Subgroups — C₆₇×#33422 #30712673

Order 17152.

600 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2164	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2163	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2162	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2151	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2112	C₂	1	1	yes	maximal, characteristic
7	C₂×C₂²⋊C₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#2108	C₂	1	2	yes	maximal, complemented
9	C₂²×M₁₆×C₆₇	C₄	1	1	yes	characteristic
10	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×#117×C₆₇	C₄	1	1	yes	characteristic
12	C₂×M₃₂×C₆₇	C₂²	1	2	yes	—
13	C₂²×C₁₆×C₆₇	C₂²	1	2	yes	—
14	#405×C₆₇	C₄	1	2	yes	—
15	#405×C₆₇	C₄	1	1	yes	characteristic
16	#405×C₆₇	C₄	1	1	yes	characteristic
17	#405×C₆₇	C₂²	1	1	yes	characteristic
18	#405×C₆₇	C₂²	1	1	yes	characteristic
19	#405×C₆₇	C₂²	1	2	yes	—
20	C₂×#97×C₆₇	C₄	1	2	yes	—
21	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
22	C₄⋊C₁₆×C₆₇	C₂²	1	4	yes	complemented
23	C₄⋊C₁₆×C₆₇	C₂²	1	4	yes	complemented
24	C₂²⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²⋊C₁₆×C₆₇	C₂²	1	2	yes	—
27	C₂²⋊C₁₆×C₆₇	C₂²	1	2	yes	—
28	C₂²⋊C₁₆×C₆₇	C₂²	1	2	yes	—
29	#346×C₆₇	C₂²	1	4	yes	complemented
30	C₄×C₁₆×C₆₇	C₂²	1	4	yes	complemented
31	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
32	C₂×M₁₆×C₆₇	—	2	4	no	—
33	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
34	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
35	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₆₇	—	2	4	no	—
37	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
44	#117×C₆₇	C₈	1	1	yes	characteristic
45	#117×C₆₇	C₈	1	1	yes	characteristic
46	#117×C₆₇	C₈	1	2	yes	—
47	#117×C₆₇	C₂×C₄	1	2	yes	—
48	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
49	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₆₇	C₈	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₆₇	C₈	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₆₇	C₈	1	2	yes	—
53	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
54	M₃₂×C₆₇	—	2	4	no	—
55	C₂×C₁₆×C₆₇	—	2	4	no	—
56	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
57	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
58	C₂×C₁₆×C₆₇	C₂³	1	4	yes	—
59	#97×C₆₇	C₂×C₄	1	2	yes	—
60	#97×C₆₇	C₂×C₄	1	2	yes	—
61	#97×C₆₇	C₂×C₄	1	2	yes	—
62	#97×C₆₇	C₂×C₄	1	2	yes	—
63	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
64	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
65	C₄×C₈×C₆₇	C₂³	1	2	yes	—
66	C₄×C₈×C₆₇	C₂³	1	2	yes	—
67	C₂⁴×C₆₇	C₂×C₈	1	1	yes	characteristic
68	C₂²×C₄×C₆₇	—	2	2	no	—
69	C₂²×C₄×C₆₇	—	2	2	no	—
70	C₂²×C₄×C₆₇	C₂×C₈	1	2	yes	—
71	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
72	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
73	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
74	C₂²×C₄×C₆₇	C₂×C₈	1	2	yes	—
75	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
78	M₁₆×C₆₇	—	2	2	no	—
79	M₁₆×C₆₇	—	2	4	no	—
80	M₁₆×C₆₇	M₁₆	1	4	yes	—
81	C₂×C₈×C₆₇	—	2	2	no	—
82	C₂×C₈×C₆₇	—	2	2	no	—
83	C₂×C₈×C₆₇	—	2	2	no	—
84	C₂×C₈×C₆₇	—	2	4	no	—
85	C₂×C₈×C₆₇	—	2	2	no	—
86	C₂×C₈×C₆₇	—	2	2	no	—
87	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
92	C₂×C₈×C₆₇	#41	1	4	yes	—
93	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
94	C₄⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
95	C₄⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
96	C₄⋊C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
97	C₄⋊C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
98	C₄⋊C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
99	C₄⋊C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
100	C₂²⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
101	C₂²⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
102	C₂²⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
103	C₂²⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
104	C₄²×C₆₇	C₂×C₈	1	2	yes	—
105	C₄²×C₆₇	C₂×C₈	1	2	yes	—
106	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
107	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
108	C₁₆×C₆₇	—	2	2	no	—
109	C₁₆×C₆₇	—	2	2	no	—
110	C₁₆×C₆₇	—	2	4	no	—
111	C₂³×C₆₇	—	2	2	no	—
112	C₂³×C₆₇	—	2	2	no	—
113	C₂³×C₆₇	—	4	1	no	—
114	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
115	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
116	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
117	C₂×C₄×C₆₇	—	2	2	no	—
118	C₂×C₄×C₆₇	—	2	4	no	—
119	C₂×C₄×C₆₇	—	2	1	no	—
120	C₂×C₄×C₆₇	—	2	1	no	—
121	C₂×C₄×C₆₇	—	2	1	no	—
122	C₂×C₄×C₆₇	—	2	1	no	—
123	C₂×C₄×C₆₇	—	2	2	no	—
124	C₂×C₄×C₆₇	—	2	2	no	—
125	C₂×C₄×C₆₇	—	4	2	no	—
126	C₂×C₄×C₆₇	#117	1	2	yes	—
127	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
128	C₂×C₄×C₆₇	C₂²×C₈	1	2	yes	—
129	C₂×C₄×C₆₇	C₂²×C₈	1	2	yes	—
130	C₂×C₄×C₆₇	C₂²×C₈	1	2	yes	—
131	C₂×C₄×C₆₇	C₂²×C₈	1	2	yes	—
132	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
133	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
135	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
136	C₈×C₆₇	—	2	1	no	—
137	C₈×C₆₇	—	2	1	no	—
138	C₈×C₆₇	—	2	2	no	—
139	C₈×C₆₇	#117	1	2	yes	—
140	C₈×C₆₇	C₂×M₁₆	1	4	yes	—
141	C₈×C₆₇	C₂×#41	1	2	yes	—
142	C₂²×C₆₇	—	2	1	no	—
143	C₂²×C₆₇	—	2	1	no	—
144	C₂²×C₆₇	—	2	1	no	—
145	C₂²×C₆₇	—	2	1	no	—
146	C₂²×C₆₇	—	2	1	no	—
147	C₂²×C₆₇	—	2	1	no	—
148	C₂²×C₆₇	—	2	1	no	—
149	C₂²×C₆₇	—	4	4	no	—
150	C₂²×C₆₇	#431	1	2	yes	—
151	C₂²×C₆₇	#504	1	2	yes	—
152	C₂²×C₆₇	C₂³×C₈	1	1	yes	characteristic
153	C₄×C₆₇	—	2	2	no	—
154	C₄×C₆₇	—	2	2	no	—
155	C₄×C₆₇	—	2	2	no	—
156	C₄×C₆₇	—	2	2	no	—
157	C₄×C₆₇	—	2	1	no	—
158	C₄×C₆₇	—	2	1	no	—
159	C₄×C₆₇	#431	1	2	yes	—
160	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
161	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
162	#33422	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂×C₆₇	—	2	2	no	—
164	C₂×C₆₇	—	2	2	no	—
165	C₂×C₆₇	—	4	1	no	—
166	C₂×C₆₇	C₂×#431	1	1	yes	characteristic
167	C₂×C₆₇	C₂×#504	1	1	yes	characteristic
168	C₂×C₆₇	#3407	1	1	yes	characteristic
169	C₂×#405	C₂×C₆₇	1	1	yes	characteristic
170	#2164	C₂×C₆₇	1	4	yes	complemented
171	#2163	C₂×C₆₇	1	2	yes	complemented
172	#2162	C₂×C₆₇	1	2	yes	complemented
173	#2151	C₂×C₆₇	1	2	yes	complemented
174	#2112	C₂×C₆₇	1	1	yes	characteristic
175	C₂×C₂²⋊C₁₆	C₂×C₆₇	1	1	yes	characteristic
176	#2108	C₂×C₆₇	1	2	yes	complemented
177	C₆₇	#33422	1	1	yes	characteristic, direct product factor, Sylow
178	C₂²×M₁₆	C₄×C₆₇	1	1	yes	characteristic
179	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
180	C₂×#117	C₄×C₆₇	1	1	yes	characteristic
181	C₂×M₃₂	C₂²×C₆₇	1	2	yes	—
182	C₂²×C₁₆	C₂²×C₆₇	1	2	yes	—
183	#405	C₄×C₆₇	1	1	yes	characteristic
184	#405	C₄×C₆₇	1	2	yes	—
185	#405	C₄×C₆₇	1	1	yes	characteristic
186	#405	C₂²×C₆₇	1	1	yes	characteristic
187	#405	C₂²×C₆₇	1	1	yes	characteristic
188	#405	C₂²×C₆₇	1	2	yes	—
189	C₂×#97	C₄×C₆₇	1	2	yes	—
190	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
191	C₄⋊C₁₆	C₂²×C₆₇	1	4	yes	complemented
192	C₄⋊C₁₆	C₂²×C₆₇	1	4	yes	complemented
193	C₂²⋊C₁₆	C₂²×C₆₇	1	1	yes	characteristic
194	C₂²⋊C₁₆	C₂²×C₆₇	1	1	yes	characteristic
195	C₂²⋊C₁₆	C₂²×C₆₇	1	2	yes	—
196	C₂²⋊C₁₆	C₂²×C₆₇	1	2	yes	—
197	C₂²⋊C₁₆	C₂²×C₆₇	1	2	yes	—
198	#346	C₂²×C₆₇	1	4	yes	complemented
199	C₄×C₁₆	C₂²×C₆₇	1	4	yes	complemented
200	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
201	C₂×M₁₆	—	2	4	no	—
202	C₂×M₁₆	C₂×C₄×C₆₇	1	1	yes	characteristic
203	C₂×M₁₆	C₂×C₄×C₆₇	1	2	yes	—
204	C₂×M₁₆	C₂×C₄×C₆₇	1	1	yes	characteristic
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
207	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
208	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
209	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
210	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
213	#117	C₈×C₆₇	1	1	yes	characteristic
214	#117	C₈×C₆₇	1	1	yes	characteristic
215	#117	C₈×C₆₇	1	2	yes	—
216	#117	C₂×C₄×C₆₇	1	2	yes	—
217	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
218	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₈×C₆₇	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₈×C₆₇	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₈×C₆₇	1	2	yes	—
222	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
223	M₃₂	—	2	4	no	—
224	C₂×C₁₆	—	2	4	no	—
225	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
226	C₂×C₁₆	C₂³×C₆₇	1	4	yes	—
227	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
228	#97	C₂×C₄×C₆₇	1	2	yes	—
229	#97	C₂×C₄×C₆₇	1	2	yes	—
230	#97	C₂×C₄×C₆₇	1	2	yes	—
231	#97	C₂×C₄×C₆₇	1	2	yes	—
232	C₄×C₈	C₂×C₄×C₆₇	1	2	yes	—
233	C₄×C₈	C₂×C₄×C₆₇	1	2	yes	—
234	C₄×C₈	C₂³×C₆₇	1	2	yes	—
235	C₄×C₈	C₂³×C₆₇	1	2	yes	—
236	C₂⁴	C₂×C₈×C₆₇	1	1	yes	characteristic
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	C₂×C₈×C₆₇	1	2	yes	—
240	C₂²×C₄	C₂×C₈×C₆₇	1	1	yes	characteristic
241	C₂²×C₄	C₂×C₈×C₆₇	1	1	yes	characteristic
242	C₂²×C₄	C₂×C₈×C₆₇	1	1	yes	characteristic
243	C₂²×C₄	C₂×C₈×C₆₇	1	2	yes	—
244	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
246	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
247	M₁₆	—	2	2	no	—
248	M₁₆	—	2	4	no	—
249	M₁₆	M₁₆×C₆₇	1	4	yes	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
257	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
258	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
259	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
260	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
261	C₂×C₈	#41×C₆₇	1	4	yes	—
262	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
263	C₄⋊C₄	C₂×C₈×C₆₇	1	2	yes	—
264	C₄⋊C₄	C₂×C₈×C₆₇	1	2	yes	—
265	C₄⋊C₄	C₂×C₈×C₆₇	1	1	yes	characteristic
266	C₄⋊C₄	C₂×C₈×C₆₇	1	1	yes	characteristic
267	C₄⋊C₄	C₂×C₈×C₆₇	1	1	yes	characteristic
268	C₄⋊C₄	C₂×C₈×C₆₇	1	1	yes	characteristic
269	C₂²⋊C₄	C₂×C₈×C₆₇	1	2	yes	—
270	C₂²⋊C₄	C₂×C₈×C₆₇	1	2	yes	—
271	C₂²⋊C₄	C₂×C₈×C₆₇	1	2	yes	—
272	C₂²⋊C₄	C₂×C₈×C₆₇	1	2	yes	—
273	C₄²	C₂×C₈×C₆₇	1	2	yes	—
274	C₄²	C₂×C₈×C₆₇	1	2	yes	—
275	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
276	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
277	C₁₆	—	2	2	no	—
278	C₁₆	—	2	2	no	—
279	C₁₆	—	2	4	no	—
280	C₂³	—	2	2	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	4	1	no	—
283	C₂³	C₂²×C₈×C₆₇	1	1	yes	characteristic
284	C₂³	C₂²×C₈×C₆₇	1	1	yes	characteristic
285	C₂³	C₂²×C₈×C₆₇	1	1	yes	characteristic
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	#117×C₆₇	1	2	yes	—
296	C₂×C₄	C₂²×C₈×C₆₇	1	1	yes	characteristic
297	C₂×C₄	C₂²×C₈×C₆₇	1	2	yes	—
298	C₂×C₄	C₂²×C₈×C₆₇	1	2	yes	—
299	C₂×C₄	C₂²×C₈×C₆₇	1	2	yes	—
300	C₂×C₄	C₂²×C₈×C₆₇	1	2	yes	—
301	C₂×C₄	C₂²×C₈×C₆₇	1	1	yes	characteristic
302	C₂×C₄	C₂²×C₈×C₆₇	1	1	yes	characteristic
303	C₂×C₄	C₂×M₁₆×C₆₇	1	2	yes	—
304	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
305	C₈	—	2	1	no	—
306	C₈	—	2	1	no	—
307	C₈	—	2	2	no	—
308	C₈	#117×C₆₇	1	2	yes	—
309	C₈	C₂×M₁₆×C₆₇	1	4	yes	—
310	C₈	C₂×#41×C₆₇	1	2	yes	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	2	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	2	1	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	4	4	no	—
319	C₂²	#431×C₆₇	1	2	yes	—
320	C₂²	#504×C₆₇	1	2	yes	—
321	C₂²	C₂³×C₈×C₆₇	1	1	yes	characteristic
322	C₄	—	2	2	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	—	2	1	no	—
327	C₄	—	2	1	no	—
328	C₄	#431×C₆₇	1	2	yes	—
329	C₄	C₂×#117×C₆₇	1	1	yes	characteristic
330	C₄	C₂²×M₁₆×C₆₇	1	1	yes	characteristic
331	C₂	—	2	2	no	—
332	C₂	—	2	2	no	—
333	C₂	—	4	1	no	—
334	C₂	C₂×#431×C₆₇	1	1	yes	characteristic
335	C₂	C₂×#504×C₆₇	1	1	yes	characteristic
336	C₂	C₆₇×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₆₇	C₂⁴
commutator	C₂²	C₂³×C₈×C₆₇
Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂³×C₈
prime radical	C₂⁴×C₆₇	C₂×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2164	C₂	semidirect
3. C₆₇×#2163	C₂	semidirect
4. C₆₇×#2162	C₂	semidirect
5. C₆₇×#2151	C₂	semidirect
8. C₆₇×#2108	C₂	semidirect
22. C₄⋊C₁₆×C₆₇	C₂²	semidirect
23. C₄⋊C₁₆×C₆₇	C₂²	semidirect
29. #346×C₆₇	C₂²	semidirect
30. C₄×C₁₆×C₆₇	C₂²	semidirect
162. #33422	C₆₇	direct (N × H)
170. #2164	C₂×C₆₇	semidirect
171. #2163	C₂×C₆₇	semidirect
172. #2162	C₂×C₆₇	semidirect
173. #2151	C₂×C₆₇	semidirect
176. #2108	C₂×C₆₇	semidirect
177. C₆₇	#33422	direct (N × H)
191. C₄⋊C₁₆	C₂²×C₆₇	semidirect
192. C₄⋊C₁₆	C₂²×C₆₇	semidirect
198. #346	C₂²×C₆₇	semidirect
199. C₄×C₁₆	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#405×C₆₇	2
C₆₇×#2164	2
C₆₇×#2163	2
C₆₇×#2162	2
C₆₇×#2151	2
C₆₇×#2112	2
C₂×C₂²⋊C₁₆×C₆₇	2
C₆₇×#2108	2
#33422	67

Subgroups — C67×#33422 #30712673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33422 #30712673