Subgroups — C₇×#17812 #13195028

Order 1792.

602 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2989	C₂	1	1	yes	maximal, characteristic
2	C₇×#2988	C₂	1	1	yes	maximal, characteristic
3	C₇×#2922	C₂	1	1	yes	maximal, characteristic
4	C₇×#1574	C₂	1	2	yes	maximal, complemented
5	C₇×#1573	C₂	1	2	yes	maximal, complemented
6	C₇×#1572	C₂	1	2	yes	maximal, complemented
7	C₇×#1571	C₂	1	2	yes	maximal, complemented
8	C₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₇×#41	C₂²	1	1	yes	characteristic
13	C₇×#446	—	2	1	no	—
14	C₇×C₈×Q₈	—	2	1	no	—
15	C₇×#436	—	2	1	no	—
16	C₇×#435	—	2	2	no	—
17	C₇×C₈×D₄	—	2	2	no	—
18	C₇×C₈×D₄	—	2	1	no	—
19	C₇×#433	C₄	1	4	yes	—
20	C₇×#432	C₂²	1	2	yes	—
21	C₇×#431	C₂²	1	1	yes	characteristic
22	C₇×#431	C₂²	1	2	yes	—
23	C₇×#431	C₂²	1	1	yes	characteristic
24	C₇×#431	C₂²	1	2	yes	—
25	C₇×#431	C₂²	1	2	yes	—
26	C₇×#424	C₄	1	2	yes	—
27	C₇×#423	C₂²	1	2	yes	—
28	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₇×#408	C₄	1	2	yes	—
32	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
34	C₇×#335	C₂²	1	2	yes	—
35	C₇×#335	C₂²	1	2	yes	—
36	C₇×#335	C₂²	1	1	yes	characteristic
37	C₇×#335	C₂²	1	1	yes	characteristic
38	C₇×#335	C₂²	1	2	yes	—
39	C₇×#335	C₂²	1	2	yes	—
40	C₇×#334	C₂²	1	1	yes	characteristic
41	C₇×#334	C₂²	1	1	yes	characteristic
42	C₇×#334	C₂²	1	2	yes	—
43	C₇×#334	C₂²	1	2	yes	—
44	#17812	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
46	C₂×C₇×M₁₆	—	2	2	no	—
47	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
48	C₂²×C₇×C₈	—	2	1	no	—
49	C₂²×C₇×C₈	—	2	2	no	—
50	C₂²×C₇×C₈	—	2	1	no	—
51	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
52	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
53	C₄×C₇×Q₈	Q₈	1	1	yes	characteristic
54	C₄×C₇×D₄	D₄	1	2	yes	—
55	C₄×C₇×D₄	D₄	1	1	yes	characteristic
56	C₄×C₇×D₄	Q₈	1	2	yes	—
57	C₄×C₇×D₄	Q₈	1	1	yes	characteristic
58	C₇×#117	C₂×C₄	1	1	yes	characteristic
59	C₇×#117	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₇	C₂³	1	2	yes	—
62	C₇×C₄⋊C₈	—	2	1	no	—
63	C₇×C₄⋊C₈	—	2	2	no	—
64	C₇×C₄⋊C₈	—	2	1	no	—
65	C₇×C₄⋊C₈	—	2	2	no	—
66	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
67	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
68	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
69	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
70	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
71	C₇×C₄⋊C₈	C₂³	1	2	yes	—
72	C₇×C₄⋊C₈	C₂³	1	2	yes	—
73	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
74	C₇×C₂²⋊C₈	—	2	1	no	—
75	C₇×C₂²⋊C₈	—	2	2	no	—
76	C₇×C₂²⋊C₈	—	2	1	no	—
77	C₇×C₂²⋊C₈	—	2	2	no	—
78	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
79	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
80	C₇×#97	—	2	2	no	—
81	C₇×#97	C₂×C₄	1	2	yes	—
82	C₄×C₇×C₈	—	2	1	no	—
83	C₄×C₇×C₈	—	2	2	no	—
84	C₄×C₇×C₈	—	2	1	no	—
85	C₄×C₇×C₈	C₂×C₄	1	2	yes	—
86	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₄×C₇×C₈	C₂³	1	2	yes	—
88	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
89	#2989	C₂×C₇	1	1	yes	characteristic
90	#2988	C₂×C₇	1	1	yes	characteristic
91	#2922	C₂×C₇	1	1	yes	characteristic
92	#1574	C₂×C₇	1	2	yes	complemented
93	#1573	C₂×C₇	1	2	yes	complemented
94	#1572	C₂×C₇	1	2	yes	complemented
95	#1571	C₂×C₇	1	2	yes	complemented
96	#1565	C₂×C₇	1	1	yes	characteristic, complemented
97	#1565	C₂×C₇	1	1	yes	characteristic, complemented
98	#1564	C₂×C₇	1	1	yes	characteristic, complemented
99	C₂×#335	C₂×C₇	1	1	yes	characteristic, complemented
100	C₇×#41	—	2	4	no	—
101	C₂×C₇×Q₈	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₇×D₄	C₄⋊C₄	1	2	yes	—
103	C₂×C₇×D₄	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
110	C₇×M₁₆	—	2	4	no	—
111	C₇×M₁₆	—	8	2	no	—
112	C₂×C₇×C₈	—	2	4	no	—
113	C₂×C₇×C₈	—	2	1	no	—
114	C₂×C₇×C₈	—	2	1	no	—
115	C₂×C₇×C₈	—	2	1	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	1	no	—
118	C₂×C₇×C₈	—	2	2	no	—
119	C₂×C₇×C₈	—	8	1	no	—
120	C₂×C₇×C₈	—	8	2	no	—
121	C₂×C₇×C₈	—	8	1	no	—
122	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
123	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
124	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
125	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
126	C₇×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
127	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
128	C₇×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
129	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
130	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
131	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
132	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₇	C₂²×C₄	1	2	yes	—
134	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₇	C₂×D₄	1	2	yes	—
136	C₄²×C₇	C₂×Q₈	1	2	yes	—
137	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
138	C₄²×C₇	C₂⁴	1	1	yes	characteristic
139	C₄×#41	C₂²×C₇	1	1	yes	characteristic
140	#446	—	2	1	no	—
141	C₈×Q₈	—	2	1	no	—
142	#436	—	2	1	no	—
143	#435	—	2	2	no	—
144	C₈×D₄	—	2	2	no	—
145	C₈×D₄	—	2	1	no	—
146	#433	C₄×C₇	1	4	yes	—
147	#432	C₂²×C₇	1	2	yes	—
148	#431	C₂²×C₇	1	1	yes	characteristic
149	#431	C₂²×C₇	1	1	yes	characteristic
150	#431	C₂²×C₇	1	2	yes	—
151	#431	C₂²×C₇	1	2	yes	—
152	#431	C₂²×C₇	1	2	yes	—
153	#424	C₄×C₇	1	2	yes	—
154	#423	C₂²×C₇	1	2	yes	—
155	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
156	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
157	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
158	#408	C₄×C₇	1	2	yes	—
159	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
160	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
161	#335	C₂²×C₇	1	2	yes	—
162	#335	C₂²×C₇	1	2	yes	—
163	#335	C₂²×C₇	1	1	yes	characteristic
164	#335	C₂²×C₇	1	1	yes	characteristic
165	#335	C₂²×C₇	1	2	yes	—
166	#335	C₂²×C₇	1	2	yes	—
167	#334	C₂²×C₇	1	1	yes	characteristic
168	#334	C₂²×C₇	1	1	yes	characteristic
169	#334	C₂²×C₇	1	2	yes	—
170	#334	C₂²×C₇	1	2	yes	—
171	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
172	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₇×Q₈	—	2	2	no	—
174	C₇×D₄	—	2	4	no	—
175	C₇×D₄	—	2	2	no	—
176	C₂×C₄×C₇	—	2	4	no	—
177	C₂×C₄×C₇	—	2	1	no	—
178	C₂×C₄×C₇	—	2	2	no	—
179	C₂×C₄×C₇	—	2	1	no	—
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	4	1	no	—
182	C₂×C₄×C₇	—	4	2	no	—
183	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
185	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
187	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₇	#131	1	4	yes	—
190	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
193	C₇×C₈	—	2	2	no	—
194	C₇×C₈	—	2	2	no	—
195	C₇×C₈	—	2	4	no	—
196	C₇×C₈	—	4	2	no	—
197	C₇×C₈	—	4	1	no	—
198	C₇×C₈	—	4	2	no	—
199	C₇×C₈	—	4	1	no	—
200	C₇×C₈	—	4	1	no	—
201	C₇×C₈	—	4	1	no	—
202	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	C₂×C₄×C₇	1	2	yes	—
205	C₂²×C₈	—	2	1	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	—	2	1	no	—
208	C₂²×C₈	C₂×C₄×C₇	1	2	yes	—
209	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
210	C₄×Q₈	C₇×Q₈	1	1	yes	characteristic
211	C₄×D₄	C₇×D₄	1	2	yes	—
212	C₄×D₄	C₇×D₄	1	1	yes	characteristic
213	C₄×D₄	C₇×Q₈	1	2	yes	—
214	C₄×D₄	C₇×Q₈	1	1	yes	characteristic
215	#117	C₂×C₄×C₇	1	1	yes	characteristic
216	#117	C₂×C₄×C₇	1	2	yes	—
217	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
218	C₂×C₄²	C₂³×C₇	1	2	yes	—
219	C₄⋊C₈	—	2	1	no	—
220	C₄⋊C₈	—	2	2	no	—
221	C₄⋊C₈	—	2	1	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
224	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
225	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
226	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
227	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
228	C₄⋊C₈	C₂³×C₇	1	2	yes	—
229	C₄⋊C₈	C₂³×C₇	1	2	yes	—
230	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
231	C₂²⋊C₈	—	2	1	no	—
232	C₂²⋊C₈	—	2	2	no	—
233	C₂²⋊C₈	—	2	1	no	—
234	C₂²⋊C₈	—	2	2	no	—
235	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
236	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
237	#97	—	2	2	no	—
238	#97	C₂×C₄×C₇	1	2	yes	—
239	C₄×C₈	—	2	1	no	—
240	C₄×C₈	—	2	2	no	—
241	C₄×C₈	—	2	1	no	—
242	C₄×C₈	C₂×C₄×C₇	1	2	yes	—
243	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
244	C₄×C₈	C₂³×C₇	1	2	yes	—
245	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
246	C₂²×C₇	—	2	1	no	—
247	C₂²×C₇	—	2	1	no	—
248	C₂²×C₇	—	2	2	no	—
249	C₂²×C₇	—	2	2	no	—
250	C₂²×C₇	—	2	2	no	—
251	C₂²×C₇	#424	1	2	yes	—
252	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
253	C₄×C₇	—	2	2	no	—
254	C₄×C₇	—	2	1	no	—
255	C₄×C₇	—	2	2	no	—
256	C₄×C₇	—	2	1	no	—
257	C₄×C₇	—	2	1	no	—
258	C₄×C₇	—	2	2	no	—
259	C₄×C₇	#424	1	2	yes	—
260	C₄×C₇	C₂×#131	1	2	yes	—
261	C₄×C₇	#576	1	1	yes	characteristic
262	C₄×C₇	#578	1	1	yes	characteristic
263	#41	—	2	4	no	—
264	C₂×Q₈	C₇×C₄⋊C₄	1	1	yes	characteristic
265	C₂×D₄	C₇×C₄⋊C₄	1	2	yes	—
266	C₂×D₄	C₇×C₄⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
271	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
272	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
273	M₁₆	—	2	4	no	—
274	M₁₆	—	8	2	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	8	1	no	—
283	C₂×C₈	—	8	2	no	—
284	C₂×C₈	—	8	1	no	—
285	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
286	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
287	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
288	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
289	C₄⋊C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
290	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
291	C₄⋊C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
292	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
293	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
294	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
295	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
296	C₄²	C₂²×C₄×C₇	1	2	yes	—
297	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
298	C₄²	C₂×C₇×D₄	1	2	yes	—
299	C₄²	C₂×C₇×Q₈	1	2	yes	—
300	C₄²	C₂×C₇×Q₈	1	1	yes	characteristic
301	C₄²	C₂⁴×C₇	1	1	yes	characteristic
302	C₂×C₇	—	2	2	no	—
303	C₂×C₇	—	4	2	no	—
304	C₂×C₇	C₂×#424	1	1	yes	characteristic
305	C₂×C₇	#2913	1	1	yes	characteristic
306	C₂×C₇	#2916	1	1	yes	characteristic
307	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
308	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
309	Q₈	—	2	2	no	—
310	D₄	—	2	4	no	—
311	D₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
320	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
321	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
322	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
323	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
324	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₇×#131	1	4	yes	—
326	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
327	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
329	C₈	—	2	2	no	—
330	C₈	—	2	2	no	—
331	C₈	—	2	4	no	—
332	C₈	—	4	2	no	—
333	C₈	—	4	1	no	—
334	C₈	—	4	2	no	—
335	C₈	—	4	1	no	—
336	C₈	—	4	1	no	—
337	C₈	—	4	1	no	—
338	C₇	#17812	1	1	yes	characteristic, direct product factor, Sylow
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	C₇×#424	1	2	yes	—
345	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
346	C₄	—	2	2	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	2	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	2	no	—
352	C₄	C₇×#424	1	2	yes	—
353	C₄	C₂×C₇×#131	1	2	yes	—
354	C₄	C₇×#576	1	1	yes	characteristic
355	C₄	C₇×#578	1	1	yes	characteristic
356	C₂	—	2	2	no	—
357	C₂	—	4	2	no	—
358	C₂	C₂×C₇×#424	1	1	yes	characteristic
359	C₂	C₇×#2913	1	1	yes	characteristic
360	C₂	C₇×#2916	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	C₂²×C₄⋊C₄
prime radical	C₂×C₇×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇×#1574	C₂	semidirect
5. C₇×#1573	C₂	semidirect
6. C₇×#1572	C₂	semidirect
7. C₇×#1571	C₂	semidirect
8. C₇×#1565	C₂	semidirect
9. C₇×#1565	C₂	semidirect
10. C₇×#1564	C₂	semidirect
11. C₂×C₇×#335	C₂	semidirect
44. #17812	C₇	direct (N × H)
92. #1574	C₂×C₇	semidirect
93. #1573	C₂×C₇	semidirect
94. #1572	C₂×C₇	semidirect
95. #1571	C₂×C₇	semidirect
96. #1565	C₂×C₇	semidirect
97. #1565	C₂×C₇	semidirect
98. #1564	C₂×C₇	semidirect
99. C₂×#335	C₂×C₇	semidirect
338. C₇	#17812	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×#2989	2
C₇×#2988	2
C₇×#2922	2
C₇×#1574	2
C₇×#1573	2
C₇×#1572	2
C₇×#1571	2
C₇×#1565	2
C₇×#1564	2
C₂×C₇×#335	2
#17812	7

Subgroups — C7×#17812 #13195028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17812 #13195028