Subgroups — C₂×C₆₇×#1958 #30700445

Order 17152.

1766 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂²×#102×C₆₇	C₂	1	2	yes	maximal
4	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1958	C₂	1	8	yes	maximal, direct product factor
7	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
10	C₂×#124×C₆₇	—	2	2	no	—
11	C₂×#124×C₆₇	—	2	4	no	—
12	C₂×#124×C₆₇	C₄	1	8	yes	complemented
13	C₂×#124×C₆₇	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₆₇	—	2	2	no	—
16	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×#103×C₆₇	—	2	8	no	—
18	C₂×#103×C₆₇	C₂²	1	8	yes	complemented
19	C₂×#102×C₆₇	—	2	8	no	—
20	C₂×#102×C₆₇	C₂²	1	8	yes	—
21	C₂×C₄×C₈×C₆₇	—	2	4	no	—
22	C₂×C₄×C₈×C₆₇	C₂²	1	4	yes	complemented
23	#382×C₆₇	—	2	2	no	—
24	#382×C₆₇	C₂²	1	4	yes	complemented
25	C₂×#95×C₆₇	—	2	2	no	—
26	C₂⁵×C₆₇	—	2	1	no	—
27	C₂²×Q₈×C₆₇	—	2	2	no	—
28	C₂²×Q₈×C₆₇	—	2	1	no	—
29	C₂²×Q₈×C₆₇	—	2	4	no	—
30	C₂²×Q₈×C₆₇	—	2	4	no	—
31	C₂²×Q₈×C₆₇	C₂×C₄	1	4	yes	—
32	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
33	C₂²×D₄×C₆₇	—	2	4	no	—
34	C₂²×D₄×C₆₇	—	2	1	no	—
35	C₂²×D₄×C₆₇	—	2	2	no	—
36	C₂²×D₄×C₆₇	—	2	4	no	—
37	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
38	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₆₇	—	2	1	no	—
40	C₂³×C₄×C₆₇	—	2	2	no	—
41	C₂³×C₄×C₆₇	D₄	1	2	yes	—
42	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₆₇	—	2	4	no	—
44	C₂²×C₈×C₆₇	—	2	4	no	—
45	C₂²×C₈×C₆₇	D₄	1	8	yes	—
46	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
47	#124×C₆₇	—	2	16	no	—
48	#124×C₆₇	—	2	8	no	—
49	#124×C₆₇	C₂×C₄	1	16	yes	complemented
50	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
54	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
55	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
56	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₆₇	D₄	1	2	yes	—
58	C₂×C₄²×C₆₇	D₄	1	4	yes	—
59	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
60	#103×C₆₇	—	2	16	no	—
61	#102×C₆₇	—	2	16	no	—
62	C₄×C₈×C₆₇	—	2	8	no	—
63	#95×C₆₇	—	2	8	no	—
64	C₂⁴×C₆₇	—	2	4	no	—
65	C₂⁴×C₆₇	—	2	2	no	—
66	C₂⁴×C₆₇	—	4	2	no	—
67	C₂⁴×C₆₇	—	4	2	no	—
68	C₂⁴×C₆₇	—	4	8	no	—
69	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
70	C₂×Q₈×C₆₇	—	2	4	no	—
71	C₂×Q₈×C₆₇	—	2	2	no	—
72	C₂×Q₈×C₆₇	—	2	16	no	—
73	C₂×Q₈×C₆₇	—	2	4	no	—
74	C₂×Q₈×C₆₇	—	2	4	no	—
75	C₂×Q₈×C₆₇	—	4	8	no	—
76	C₂×Q₈×C₆₇	—	4	2	no	—
77	C₂×Q₈×C₆₇	—	4	2	no	—
78	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
79	C₂×D₄×C₆₇	—	2	4	no	—
80	C₂×D₄×C₆₇	—	2	16	no	—
81	C₂×D₄×C₆₇	—	2	4	no	—
82	C₂×D₄×C₆₇	—	2	2	no	—
83	C₂×D₄×C₆₇	—	2	4	no	—
84	C₂×D₄×C₆₇	—	4	8	no	—
85	C₂×D₄×C₆₇	—	4	2	no	—
86	C₂×D₄×C₆₇	—	4	2	no	—
87	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₆₇	—	2	8	no	—
89	C₂²×C₄×C₆₇	—	2	4	no	—
90	C₂²×C₄×C₆₇	—	2	2	no	—
91	C₂²×C₄×C₆₇	—	2	4	no	—
92	C₂²×C₄×C₆₇	—	4	2	no	—
93	C₂²×C₄×C₆₇	—	4	2	no	—
94	C₂²×C₄×C₆₇	—	4	4	no	—
95	C₂²×C₄×C₆₇	—	4	8	no	—
96	C₂²×C₄×C₆₇	C₂²⋊C₄	1	8	yes	—
97	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₆₇	#41	1	4	yes	—
103	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₆₇	—	2	16	no	—
105	C₂×C₈×C₆₇	—	2	4	no	—
106	C₂×C₈×C₆₇	—	2	4	no	—
107	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	—
108	C₄⋊C₄×C₆₇	—	2	4	no	—
109	C₄⋊C₄×C₆₇	—	2	4	no	—
110	C₄⋊C₄×C₆₇	—	4	4	no	—
111	C₂²⋊C₄×C₆₇	—	2	32	no	—
112	C₄²×C₆₇	C₂²⋊C₄	1	8	yes	—
113	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
114	C₄²×C₆₇	C₂×D₄	1	4	yes	—
115	C₂³×C₆₇	—	2	4	no	—
116	C₂³×C₆₇	—	4	2	no	—
117	C₂³×C₆₇	—	4	2	no	—
118	C₂³×C₆₇	—	4	8	no	—
119	C₂³×C₆₇	—	4	8	no	—
120	C₂³×C₆₇	—	4	16	no	—
121	C₂³×C₆₇	—	8	8	no	—
122	C₂³×C₆₇	—	8	8	no	—
123	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
124	C₂³×C₆₇	#124	1	2	yes	—
125	C₂³×C₆₇	#127	1	2	yes	—
126	C₂³×C₆₇	#135	1	8	yes	—
127	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₆₇	—	2	8	no	—
129	Q₈×C₆₇	—	4	4	no	—
130	Q₈×C₆₇	—	4	8	no	—
131	D₄×C₆₇	—	2	8	no	—
132	D₄×C₆₇	—	4	4	no	—
133	D₄×C₆₇	—	4	8	no	—
134	C₂×C₄×C₆₇	—	2	8	no	—
135	C₂×C₄×C₆₇	—	2	16	no	—
136	C₂×C₄×C₆₇	—	2	4	no	—
137	C₂×C₄×C₆₇	—	4	2	no	—
138	C₂×C₄×C₆₇	—	4	2	no	—
139	C₂×C₄×C₆₇	—	4	8	no	—
140	C₂×C₄×C₆₇	—	4	4	no	—
141	C₂×C₄×C₆₇	—	4	8	no	—
142	C₂×C₄×C₆₇	—	8	8	no	—
143	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	8	yes	—
144	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
146	C₂×C₄×C₆₇	#121	1	8	yes	—
147	C₂×C₄×C₆₇	#124	1	2	yes	—
148	C₂×C₄×C₆₇	#127	1	2	yes	—
149	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
153	C₈×C₆₇	—	2	8	no	—
154	C₂²×C₆₇	—	4	8	no	—
155	C₂²×C₆₇	—	4	4	no	—
156	C₂²×C₆₇	—	8	4	no	—
157	C₂²×C₆₇	—	8	4	no	—
158	C₂²×C₆₇	—	8	16	no	—
159	C₂²×C₆₇	#390	1	4	yes	—
160	C₂²×C₆₇	#416	1	8	yes	—
161	C₂²×C₆₇	#488	1	8	yes	—
162	C₂²×C₆₇	#495	1	8	yes	—
163	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₆₇	C₂×#124	1	1	yes	characteristic
165	C₂²×C₆₇	C₂×#127	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×#135	1	4	yes	—
167	C₄×C₆₇	—	2	8	no	—
168	C₄×C₆₇	—	4	4	no	—
169	C₄×C₆₇	—	8	4	no	—
170	C₄×C₆₇	#390	1	4	yes	—
171	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
172	C₄×C₆₇	C₂×#121	1	2	yes	—
173	C₂×#1958	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₆₇	—	8	4	no	—
175	C₂×C₆₇	#1958	1	8	yes	direct product factor
176	C₂×C₆₇	C₂×#390	1	1	yes	characteristic
177	C₂×C₆₇	C₂×#416	1	2	yes	—
178	C₂×C₆₇	C₂×#488	1	2	yes	—
179	C₂×C₆₇	C₂×#495	1	2	yes	—
180	C₂²×#124	C₂×C₆₇	1	1	yes	characteristic
181	C₂²×#103	C₂×C₆₇	1	2	yes	complemented
182	C₂²×#102	C₂×C₆₇	1	2	yes	—
183	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
184	C₂×#382	C₂×C₆₇	1	1	yes	characteristic, complemented
185	#1958	C₂×C₆₇	1	8	yes	direct product factor
186	C₆₇	C₂×#1958	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
188	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
189	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
190	C₂×#124	—	2	2	no	—
191	C₂×#124	—	2	4	no	—
192	C₂×#124	C₄×C₆₇	1	8	yes	complemented
193	C₂×#124	C₂²×C₆₇	1	4	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
195	C₂²×C₂²⋊C₄	—	2	2	no	—
196	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
197	C₂×#103	—	2	8	no	—
198	C₂×#103	C₂²×C₆₇	1	8	yes	complemented
199	C₂×#102	—	2	8	no	—
200	C₂×#102	C₂²×C₆₇	1	8	yes	—
201	C₂×C₄×C₈	—	2	4	no	—
202	C₂×C₄×C₈	C₂²×C₆₇	1	4	yes	complemented
203	#382	—	2	2	no	—
204	#382	C₂²×C₆₇	1	4	yes	complemented
205	C₂×#95	—	2	2	no	—
206	C₂⁵	—	2	1	no	—
207	C₂²×Q₈	—	2	2	no	—
208	C₂²×Q₈	—	2	1	no	—
209	C₂²×Q₈	—	2	4	no	—
210	C₂²×Q₈	—	2	4	no	—
211	C₂²×Q₈	C₂×C₄×C₆₇	1	4	yes	—
212	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	2	1	no	—
215	C₂²×D₄	—	2	2	no	—
216	C₂²×D₄	—	2	4	no	—
217	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
218	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	—	2	2	no	—
221	C₂³×C₄	D₄×C₆₇	1	2	yes	—
222	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
223	C₂²×C₈	—	2	4	no	—
224	C₂²×C₈	—	2	4	no	—
225	C₂²×C₈	D₄×C₆₇	1	8	yes	—
226	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
227	#124	—	2	16	no	—
228	#124	—	2	8	no	—
229	#124	C₂×C₄×C₆₇	1	16	yes	complemented
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
234	C₂×C₂²⋊C₄	—	2	16	no	—
235	C₂×C₂²⋊C₄	—	2	8	no	—
236	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
237	C₂×C₄²	D₄×C₆₇	1	2	yes	—
238	C₂×C₄²	D₄×C₆₇	1	4	yes	—
239	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
240	#103	—	2	16	no	—
241	#102	—	2	16	no	—
242	C₄×C₈	—	2	8	no	—
243	#95	—	2	8	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	—	2	2	no	—
246	C₂⁴	—	4	2	no	—
247	C₂⁴	—	4	2	no	—
248	C₂⁴	—	4	8	no	—
249	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
250	C₂×Q₈	—	2	4	no	—
251	C₂×Q₈	—	2	2	no	—
252	C₂×Q₈	—	2	16	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	—	4	8	no	—
256	C₂×Q₈	—	4	2	no	—
257	C₂×Q₈	—	4	2	no	—
258	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	16	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	4	8	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	—	4	8	no	—
276	C₂²×C₄	C₂²⋊C₄×C₆₇	1	8	yes	—
277	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
279	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
282	C₂²×C₄	#41×C₆₇	1	4	yes	—
283	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
284	C₂×C₈	—	2	16	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₂²⋊C₄	—	2	32	no	—
292	C₄²	C₂²⋊C₄×C₆₇	1	8	yes	—
293	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
294	C₄²	C₂×D₄×C₆₇	1	4	yes	—
295	C₂³	—	2	4	no	—
296	C₂³	—	4	2	no	—
297	C₂³	—	4	2	no	—
298	C₂³	—	4	8	no	—
299	C₂³	—	4	8	no	—
300	C₂³	—	4	16	no	—
301	C₂³	—	8	8	no	—
302	C₂³	—	8	8	no	—
303	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
304	C₂³	#124×C₆₇	1	2	yes	—
305	C₂³	#127×C₆₇	1	2	yes	—
306	C₂³	#135×C₆₇	1	8	yes	—
307	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
308	Q₈	—	2	8	no	—
309	Q₈	—	4	4	no	—
310	Q₈	—	4	8	no	—
311	D₄	—	2	8	no	—
312	D₄	—	4	4	no	—
313	D₄	—	4	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	16	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	8	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	—	8	8	no	—
323	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	8	yes	—
324	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
325	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
326	C₂×C₄	#121×C₆₇	1	8	yes	—
327	C₂×C₄	#124×C₆₇	1	2	yes	—
328	C₂×C₄	#127×C₆₇	1	2	yes	—
329	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
330	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
331	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
332	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
333	C₈	—	2	8	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	4	8	no	—
336	C₂²	—	8	4	no	—
337	C₂²	—	8	4	no	—
338	C₂²	—	8	16	no	—
339	C₂²	#390×C₆₇	1	4	yes	—
340	C₂²	#416×C₆₇	1	8	yes	—
341	C₂²	#488×C₆₇	1	8	yes	—
342	C₂²	#495×C₆₇	1	8	yes	—
343	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
344	C₂²	C₂×#124×C₆₇	1	1	yes	characteristic
345	C₂²	C₂×#127×C₆₇	1	1	yes	characteristic
346	C₂²	C₂×#135×C₆₇	1	4	yes	—
347	C₄	—	2	8	no	—
348	C₄	—	4	4	no	—
349	C₄	—	8	4	no	—
350	C₄	#390×C₆₇	1	4	yes	—
351	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
352	C₄	C₂×#121×C₆₇	1	2	yes	—
353	C₂	—	8	4	no	—
354	C₂	C₆₇×#1958	1	8	yes	direct product factor
355	C₂	C₂×#390×C₆₇	1	1	yes	characteristic
356	C₂	C₂×#416×C₆₇	1	2	yes	—
357	C₂	C₂×#488×C₆₇	1	2	yes	—
358	C₂	C₂×#495×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#103×C₆₇	C₂	semidirect
4. C₂²×C₄×C₈×C₆₇	C₂	semidirect
5. C₂×#382×C₆₇	C₂	semidirect
6. C₆₇×#1958	C₂	direct (N × H)
12. C₂×#124×C₆₇	C₄	semidirect
18. C₂×#103×C₆₇	C₂²	semidirect
22. C₂×C₄×C₈×C₆₇	C₂²	semidirect
24. #382×C₆₇	C₂²	semidirect
49. #124×C₆₇	C₂×C₄	semidirect
173. C₂×#1958	C₆₇	direct (N × H)
175. C₂×C₆₇	#1958	direct (N × H)
181. C₂²×#103	C₂×C₆₇	semidirect
183. C₂²×C₄×C₈	C₂×C₆₇	semidirect
184. C₂×#382	C₂×C₆₇	semidirect
185. #1958	C₂×C₆₇	direct (N × H)
186. C₆₇	C₂×#1958	direct (N × H)
192. C₂×#124	C₄×C₆₇	semidirect
198. C₂×#103	C₂²×C₆₇	semidirect
202. C₂×C₄×C₈	C₂²×C₆₇	semidirect
204. #382	C₂²×C₆₇	semidirect
229. #124	C₂×C₄×C₆₇	semidirect
354. C₂	C₆₇×#1958	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₆₇	2
C₂²×#103×C₆₇	2
C₂²×#102×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₂×#382×C₆₇	2
C₆₇×#1958	2
C₂×#1958	67

Subgroups — C2×C67×#1958 #30700445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1958 #30700445