Subgroups — C₇×#17960 #13195176

Order 1792.

666 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3167	C₂	1	1	yes	maximal, characteristic
2	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2931	C₂	1	1	yes	maximal, characteristic
4	C₇×#1592	C₂	1	4	yes	maximal, complemented
5	C₇×SD₁₆⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₇×#1567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1493	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1492	C₂	1	1	yes	maximal, characteristic
9	C₂×C₇×#322	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#131	—	2	1	no	—
11	C₇×#533	C₂²	1	1	yes	characteristic
12	C₇×#532	C₂²	1	1	yes	characteristic
13	C₇×#498	C₄	1	1	yes	characteristic
14	C₇×#492	C₄	1	1	yes	characteristic
15	C₇×#487	C₄	1	1	yes	characteristic
16	C₇×#486	C₄	1	1	yes	characteristic
17	C₇×#465	C₄	1	4	yes	—
18	C₇×#446	—	2	1	no	—
19	C₇×#446	C₂²	1	2	yes	—
20	C₇×C₈×Q₈	—	2	1	no	—
21	C₇×C₈×Q₈	C₂²	1	2	yes	—
22	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
23	C₇×#436	—	2	1	no	—
24	C₇×#436	C₂²	1	2	yes	—
25	C₇×C₈×D₄	—	2	1	no	—
26	C₇×C₈×D₄	C₂²	1	2	yes	—
27	C₇×#424	—	2	1	no	—
28	C₇×#423	C₂²	1	1	yes	characteristic
29	C₇×#423	C₂²	1	1	yes	characteristic
30	C₇×#408	—	2	1	no	—
31	C₇×#405	—	2	1	no	—
32	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
35	C₇×#335	C₂²	1	4	yes	—
36	C₇×Q₈⋊C₈	C₂²	1	4	yes	—
37	C₇×D₄⋊C₈	C₂²	1	4	yes	—
38	C₇×#322	C₂²	1	2	yes	—
39	C₇×#322	C₂²	1	2	yes	—
40	#17960	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×C₇×#41	—	2	1	no	—
42	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
43	C₇×#131	—	4	4	no	—
44	C₂×C₇×M₁₆	—	2	1	no	—
45	C₂×C₇×M₁₆	—	2	1	no	—
46	C₂×C₇×M₁₆	—	2	2	no	—
47	C₂²×C₇×C₈	—	2	1	no	—
48	C₂²×C₇×C₈	—	2	2	no	—
49	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
50	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
51	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
52	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₇×#127	C₂×C₄	1	1	yes	characteristic
56	C₇×#125	—	2	1	no	—
57	C₇×#124	—	2	1	no	—
58	C₇×C₂²⋊Q₈	—	2	1	no	—
59	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
60	C₇×#121	—	2	1	no	—
61	C₇×#121	C₂×C₄	1	2	yes	—
62	C₄×C₇×Q₈	—	2	1	no	—
63	C₄×C₇×Q₈	C₂³	1	2	yes	—
64	C₄×C₇×D₄	—	2	1	no	—
65	C₄×C₇×D₄	C₂³	1	2	yes	—
66	C₇×#117	—	2	1	no	—
67	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
68	C₇×#106	C₂×C₄	1	4	yes	—
69	C₇×C₄⋊C₈	—	2	2	no	—
70	C₇×C₄⋊C₈	—	2	2	no	—
71	C₇×C₄⋊C₈	—	2	1	no	—
72	C₇×C₄⋊C₈	—	2	1	no	—
73	C₇×C₄⋊C₈	C₂³	1	2	yes	—
74	C₇×C₄⋊C₈	C₂³	1	2	yes	—
75	C₇×#103	C₂×C₄	1	4	yes	—
76	C₇×#102	C₂×C₄	1	4	yes	—
77	C₇×C₂²⋊C₈	—	2	2	no	—
78	C₇×C₂²⋊C₈	—	2	2	no	—
79	C₇×#97	—	2	2	no	—
80	C₄×C₇×C₈	—	2	2	no	—
81	C₄×C₇×C₈	—	2	1	no	—
82	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
84	C₄×C₇×C₈	D₄	1	1	yes	characteristic
85	C₄×C₇×C₈	D₄	1	1	yes	characteristic
86	C₄×C₇×C₈	C₂³	1	2	yes	—
87	C₄×C₇×C₈	C₂³	1	2	yes	—
88	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
89	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
90	#3167	C₂×C₇	1	1	yes	characteristic
91	#2960	C₂×C₇	1	1	yes	characteristic, complemented
92	#2931	C₂×C₇	1	1	yes	characteristic
93	#1592	C₂×C₇	1	4	yes	complemented
94	SD₁₆⋊C₈	C₂×C₇	1	4	yes	complemented
95	#1567	C₂×C₇	1	1	yes	characteristic, complemented
96	#1493	C₂×C₇	1	1	yes	characteristic, complemented
97	#1492	C₂×C₇	1	1	yes	characteristic
98	C₂×#322	C₂×C₇	1	1	yes	characteristic, complemented
99	C₇×#41	—	4	2	no	—
100	C₇×#41	—	4	2	no	—
101	C₂×C₇×Q₈	—	2	1	no	—
102	C₂×C₇×Q₈	—	2	1	no	—
103	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
104	C₂×C₇×D₄	—	2	2	no	—
105	C₂×C₇×D₄	—	2	1	no	—
106	C₂×C₇×D₄	—	2	1	no	—
107	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₇	—	2	2	no	—
109	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	#41	1	1	yes	characteristic
112	C₇×SD₁₆	—	2	8	no	—
113	C₇×M₁₆	—	4	4	no	—
114	C₇×M₁₆	—	4	2	no	—
115	C₇×M₁₆	—	4	2	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	—	2	4	no	—
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	4	4	no	—
123	C₂×C₇×C₈	—	4	2	no	—
124	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
125	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
127	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
130	C₇×C₄⋊C₄	—	2	1	no	—
131	C₇×C₄⋊C₄	—	2	1	no	—
132	C₇×C₄⋊C₄	—	2	1	no	—
133	C₇×C₄⋊C₄	—	2	1	no	—
134	C₇×C₄⋊C₄	—	2	2	no	—
135	C₇×C₄⋊C₄	—	2	2	no	—
136	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
137	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
138	C₇×C₂²⋊C₄	—	2	2	no	—
139	C₇×C₂²⋊C₄	—	2	2	no	—
140	C₇×C₂²⋊C₄	—	2	2	no	—
141	C₄²×C₇	—	2	2	no	—
142	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₇	#41	1	1	yes	characteristic
145	C₄²×C₇	C₂⁴	1	1	yes	characteristic
146	C₂×#131	—	2	1	no	—
147	#533	C₂²×C₇	1	1	yes	characteristic
148	#532	C₂²×C₇	1	1	yes	characteristic
149	#498	C₄×C₇	1	1	yes	characteristic
150	#492	C₄×C₇	1	1	yes	characteristic
151	#487	C₄×C₇	1	1	yes	characteristic
152	#486	C₄×C₇	1	1	yes	characteristic
153	#465	C₄×C₇	1	4	yes	—
154	#446	—	2	1	no	—
155	#446	C₂²×C₇	1	2	yes	—
156	C₈×Q₈	—	2	1	no	—
157	C₈×Q₈	C₂²×C₇	1	2	yes	—
158	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
159	#436	—	2	1	no	—
160	#436	C₂²×C₇	1	2	yes	—
161	C₈×D₄	—	2	1	no	—
162	C₈×D₄	C₂²×C₇	1	2	yes	—
163	#424	—	2	1	no	—
164	#423	C₂²×C₇	1	1	yes	characteristic
165	#423	C₂²×C₇	1	1	yes	characteristic
166	#408	—	2	1	no	—
167	#405	—	2	1	no	—
168	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
170	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
171	#335	C₂²×C₇	1	4	yes	—
172	Q₈⋊C₈	C₂²×C₇	1	4	yes	—
173	D₄⋊C₈	C₂²×C₇	1	4	yes	—
174	#322	C₂²×C₇	1	2	yes	—
175	#322	C₂²×C₇	1	2	yes	—
176	C₂³×C₇	—	2	2	no	—
177	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
178	C₇×Q₈	—	2	4	no	—
179	C₇×Q₈	—	4	2	no	—
180	C₇×Q₈	—	4	2	no	—
181	C₇×D₄	—	2	4	no	—
182	C₇×D₄	—	4	4	no	—
183	C₇×D₄	—	4	2	no	—
184	C₇×D₄	—	4	2	no	—
185	C₂×C₄×C₇	—	2	2	no	—
186	C₂×C₄×C₇	—	2	2	no	—
187	C₂×C₄×C₇	—	2	2	no	—
188	C₂×C₄×C₇	—	2	2	no	—
189	C₂×C₄×C₇	—	2	2	no	—
190	C₂×C₄×C₇	—	4	2	no	—
191	C₂×C₄×C₇	—	4	2	no	—
192	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
196	C₂×C₄×C₇	#137	1	2	yes	—
197	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
200	C₇×C₈	—	2	2	no	—
201	C₇×C₈	—	2	1	no	—
202	C₇×C₈	—	2	1	no	—
203	C₇×C₈	—	2	1	no	—
204	C₇×C₈	—	2	1	no	—
205	C₇×C₈	—	4	2	no	—
206	C₇×C₈	—	4	2	no	—
207	C₇×C₈	—	4	2	no	—
208	C₇×C₈	#131	1	4	yes	complemented
209	C₂×#41	—	2	1	no	—
210	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
211	#131	—	4	4	no	—
212	C₂×M₁₆	—	2	1	no	—
213	C₂×M₁₆	—	2	1	no	—
214	C₂×M₁₆	—	2	2	no	—
215	C₂²×C₈	—	2	1	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
218	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
219	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
220	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
221	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
222	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
223	#127	C₂×C₄×C₇	1	1	yes	characteristic
224	#125	—	2	1	no	—
225	#124	—	2	1	no	—
226	C₂²⋊Q₈	—	2	1	no	—
227	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
228	#121	—	2	1	no	—
229	#121	C₂×C₄×C₇	1	2	yes	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	C₂³×C₇	1	2	yes	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	C₂³×C₇	1	2	yes	—
234	#117	—	2	1	no	—
235	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
236	#106	C₂×C₄×C₇	1	4	yes	—
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	2	1	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	C₂³×C₇	1	2	yes	—
242	C₄⋊C₈	C₂³×C₇	1	2	yes	—
243	#103	C₂×C₄×C₇	1	4	yes	—
244	#102	C₂×C₄×C₇	1	4	yes	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	#97	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	2	1	no	—
250	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
251	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
252	C₄×C₈	C₇×D₄	1	1	yes	characteristic
253	C₄×C₈	C₇×D₄	1	1	yes	characteristic
254	C₄×C₈	C₂³×C₇	1	2	yes	—
255	C₄×C₈	C₂³×C₇	1	2	yes	—
256	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
257	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
258	C₂²×C₇	—	2	1	no	—
259	C₂²×C₇	—	2	1	no	—
260	C₂²×C₇	—	4	2	no	—
261	C₂²×C₇	—	4	2	no	—
262	C₂²×C₇	—	4	2	no	—
263	C₂²×C₇	#440	1	2	yes	—
264	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
265	C₄×C₇	—	2	1	no	—
266	C₄×C₇	—	2	1	no	—
267	C₄×C₇	—	4	2	no	—
268	C₄×C₇	—	4	2	no	—
269	C₄×C₇	—	4	2	no	—
270	C₄×C₇	#440	1	2	yes	—
271	C₄×C₇	#444	1	2	yes	—
272	C₄×C₇	C₂×#131	1	2	yes	—
273	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₄×C₇	C₂×#137	1	1	yes	characteristic
275	#41	—	4	2	no	—
276	#41	—	4	2	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
287	C₂²×C₄	C₇×#41	1	1	yes	characteristic
288	SD₁₆	—	2	8	no	—
289	M₁₆	—	4	4	no	—
290	M₁₆	—	4	2	no	—
291	M₁₆	—	4	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	4	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
301	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
302	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
303	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
304	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
305	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
313	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
319	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
320	C₄²	C₇×#41	1	1	yes	characteristic
321	C₄²	C₂⁴×C₇	1	1	yes	characteristic
322	C₂×C₇	—	2	2	no	—
323	C₂×C₇	—	8	2	no	—
324	C₂×C₇	#2931	1	1	yes	characteristic
325	C₂×C₇	C₂×#440	1	1	yes	characteristic
326	C₂×C₇	C₂×#444	1	1	yes	characteristic
327	C₂³	—	2	2	no	—
328	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
329	Q₈	—	2	4	no	—
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	D₄	—	2	4	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
344	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
345	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
346	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
347	C₂×C₄	C₇×#137	1	2	yes	—
348	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
349	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
350	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
351	C₈	—	2	2	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	2	no	—
359	C₈	C₇×#131	1	4	yes	complemented
360	C₇	#17960	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	C₇×#440	1	2	yes	—
367	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	2	no	—
373	C₄	C₇×#440	1	2	yes	—
374	C₄	C₇×#444	1	2	yes	—
375	C₄	C₂×C₇×#131	1	2	yes	—
376	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₄	C₂×C₇×#137	1	1	yes	characteristic
378	C₂	—	2	2	no	—
379	C₂	—	8	2	no	—
380	C₂	C₇×#2931	1	1	yes	characteristic
381	C₂	C₂×C₇×#440	1	1	yes	characteristic
382	C₂	C₂×C₇×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2960	C₂	semidirect
4. C₇×#1592	C₂	semidirect
5. C₇×SD₁₆⋊C₈	C₂	semidirect
6. C₇×#1567	C₂	semidirect
7. C₇×#1493	C₂	semidirect
9. C₂×C₇×#322	C₂	semidirect
40. #17960	C₇	direct (N × H)
91. #2960	C₂×C₇	semidirect
93. #1592	C₂×C₇	semidirect
94. SD₁₆⋊C₈	C₂×C₇	semidirect
95. #1567	C₂×C₇	semidirect
96. #1493	C₂×C₇	semidirect
98. C₂×#322	C₂×C₇	semidirect
208. C₇×C₈	#131	semidirect
359. C₈	C₇×#131	semidirect
360. C₇	#17960	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3167	2
C₇×#2960	2
C₇×#2931	2
C₇×#1592	2
C₇×SD₁₆⋊C₈	2
C₇×#1567	2
C₇×#1493	2
C₇×#1492	2
C₂×C₇×#322	2
#17960	7

Subgroups — C7×#17960 #13195176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17960 #13195176