Subgroups — C₆₇×#17992 #30697243

Order 17152.

576 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3168	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
3	C₆₇×#1588	C₂	1	2	yes	maximal, complemented
4	C₆₇×#1585	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1584	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1581	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1495	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	#529×C₆₇	C₂²	1	2	yes	—
11	#499×C₆₇	C₄	1	1	yes	characteristic
12	#495×C₆₇	C₄	1	1	yes	characteristic
13	#488×C₆₇	C₄	1	2	yes	—
14	#467×C₆₇	C₄	1	1	yes	characteristic
15	#466×C₆₇	C₄	1	1	yes	characteristic
16	#465×C₆₇	C₄	1	2	yes	—
17	#446×C₆₇	C₂²	1	2	yes	—
18	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
19	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
21	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
22	#436×C₆₇	—	2	2	no	—
23	#436×C₆₇	C₂²	1	2	yes	—
24	#435×C₆₇	—	2	2	no	—
25	C₈×D₄×C₆₇	C₂²	1	2	yes	—
26	#433×C₆₇	—	2	2	no	—
27	#431×C₆₇	C₂²	1	1	yes	characteristic
28	#431×C₆₇	C₂²	1	1	yes	characteristic
29	#424×C₆₇	—	2	2	no	—
30	#423×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
32	#335×C₆₇	C₂²	1	2	yes	—
33	#335×C₆₇	C₂²	1	1	yes	characteristic
34	#335×C₆₇	C₂²	1	1	yes	characteristic
35	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
36	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
37	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
38	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
39	#322×C₆₇	C₂²	1	2	yes	—
40	#322×C₆₇	C₂²	1	2	yes	—
41	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
42	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
43	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₆₇	—	2	2	no	—
45	C₂×M₁₆×C₆₇	—	2	2	no	—
46	C₂²×C₈×C₆₇	—	2	2	no	—
47	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
49	#126×C₆₇	—	2	2	no	—
50	#125×C₆₇	C₂×C₄	1	2	yes	—
51	#124×C₆₇	C₂×C₄	1	2	yes	—
52	#123×C₆₇	—	2	2	no	—
53	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
54	#121×C₆₇	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
56	C₄×D₄×C₆₇	—	2	2	no	—
57	C₄×D₄×C₆₇	C₂³	1	2	yes	—
58	#117×C₆₇	—	2	2	no	—
59	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
60	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
61	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
62	#106×C₆₇	C₂×C₄	1	2	yes	—
63	C₄⋊C₈×C₆₇	—	2	2	no	—
64	C₄⋊C₈×C₆₇	—	2	2	no	—
65	C₄⋊C₈×C₆₇	—	2	2	no	—
66	C₄⋊C₈×C₆₇	—	2	1	no	—
67	C₄⋊C₈×C₆₇	D₄	1	1	yes	characteristic
68	C₄⋊C₈×C₆₇	D₄	1	1	yes	characteristic
69	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
70	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
71	#103×C₆₇	C₂×C₄	1	2	yes	—
72	#103×C₆₇	C₂×C₄	1	2	yes	—
73	#102×C₆₇	C₂×C₄	1	2	yes	—
74	#102×C₆₇	C₂×C₄	1	2	yes	—
75	C₂²⋊C₈×C₆₇	—	2	1	no	—
76	C₂²⋊C₈×C₆₇	—	2	2	no	—
77	C₂²⋊C₈×C₆₇	—	2	2	no	—
78	C₂²⋊C₈×C₆₇	D₄	1	2	yes	—
79	#97×C₆₇	—	2	2	no	—
80	C₄×C₈×C₆₇	—	2	2	no	—
81	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₆₇	C₂³	1	2	yes	—
84	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₆₇	C₂³	1	2	yes	—
87	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₆₇	—	2	2	no	—
89	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₆₇	—	2	2	no	—
91	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
94	Q₁₆×C₆₇	—	4	1	no	—
95	SD₁₆×C₆₇	—	4	2	no	—
96	D₈×C₆₇	—	4	1	no	—
97	M₁₆×C₆₇	—	8	2	no	—
98	M₁₆×C₆₇	—	8	2	no	—
99	C₂×C₈×C₆₇	—	2	2	no	—
100	C₂×C₈×C₆₇	—	2	2	no	—
101	C₂×C₈×C₆₇	—	2	2	no	—
102	C₂×C₈×C₆₇	—	4	1	no	—
103	C₂×C₈×C₆₇	—	4	1	no	—
104	C₂×C₈×C₆₇	—	8	2	no	—
105	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
111	C₄⋊C₄×C₆₇	—	2	2	no	—
112	C₄⋊C₄×C₆₇	—	2	2	no	—
113	C₄⋊C₄×C₆₇	—	2	2	no	—
114	C₄⋊C₄×C₆₇	—	2	2	no	—
115	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
116	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
117	C₂²⋊C₄×C₆₇	—	2	2	no	—
118	C₂²⋊C₄×C₆₇	—	2	2	no	—
119	C₂²⋊C₄×C₆₇	—	2	2	no	—
120	C₂²⋊C₄×C₆₇	—	2	2	no	—
121	C₂²⋊C₄×C₆₇	—	2	2	no	—
122	C₄²×C₆₇	—	2	2	no	—
123	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₆₇	#41	1	1	yes	characteristic
126	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
127	C₂³×C₆₇	—	2	2	no	—
128	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
129	Q₈×C₆₇	—	2	2	no	—
130	Q₈×C₆₇	—	2	2	no	—
131	D₄×C₆₇	—	2	2	no	—
132	D₄×C₆₇	—	2	2	no	—
133	D₄×C₆₇	—	8	2	no	—
134	C₂×C₄×C₆₇	—	2	1	no	—
135	C₂×C₄×C₆₇	—	2	1	no	—
136	C₂×C₄×C₆₇	—	2	1	no	—
137	C₂×C₄×C₆₇	—	2	1	no	—
138	C₂×C₄×C₆₇	—	2	2	no	—
139	C₂×C₄×C₆₇	—	2	2	no	—
140	C₂×C₄×C₆₇	—	2	2	no	—
141	C₂×C₄×C₆₇	—	4	1	no	—
142	C₂×C₄×C₆₇	—	4	2	no	—
143	C₂×C₄×C₆₇	—	4	2	no	—
144	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
150	C₈×C₆₇	—	2	1	no	—
151	C₈×C₆₇	—	2	1	no	—
152	C₈×C₆₇	—	2	1	no	—
153	C₈×C₆₇	—	2	1	no	—
154	C₈×C₆₇	—	2	2	no	—
155	C₈×C₆₇	—	2	2	no	—
156	C₈×C₆₇	—	4	2	no	—
157	C₈×C₆₇	—	4	2	no	—
158	C₈×C₆₇	—	4	2	no	—
159	C₂²×C₆₇	—	2	1	no	—
160	C₂²×C₆₇	—	2	1	no	—
161	C₂²×C₆₇	—	2	1	no	—
162	C₂²×C₆₇	—	4	2	no	—
163	C₂²×C₆₇	—	4	2	no	—
164	C₂²×C₆₇	—	4	2	no	—
165	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
166	C₄×C₆₇	—	2	1	no	—
167	C₄×C₆₇	—	2	1	no	—
168	C₄×C₆₇	—	2	1	no	—
169	C₄×C₆₇	—	2	1	no	—
170	C₄×C₆₇	—	4	2	no	—
171	C₄×C₆₇	—	4	2	no	—
172	C₄×C₆₇	—	4	2	no	—
173	C₄×C₆₇	#568	1	1	yes	characteristic
174	C₄×C₆₇	#568	1	1	yes	characteristic
175	C₄×C₆₇	#576	1	1	yes	characteristic
176	C₄×C₆₇	#578	1	1	yes	characteristic
177	#17992	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₆₇	—	4	1	no	—
179	C₂×C₆₇	—	8	2	no	—
180	C₂×C₆₇	#2932	1	1	yes	characteristic
181	C₂×C₆₇	#2951	1	1	yes	characteristic
182	C₂×C₆₇	#2957	1	1	yes	characteristic
183	#3168	C₂×C₆₇	1	1	yes	characteristic
184	#2993	C₂×C₆₇	1	2	yes	complemented
185	#1588	C₂×C₆₇	1	2	yes	complemented
186	#1585	C₂×C₆₇	1	2	yes	complemented
187	#1584	C₂×C₆₇	1	2	yes	complemented
188	#1581	C₂×C₆₇	1	2	yes	complemented
189	#1567	C₂×C₆₇	1	1	yes	characteristic, complemented
190	#1495	C₂×C₆₇	1	2	yes	complemented
191	#1452	C₂×C₆₇	1	1	yes	characteristic, complemented
192	C₆₇	#17992	1	1	yes	characteristic, direct product factor, Sylow
193	#529	C₂²×C₆₇	1	2	yes	—
194	#499	C₄×C₆₇	1	1	yes	characteristic
195	#495	C₄×C₆₇	1	1	yes	characteristic
196	#488	C₄×C₆₇	1	2	yes	—
197	#467	C₄×C₆₇	1	1	yes	characteristic
198	#466	C₄×C₆₇	1	1	yes	characteristic
199	#465	C₄×C₆₇	1	2	yes	—
200	#446	C₂²×C₆₇	1	2	yes	—
201	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
202	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
203	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
204	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
205	#436	—	2	2	no	—
206	#436	C₂²×C₆₇	1	2	yes	—
207	#435	—	2	2	no	—
208	C₈×D₄	C₂²×C₆₇	1	2	yes	—
209	#433	—	2	2	no	—
210	#431	C₂²×C₆₇	1	1	yes	characteristic
211	#431	C₂²×C₆₇	1	1	yes	characteristic
212	#424	—	2	2	no	—
213	#423	C₂²×C₆₇	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
215	#335	C₂²×C₆₇	1	2	yes	—
216	#335	C₂²×C₆₇	1	1	yes	characteristic
217	#335	C₂²×C₆₇	1	1	yes	characteristic
218	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
219	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
220	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
221	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
222	#322	C₂²×C₆₇	1	2	yes	—
223	#322	C₂²×C₆₇	1	2	yes	—
224	C₂×Q₁₆	C₂×C₄×C₆₇	1	1	yes	characteristic
225	C₂×SD₁₆	C₂×C₄×C₆₇	1	2	yes	—
226	C₂×D₈	C₂×C₄×C₆₇	1	1	yes	characteristic
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
231	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
232	#126	—	2	2	no	—
233	#125	C₂×C₄×C₆₇	1	2	yes	—
234	#124	C₂×C₄×C₆₇	1	2	yes	—
235	#123	—	2	2	no	—
236	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
237	#121	C₂×C₄×C₆₇	1	2	yes	—
238	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
239	C₄×D₄	—	2	2	no	—
240	C₄×D₄	C₂³×C₆₇	1	2	yes	—
241	#117	—	2	2	no	—
242	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
243	#107	C₂×C₄×C₆₇	1	1	yes	characteristic
244	#107	C₂×C₄×C₆₇	1	1	yes	characteristic
245	#106	C₂×C₄×C₆₇	1	2	yes	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	D₄×C₆₇	1	1	yes	characteristic
251	C₄⋊C₈	D₄×C₆₇	1	1	yes	characteristic
252	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
253	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
254	#103	C₂×C₄×C₆₇	1	2	yes	—
255	#103	C₂×C₄×C₆₇	1	2	yes	—
256	#102	C₂×C₄×C₆₇	1	2	yes	—
257	#102	C₂×C₄×C₆₇	1	2	yes	—
258	C₂²⋊C₈	—	2	1	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₂²⋊C₈	—	2	2	no	—
261	C₂²⋊C₈	D₄×C₆₇	1	2	yes	—
262	#97	—	2	2	no	—
263	C₄×C₈	—	2	2	no	—
264	C₄×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
265	C₄×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₆₇	1	2	yes	—
267	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₆₇	1	2	yes	—
270	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
276	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
277	Q₁₆	—	4	1	no	—
278	SD₁₆	—	4	2	no	—
279	D₈	—	4	1	no	—
280	M₁₆	—	8	2	no	—
281	M₁₆	—	8	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	4	1	no	—
286	C₂×C₈	—	4	1	no	—
287	C₂×C₈	—	8	2	no	—
288	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
289	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
290	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
291	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
292	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
293	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
299	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
307	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
308	C₄²	#41×C₆₇	1	1	yes	characteristic
309	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
310	C₂³	—	2	2	no	—
311	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
312	Q₈	—	2	2	no	—
313	Q₈	—	2	2	no	—
314	D₄	—	2	2	no	—
315	D₄	—	2	2	no	—
316	D₄	—	8	2	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
328	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
329	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
330	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
332	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
333	C₈	—	2	1	no	—
334	C₈	—	2	1	no	—
335	C₈	—	2	1	no	—
336	C₈	—	2	1	no	—
337	C₈	—	2	2	no	—
338	C₈	—	2	2	no	—
339	C₈	—	4	2	no	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	2	no	—
356	C₄	#568×C₆₇	1	1	yes	characteristic
357	C₄	#568×C₆₇	1	1	yes	characteristic
358	C₄	#576×C₆₇	1	1	yes	characteristic
359	C₄	#578×C₆₇	1	1	yes	characteristic
360	C₂	—	4	1	no	—
361	C₂	—	8	2	no	—
362	C₂	C₆₇×#2932	1	1	yes	characteristic
363	C₂	C₆₇×#2951	1	1	yes	characteristic
364	C₂	C₆₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₄²	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#466×C₆₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ #431×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2993	C₂	semidirect
3. C₆₇×#1588	C₂	semidirect
4. C₆₇×#1585	C₂	semidirect
5. C₆₇×#1584	C₂	semidirect
6. C₆₇×#1581	C₂	semidirect
7. C₆₇×#1567	C₂	semidirect
8. C₆₇×#1495	C₂	semidirect
9. C₆₇×#1452	C₂	semidirect
177. #17992	C₆₇	direct (N × H)
184. #2993	C₂×C₆₇	semidirect
185. #1588	C₂×C₆₇	semidirect
186. #1585	C₂×C₆₇	semidirect
187. #1584	C₂×C₆₇	semidirect
188. #1581	C₂×C₆₇	semidirect
189. #1567	C₂×C₆₇	semidirect
190. #1495	C₂×C₆₇	semidirect
191. #1452	C₂×C₆₇	semidirect
192. C₆₇	#17992	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3168	2
C₆₇×#2993	2
C₆₇×#1588	2
C₆₇×#1585	2
C₆₇×#1584	2
C₆₇×#1581	2
C₆₇×#1567	2
C₆₇×#1495	2
C₆₇×#1452	2
#17992	67

Subgroups — C67×#17992 #30697243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#17992 #30697243