Subgroups — C₂×C₆₇×#3142 #30739868

Order 17152.

2182 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3142	C₂	1	16	yes	maximal, direct product factor
4	C₂×#491×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#490×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#488×C₆₇	C₂	1	4	yes	maximal, complemented
7	C₂×#417×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₆₇	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
11	#532×C₆₇	—	2	4	no	—
12	#532×C₆₇	C₂²	1	8	yes	—
13	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#125×C₆₇	—	2	2	no	—
16	C₂×#125×C₆₇	—	2	4	no	—
17	C₂×#125×C₆₇	C₂²	1	2	yes	—
18	C₂×#125×C₆₇	C₂²	1	2	yes	—
19	C₂×#125×C₆₇	C₂²	1	8	yes	complemented
20	C₂×#124×C₆₇	C₂²	1	2	yes	—
21	C₂×#121×C₆₇	—	2	2	no	—
22	C₂×C₄×D₄×C₆₇	—	2	2	no	—
23	C₂²×C₄⋊C₄×C₆₇	—	2	2	no	—
24	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	#491×C₆₇	C₂²	1	16	yes	complemented
27	#490×C₆₇	C₂²	1	16	yes	complemented
28	#488×C₆₇	C₂²	1	32	yes	complemented
29	#417×C₆₇	C₂²	1	32	yes	complemented
30	C₂×#103×C₆₇	C₂²	1	8	yes	—
31	C₂×#102×C₆₇	C₂²	1	8	yes	—
32	C₄×M₁₆×C₆₇	C₂²	1	8	yes	complemented
33	C₂×#97×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
35	C₂×#41×C₆₇	—	2	4	no	—
36	C₂×#41×C₆₇	—	2	16	no	—
37	C₂×#41×C₆₇	C₂³	1	8	yes	—
38	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
39	C₂²×D₄×C₆₇	—	2	2	no	—
40	C₂²×D₄×C₆₇	—	2	2	no	—
41	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
42	C₂³×C₄×C₆₇	—	2	2	no	—
43	C₂³×C₄×C₆₇	—	2	2	no	—
44	C₂³×C₄×C₆₇	D₄	1	2	yes	—
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₆₇	—	2	8	no	—
47	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
48	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
49	C₄⋊Q₈×C₆₇	—	2	2	no	—
50	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
51	#127×C₆₇	—	2	2	no	—
52	#127×C₆₇	C₂³	1	4	yes	—
53	#125×C₆₇	—	2	4	no	—
54	#125×C₆₇	—	2	4	no	—
55	#125×C₆₇	—	2	16	no	—
56	#125×C₆₇	C₂³	1	8	yes	—
57	#125×C₆₇	C₂³	1	8	yes	—
58	#124×C₆₇	—	2	4	no	—
59	#124×C₆₇	C₂³	1	8	yes	—
60	#121×C₆₇	—	2	16	no	—
61	C₄×D₄×C₆₇	—	2	16	no	—
62	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
63	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
64	C₂×C₄⋊C₄×C₆₇	—	2	16	no	—
65	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
66	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
71	C₂×C₄²×C₆₇	D₄	1	2	yes	—
72	C₂×C₄²×C₆₇	D₄	1	4	yes	—
73	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
76	#103×C₆₇	C₂³	1	32	yes	—
77	#102×C₆₇	C₂³	1	32	yes	—
78	#97×C₆₇	C₂³	1	8	yes	—
79	C₄×C₈×C₆₇	C₂³	1	8	yes	—
80	C₂⁴×C₆₇	—	2	2	no	—
81	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
82	#41×C₆₇	—	2	32	no	—
83	#41×C₆₇	—	4	16	no	—
84	C₂×Q₈×C₆₇	—	2	2	no	—
85	C₂×Q₈×C₆₇	—	2	8	no	—
86	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
87	C₂×D₄×C₆₇	—	2	8	no	—
88	C₂×D₄×C₆₇	—	2	8	no	—
89	C₂×D₄×C₆₇	—	2	2	no	—
90	C₂×D₄×C₆₇	—	2	8	no	—
91	C₂×D₄×C₆₇	—	4	8	no	—
92	C₂×D₄×C₆₇	—	4	8	no	—
93	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
94	C₂²×C₄×C₆₇	—	2	8	no	—
95	C₂²×C₄×C₆₇	—	2	2	no	—
96	C₂²×C₄×C₆₇	—	2	4	no	—
97	C₂²×C₄×C₆₇	—	2	8	no	—
98	C₂²×C₄×C₆₇	—	4	4	no	—
99	C₂²×C₄×C₆₇	—	4	8	no	—
100	C₂²×C₄×C₆₇	—	4	8	no	—
101	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₇	#41	1	8	yes	—
107	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
108	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
109	M₁₆×C₆₇	—	2	16	no	—
110	C₂×C₈×C₆₇	—	2	8	no	—
111	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
112	C₄⋊C₄×C₆₇	—	2	16	no	—
113	C₄⋊C₄×C₆₇	—	2	16	no	—
114	C₄⋊C₄×C₆₇	—	2	8	no	—
115	C₄⋊C₄×C₆₇	—	2	4	no	—
116	C₄⋊C₄×C₆₇	—	2	8	no	—
117	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
118	C₂²⋊C₄×C₆₇	—	2	16	no	—
119	C₄²×C₆₇	C₂×D₄	1	8	yes	—
120	C₄²×C₆₇	C₂×D₄	1	2	yes	—
121	C₄²×C₆₇	C₂×D₄	1	2	yes	—
122	C₄²×C₆₇	C₂⁴	1	2	yes	—
123	C₄²×C₆₇	C₂⁴	1	2	yes	—
124	C₂³×C₆₇	—	2	4	no	—
125	C₂³×C₆₇	—	2	4	no	—
126	C₂³×C₆₇	—	4	4	no	—
127	C₂³×C₆₇	—	4	8	no	—
128	C₂³×C₆₇	#124	1	4	yes	—
129	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
130	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
131	Q₈×C₆₇	—	2	8	no	—
132	Q₈×C₆₇	—	4	4	no	—
133	D₄×C₆₇	—	2	8	no	—
134	D₄×C₆₇	—	4	16	no	—
135	D₄×C₆₇	—	4	16	no	—
136	D₄×C₆₇	—	4	4	no	—
137	C₂×C₄×C₆₇	—	2	4	no	—
138	C₂×C₄×C₆₇	—	2	4	no	—
139	C₂×C₄×C₆₇	—	2	4	no	—
140	C₂×C₄×C₆₇	—	2	8	no	—
141	C₂×C₄×C₆₇	—	4	8	no	—
142	C₂×C₄×C₆₇	—	4	16	no	—
143	C₂×C₄×C₆₇	—	4	4	no	—
144	C₂×C₄×C₆₇	—	4	8	no	—
145	C₂×C₄×C₆₇	—	4	16	no	—
146	C₂×C₄×C₆₇	#124	1	4	yes	—
147	C₂×C₄×C₆₇	#124	1	8	yes	—
148	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
149	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
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	4	yes	—
153	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
154	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
155	C₈×C₆₇	—	2	8	no	—
156	C₂²×C₆₇	—	2	8	no	—
157	C₂²×C₆₇	—	2	4	no	—
158	C₂²×C₆₇	—	4	4	no	—
159	C₂²×C₆₇	—	4	8	no	—
160	C₂²×C₆₇	—	8	8	no	—
161	C₂²×C₆₇	C₂×#124	1	4	yes	—
162	C₂²×C₆₇	C₂×#124	1	2	yes	—
163	C₂²×C₆₇	#575	1	4	yes	—
164	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
165	C₄×C₆₇	—	2	4	no	—
166	C₄×C₆₇	—	2	4	no	—
167	C₄×C₆₇	—	4	4	no	—
168	C₄×C₆₇	—	4	8	no	—
169	C₄×C₆₇	C₂×#124	1	4	yes	—
170	C₄×C₆₇	C₂×#124	1	2	yes	—
171	C₄×C₆₇	C₂²×#41	1	2	yes	—
172	C₂×#3142	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂×C₆₇	—	2	4	no	—
174	C₂×C₆₇	—	8	4	no	—
175	C₂×C₆₇	#3142	1	4	yes	direct product factor
176	C₂×C₆₇	C₂²×#124	1	1	yes	characteristic
177	C₂×C₆₇	C₂×#575	1	2	yes	—
178	C₂×#532	C₂×C₆₇	1	1	yes	characteristic
179	C₂²×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
180	#3142	C₂×C₆₇	1	16	yes	direct product factor
181	C₂×#491	C₂×C₆₇	1	2	yes	complemented
182	C₂×#490	C₂×C₆₇	1	2	yes	complemented
183	C₂×#488	C₂×C₆₇	1	4	yes	complemented
184	C₂×#417	C₂×C₆₇	1	4	yes	complemented
185	C₂×C₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
186	C₆₇	C₂×#3142	1	1	yes	characteristic, direct product factor, Sylow
187	C₂²×#41	C₂²×C₆₇	1	2	yes	—
188	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
189	#532	—	2	4	no	—
190	#532	C₂²×C₆₇	1	8	yes	—
191	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
192	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
193	C₂×#125	—	2	2	no	—
194	C₂×#125	—	2	4	no	—
195	C₂×#125	C₂²×C₆₇	1	2	yes	—
196	C₂×#125	C₂²×C₆₇	1	2	yes	—
197	C₂×#125	C₂²×C₆₇	1	8	yes	complemented
198	C₂×#124	C₂²×C₆₇	1	2	yes	—
199	C₂×#121	—	2	2	no	—
200	C₂×C₄×D₄	—	2	2	no	—
201	C₂²×C₄⋊C₄	—	2	2	no	—
202	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
203	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
204	#491	C₂²×C₆₇	1	16	yes	complemented
205	#490	C₂²×C₆₇	1	16	yes	complemented
206	#488	C₂²×C₆₇	1	32	yes	complemented
207	#417	C₂²×C₆₇	1	32	yes	complemented
208	C₂×#103	C₂²×C₆₇	1	8	yes	—
209	C₂×#102	C₂²×C₆₇	1	8	yes	—
210	C₄×M₁₆	C₂²×C₆₇	1	8	yes	complemented
211	C₂×#97	C₂²×C₆₇	1	2	yes	—
212	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
213	C₂×#41	—	2	4	no	—
214	C₂×#41	—	2	16	no	—
215	C₂×#41	C₂³×C₆₇	1	8	yes	—
216	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
217	C₂²×D₄	—	2	2	no	—
218	C₂²×D₄	—	2	2	no	—
219	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
220	C₂³×C₄	—	2	2	no	—
221	C₂³×C₄	—	2	2	no	—
222	C₂³×C₄	D₄×C₆₇	1	2	yes	—
223	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
224	C₂×M₁₆	—	2	8	no	—
225	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
226	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
229	#127	—	2	2	no	—
230	#127	C₂³×C₆₇	1	4	yes	—
231	#125	—	2	4	no	—
232	#125	—	2	4	no	—
233	#125	—	2	16	no	—
234	#125	C₂³×C₆₇	1	8	yes	—
235	#125	C₂³×C₆₇	1	8	yes	—
236	#124	—	2	4	no	—
237	#124	C₂³×C₆₇	1	8	yes	—
238	#121	—	2	16	no	—
239	C₄×D₄	—	2	16	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	16	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
247	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
248	C₂×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₄²	D₄×C₆₇	1	2	yes	—
250	C₂×C₄²	D₄×C₆₇	1	4	yes	—
251	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
254	#103	C₂³×C₆₇	1	32	yes	—
255	#102	C₂³×C₆₇	1	32	yes	—
256	#97	C₂³×C₆₇	1	8	yes	—
257	C₄×C₈	C₂³×C₆₇	1	8	yes	—
258	C₂⁴	—	2	2	no	—
259	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
260	#41	—	2	32	no	—
261	#41	—	4	16	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	8	no	—
264	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	8	no	—
269	C₂×D₄	—	4	8	no	—
270	C₂×D₄	—	4	8	no	—
271	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	8	no	—
278	C₂²×C₄	—	4	8	no	—
279	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
282	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
284	C₂²×C₄	#41×C₆₇	1	8	yes	—
285	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
286	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
287	M₁₆	—	2	16	no	—
288	C₂×C₈	—	2	8	no	—
289	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
290	C₄⋊C₄	—	2	16	no	—
291	C₄⋊C₄	—	2	16	no	—
292	C₄⋊C₄	—	2	8	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
296	C₂²⋊C₄	—	2	16	no	—
297	C₄²	C₂×D₄×C₆₇	1	8	yes	—
298	C₄²	C₂×D₄×C₆₇	1	2	yes	—
299	C₄²	C₂×D₄×C₆₇	1	2	yes	—
300	C₄²	C₂⁴×C₆₇	1	2	yes	—
301	C₄²	C₂⁴×C₆₇	1	2	yes	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	4	4	no	—
305	C₂³	—	4	8	no	—
306	C₂³	#124×C₆₇	1	4	yes	—
307	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
308	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
309	Q₈	—	2	8	no	—
310	Q₈	—	4	4	no	—
311	D₄	—	2	8	no	—
312	D₄	—	4	16	no	—
313	D₄	—	4	16	no	—
314	D₄	—	4	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	4	8	no	—
320	C₂×C₄	—	4	16	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	8	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	#124×C₆₇	1	4	yes	—
325	C₂×C₄	#124×C₆₇	1	8	yes	—
326	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
327	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
328	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
329	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
331	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
332	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
333	C₈	—	2	8	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	4	8	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	8	8	no	—
339	C₂²	C₂×#124×C₆₇	1	4	yes	—
340	C₂²	C₂×#124×C₆₇	1	2	yes	—
341	C₂²	#575×C₆₇	1	4	yes	—
342	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
343	C₄	—	2	4	no	—
344	C₄	—	2	4	no	—
345	C₄	—	4	8	no	—
346	C₄	—	4	4	no	—
347	C₄	C₂×#124×C₆₇	1	4	yes	—
348	C₄	C₂×#124×C₆₇	1	2	yes	—
349	C₄	C₂²×#41×C₆₇	1	2	yes	—
350	C₂	—	2	4	no	—
351	C₂	—	8	4	no	—
352	C₂	C₆₇×#3142	1	4	yes	direct product factor
353	C₂	C₂²×#124×C₆₇	1	1	yes	characteristic
354	C₂	C₂×#575×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂×#532×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#125×C₆₇	C₂	semidirect
3. C₆₇×#3142	C₂	direct (N × H)
4. C₂×#491×C₆₇	C₂	semidirect
5. C₂×#490×C₆₇	C₂	semidirect
6. C₂×#488×C₆₇	C₂	semidirect
7. C₂×#417×C₆₇	C₂	semidirect
8. C₂×C₄×M₁₆×C₆₇	C₂	semidirect
19. C₂×#125×C₆₇	C₂²	semidirect
26. #491×C₆₇	C₂²	semidirect
27. #490×C₆₇	C₂²	semidirect
28. #488×C₆₇	C₂²	semidirect
29. #417×C₆₇	C₂²	semidirect
32. C₄×M₁₆×C₆₇	C₂²	semidirect
172. C₂×#3142	C₆₇	direct (N × H)
175. C₂×C₆₇	#3142	direct (N × H)
179. C₂²×#125	C₂×C₆₇	semidirect
180. #3142	C₂×C₆₇	direct (N × H)
181. C₂×#491	C₂×C₆₇	semidirect
182. C₂×#490	C₂×C₆₇	semidirect
183. C₂×#488	C₂×C₆₇	semidirect
184. C₂×#417	C₂×C₆₇	semidirect
185. C₂×C₄×M₁₆	C₂×C₆₇	semidirect
186. C₆₇	C₂×#3142	direct (N × H)
197. C₂×#125	C₂²×C₆₇	semidirect
204. #491	C₂²×C₆₇	semidirect
205. #490	C₂²×C₆₇	semidirect
206. #488	C₂²×C₆₇	semidirect
207. #417	C₂²×C₆₇	semidirect
210. C₄×M₁₆	C₂²×C₆₇	semidirect
352. C₂	C₆₇×#3142	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#532×C₆₇	2
C₂²×#125×C₆₇	2
C₆₇×#3142	2
C₂×#491×C₆₇	2
C₂×#490×C₆₇	2
C₂×#488×C₆₇	2
C₂×#417×C₆₇	2
C₂×C₄×M₁₆×C₆₇	2
C₂×#3142	67

Subgroups — C2×C67×#3142 #30739868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3142 #30739868