₄×Dic₁₇	—	2	8	no	—
110	C₄×Dic₁₇	—	4	4	no	—
111	C₄×Dic₁₇	—	4	4	no	—
112	#63223	—	4	4	no	—
113	C₂×#3622	—	2	4	no	—
114	#8052	—	17	1	no	maximal, Sylow
115	C₂³×C₁₇	—	2	2	no	—
116	C₂³×C₁₇	—	2	2	no	—
117	C₂³×C₁₇	—	4	1	no	—
118	C₂³×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₇	—	2	2	no	—
122	C₂×C₄×C₁₇	—	2	2	no	—
123	C₂×C₄×C₁₇	—	2	2	no	—
124	C₂×C₄×C₁₇	—	2	2	no	—
125	C₂×C₄×C₁₇	—	2	2	no	—
126	C₂×C₄×C₁₇	—	2	2	no	—
127	C₂×C₄×C₁₇	—	2	2	no	—
128	C₂×C₄×C₁₇	—	2	2	no	—
129	C₂×C₄×C₁₇	—	2	2	no	—
130	C₂×C₄×C₁₇	—	2	2	no	—
131	C₂×C₄×C₁₇	—	4	1	no	—
132	C₂×C₄×C₁₇	—	4	1	no	—
133	C₂×C₄×C₁₇	—	4	1	no	—
134	C₂×C₄×C₁₇	—	4	1	no	—
135	C₂×C₄×C₁₇	—	4	1	no	—
136	C₂×C₄×C₁₇	—	4	1	no	—
137	C₂×C₄×C₁₇	—	4	1	no	—
138	C₂×C₄×C₁₇	—	4	4	no	—
139	C₂×C₄×C₁₇	—	4	4	no	—
140	C₂×C₄×C₁₇	—	4	4	no	—
141	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
148	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
149	C₂×C₄×C₁₇	#104	1	4	yes	—
150	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×Dic₁₇	—	2	8	no	—
155	C₂×Dic₁₇	—	4	4	no	—
156	C₂×Dic₁₇	—	4	4	no	—
157	#3622	—	4	4	no	—
158	#2920	—	17	1	no	—
159	#2283	D₁₇	1	1	yes	characteristic
160	C₄×#117	—	17	1	no	—
161	#1297	—	17	4	no	—
162	C₂²×C₁₇	—	2	1	no	—
163	C₂²×C₁₇	—	2	1	no	—
164	C₂²×C₁₇	—	2	1	no	—
165	C₂²×C₁₇	—	2	1	no	—
166	C₂²×C₁₇	—	2	1	no	—
167	C₂²×C₁₇	—	2	1	no	—
168	C₂²×C₁₇	—	2	1	no	—
169	C₂²×C₁₇	—	4	4	no	—
170	C₂²×C₁₇	C₂×#95	1	1	yes	characteristic
171	C₂²×C₁₇	C₂×#104	1	2	yes	—
172	C₂²×C₁₇	#421	1	2	yes	—
173	C₄×C₁₇	—	2	1	no	—
174	C₄×C₁₇	—	2	1	no	—
175	C₄×C₁₇	—	2	1	no	—
176	C₄×C₁₇	—	2	1	no	—
177	C₄×C₁₇	—	2	1	no	—
178	C₄×C₁₇	—	2	1	no	—
179	C₄×C₁₇	—	2	1	no	—
180	C₄×C₁₇	—	2	1	no	—
181	C₄×C₁₇	—	2	1	no	—
182	C₄×C₁₇	—	8	4	no	—
183	C₄×C₁₇	#339	1	2	yes	—
184	C₄×C₁₇	#339	1	2	yes	—
185	C₄×C₁₇	#410	1	2	yes	—
186	Dic₁₇	—	4	8	no	—
187	C₂×#117	—	34	1	no	—
188	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
189	#432	—	34	1	no	—
190	#432	—	34	1	no	—
191	#431	—	34	1	no	—
192	#431	—	34	1	no	—
193	#423	—	17	2	no	—
194	#407	—	17	2	no	—
195	C₄×M₁₆	—	17	2	no	—
196	#383	Dic₁₇	1	2	yes	complemented
197	#382	Dic₁₇	1	2	yes	complemented
198	#381	—	2	1	no	—
199	#380	—	2	1	no	—
200	C₄×C₄⋊C₄	—	2	1	no	—
201	C₄×C₄⋊C₄	—	17	2	no	—
202	C₄×C₄⋊C₄	—	34	1	no	—
203	C₄×C₂²⋊C₄	—	17	2	no	—
204	C₄×C₂²⋊C₄	—	34	1	no	—
205	C₄×C₂²⋊C₄	C₂×D₁₇	1	2	yes	—
206	#376	—	2	1	no	—
207	#376	—	17	2	no	—
208	C₄³	—	34	1	no	—
209	C₂×C₁₇	—	2	2	no	—
210	C₂×C₁₇	—	2	2	no	—
211	C₂×C₁₇	—	4	1	no	—
212	C₂×C₁₇	C₂×#339	1	1	yes	characteristic
213	C₂×C₁₇	#1733	1	1	yes	characteristic
214	C₂×C₁₇	#1740	1	1	yes	characteristic
215	C₂³×C₄	C₂²⋊D₁₇	1	1	yes	characteristic
216	C₂³×C₄	C₂²⋊D₁₇	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
218	C₂×M₁₆	—	17	4	no	—
219	#117	—	34	8	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	34	2	no	—
222	C₂×C₂²⋊C₄	—	2	2	no	—
223	C₂×C₂²⋊C₄	—	34	2	no	—
224	C₂×C₄²	—	2	2	no	—
225	C₂×C₄²	—	34	2	no	—
226	C₂×C₄²	—	34	2	no	—
227	C₂×C₄²	—	34	2	no	—
228	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
229	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
230	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
234	C₂×C₄²	D₆₈	1	1	yes	characteristic
235	C₂×C₄²	D₆₈	1	1	yes	characteristic
236	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
237	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
240	C₄⋊C₈	—	34	2	no	—
241	C₄⋊C₈	—	34	2	no	—
242	C₂²⋊C₈	—	34	2	no	—
243	C₂²⋊C₈	—	34	2	no	—
244	#97	—	34	2	no	—
245	C₄×C₈	—	34	2	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	—	17	4	no	—
250	#95	—	34	2	no	—
251	#95	C₂×Dic₁₇	1	4	yes	—
252	C₁₇	#8052	1	1	yes	characteristic, complemented, Sylow
253	C₂⁴	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	34	4	no	—
259	C₂²×C₄	#63225	1	1	yes	characteristic
260	C₂²×C₄	#63225	1	1	yes	characteristic
261	C₂²×C₄	#63225	1	1	yes	characteristic
262	C₂²×C₄	#63225	1	1	yes	characteristic
263	C₂²×C₄	#63227	1	1	yes	characteristic
264	C₂²×C₄	#63227	1	1	yes	characteristic
265	C₂²×C₄	#63227	1	1	yes	characteristic
266	C₂²×C₄	#63227	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
277	M₁₆	—	68	4	no	—
278	C₂×C₈	—	34	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	34	8	no	—
281	C₂²⋊C₄	—	4	4	no	—
282	C₂²⋊C₄	—	34	8	no	—
283	C₄²	—	4	4	no	—
284	C₄²	—	34	8	no	—
285	C₄²	—	68	4	no	—
286	C₄²	—	68	4	no	—
287	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
288	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
289	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
290	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
291	C₄²	#63225	1	1	yes	characteristic
292	C₄²	#63225	1	1	yes	characteristic
293	C₄²	#63225	1	1	yes	characteristic
294	C₄²	#63225	1	1	yes	characteristic
295	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
296	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
297	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
298	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
299	C₄²	#63227	1	1	yes	characteristic
300	C₄²	#63227	1	1	yes	characteristic
301	C₄²	#63227	1	1	yes	characteristic
302	C₄²	#63227	1	1	yes	characteristic
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	C₂×#63225	1	1	yes	characteristic
307	C₂³	C₂×#63227	1	1	yes	characteristic
308	C₂³	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	34	8	no	—
330	C₂×C₄	—	68	4	no	—
331	C₂×C₄	—	68	4	no	—
332	C₂×C₄	#10587502	1	1	yes	characteristic
333	C₂×C₄	#10587502	1	1	yes	characteristic
334	C₂×C₄	#10587502	1	1	yes	characteristic
335	C₂×C₄	#10587502	1	1	yes	characteristic
336	C₂×C₄	#10587502	1	1	yes	characteristic
337	C₂×C₄	#10587502	1	1	yes	characteristic
338	C₂×C₄	#10587502	1	1	yes	characteristic
339	C₂×C₄	#10587502	1	1	yes	characteristic
340	C₂×C₄	#10587508	1	4	yes	—
341	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
342	C₂×C₄	C₂×#63225	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
344	C₂×C₄	C₂×#63227	1	1	yes	characteristic
345	C₈	—	68	4	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	4	4	no	—
354	C₂²	C₂×#10587502	1	1	yes	characteristic
355	C₂²	C₂×#10587508	1	2	yes	—
356	C₂²	#11762827	1	2	yes	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	8	4	no	—
367	C₄	—	68	8	no	—
368	C₄	#11762568	1	2	yes	—
369	C₄	#11762568	1	2	yes	—
370	C₄	#11762782	1	2	yes	—
371	C₂	—	2	2	no	—
372	C₂	—	2	2	no	—
373	C₂	—	4	1	no	—
374	C₂	C₂×#11762568	1	1	yes	characteristic
375	C₂	#14528494	1	1	yes	characteristic
376	C₂	#14528516	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#63227
commutator	C₂×C₄×C₁₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₇
Fitting	C₁₇×#2283	C₂
socle	C₂²×C₁₇	C₂×#95
prime radical	C₂⁴×C₁₇	C₂×D₄
cosocle	C₂³×C₄×C₁₇	C₂³
hypercenter	#2283	D₁₇
hypocenter	C₁₇	#8052
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2283

Complements

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

N	H ≅ G/N	type
10. #11762833	C₄	semidirect
12. C₄×#63223	C₄	semidirect
14. C₄×C₄⋊Dic₁₇	C₄	semidirect
17. #11762655	C₄	semidirect
20. C₁₇×#383	C₄	semidirect
21. C₁₇×#382	C₄	semidirect
196. #383	Dic₁₇	semidirect
197. #382	Dic₁₇	semidirect
252. C₁₇	#8052	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14537417	2
C₄×#10587612	2
#14526670	2
C₁₇×#2283	2
#8052	17