Subgroups — #1379×D₆₇ #30770698

Order 17152.

606 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₆×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#405×D₆₇	C₂	1	1	yes	maximal, characteristic
4	#22558299	C₂	1	1	yes	maximal, characteristic, complemented
5	#22558298	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558297	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1379	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₆₇	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
10	#117×D₆₇	C₄	1	1	yes	characteristic
11	C₂×#14523983	C₂²	1	1	yes	characteristic
12	C₂×#14523982	—	2	1	no	—
13	M₃₂×D₆₇	—	2	2	no	—
14	M₃₂×D₆₇	C₄	1	4	yes	complemented
15	C₂²×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×D₆₇	—	2	2	no	—
17	C₂×C₁₆×D₆₇	—	2	1	no	—
18	C₂×C₁₆×D₆₇	—	2	1	no	—
19	C₂×C₁₆×D₆₇	—	2	1	no	—
20	C₂×C₁₆×D₆₇	C₄	1	4	yes	complemented
21	#16863354	C₄	1	1	yes	characteristic
22	#16863353	—	2	1	no	—
23	#16863352	C₄	1	1	yes	characteristic
24	#16863351	C₂²	1	1	yes	characteristic
25	#16863350	—	2	1	no	—
26	#97×D₆₇	—	2	1	no	—
27	C₄×C₈×D₆₇	—	2	1	no	—
28	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
30	#405×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
32	C₂×#11761612	C₂×C₄	1	1	yes	characteristic
33	C₂×#11761611	—	2	1	no	—
34	M₁₆×D₆₇	—	2	2	no	—
35	M₁₆×D₆₇	C₈	1	4	yes	—
36	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₈×D₆₇	—	2	1	no	—
38	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₆₇	D₄	1	2	yes	—
41	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
42	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
43	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
44	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
45	C₂×C₈×D₆₇	Q₈	1	2	yes	—
46	#14524002	C₂×C₄	1	1	yes	characteristic
47	#14524001	C₈	1	2	yes	—
48	#14524000	—	2	1	no	—
49	#14523999	—	2	1	no	—
50	C₄⋊C₄×D₆₇	C₈	1	2	yes	—
51	C₂²⋊C₄×D₆₇	—	2	1	no	—
52	C₄²×D₆₇	—	2	1	no	—
53	#14523983	—	2	1	no	—
54	#14523983	C₂×C₄	1	2	yes	complemented
55	#14523982	—	2	4	no	—
56	C₂×C₆₇⋊C₁₆	—	2	1	no	—
57	C₂×C₆₇⋊C₁₆	—	2	1	no	—
58	C₂×C₆₇⋊C₁₆	—	2	1	no	—
59	C₂×C₆₇⋊C₁₆	C₂×C₄	1	2	yes	complemented
60	C₁₆×D₆₇	—	2	4	no	—
61	C₁₆×D₆₇	—	2	4	no	—
62	C₁₆×D₆₇	—	2	4	no	—
63	#14523954	—	2	1	no	—
64	#14523953	—	2	1	no	—
65	#14523953	—	2	1	no	—
66	C₄×C₆₇⋊C₈	—	2	1	no	—
67	C₈×Dic₆₇	—	2	1	no	—
68	C₈×Dic₆₇	—	2	1	no	—
69	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
71	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
72	M₃₂×C₆₇	—	2	1	no	—
73	M₃₂×C₆₇	C₂×C₄	1	2	yes	complemented
74	C₂×C₁₆×C₆₇	—	2	1	no	—
75	C₂×C₁₆×C₆₇	—	2	1	no	—
76	C₂×C₁₆×C₆₇	—	2	1	no	—
77	C₂×C₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
78	#97×C₆₇	—	2	1	no	—
79	C₄×C₈×C₆₇	—	2	1	no	—
80	C₂³×D₆₇	M₁₆	1	1	yes	characteristic
81	C₂²×Dic₆₇	M₁₆	1	1	yes	characteristic
82	C₂×C₄×D₆₇	—	2	2	no	—
83	C₂×C₄×D₆₇	C₄²	1	2	yes	—
84	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₆₇	C₄⋊C₄	1	2	yes	—
87	C₂×C₄×D₆₇	C₂×C₈	1	2	yes	—
88	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₆₇	M₁₆	1	2	yes	—
91	#11761612	—	2	1	no	—
92	#11761612	C₂×C₈	1	2	yes	—
93	#11761611	—	2	4	no	—
94	C₂×C₆₇⋊C₈	—	2	1	no	—
95	C₂×C₆₇⋊C₈	C₄²	1	2	yes	—
96	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₆₇⋊C₈	C₄⋊C₄	1	2	yes	—
99	C₈×D₆₇	—	2	4	no	—
100	C₈×D₆₇	C₂²⋊C₄	1	2	yes	—
101	C₈×D₆₇	C₂²⋊C₄	1	2	yes	—
102	C₈×D₆₇	C₂²⋊C₄	1	2	yes	—
103	C₈×D₆₇	C₂²⋊C₄	1	2	yes	—
104	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
105	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
106	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
107	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
108	C₄⋊Dic₆₇	C₂×C₈	1	2	yes	—
109	Dic₆₇⋊C₄	—	2	2	no	—
110	C₂²⋊Dic₆₇	—	2	1	no	—
111	(C₂×D₆₇)⋊C₄	—	2	2	no	—
112	C₄×Dic₆₇	—	2	1	no	—
113	C₄×Dic₆₇	—	2	2	no	—
114	C₆₇⋊C₁₆	—	2	2	no	—
115	C₆₇⋊C₁₆	—	2	2	no	—
116	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
117	M₁₆×C₆₇	—	2	1	no	—
118	M₁₆×C₆₇	C₂×C₈	1	2	yes	—
119	C₂×C₈×C₆₇	—	2	1	no	—
120	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
126	C₄⋊C₄×C₆₇	C₂×C₈	1	2	yes	—
127	C₂²⋊C₄×C₆₇	—	2	1	no	—
128	C₄²×C₆₇	—	2	1	no	—
129	C₁₆×C₆₇	—	2	2	no	—
130	C₁₆×C₆₇	—	2	2	no	—
131	C₂³×C₆₇	C₂×M₁₆	1	1	yes	characteristic
132	C₂²×D₆₇	—	2	4	no	—
133	C₂²×D₆₇	#97	1	2	yes	—
134	C₂²×D₆₇	C₂²⋊C₈	1	1	yes	characteristic
135	C₂²×D₆₇	C₂²⋊C₈	1	1	yes	characteristic
136	C₂²×D₆₇	C₄⋊C₈	1	2	yes	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
144	C₂×Dic₆₇	—	2	2	no	—
145	C₂×Dic₆₇	#97	1	2	yes	—
146	C₂×Dic₆₇	C₂²⋊C₈	1	1	yes	characteristic
147	C₂×Dic₆₇	C₂²⋊C₈	1	1	yes	characteristic
148	C₂×Dic₆₇	C₄⋊C₈	1	2	yes	—
149	C₄×D₆₇	—	4	4	no	—
150	C₄×D₆₇	#95	1	2	yes	—
151	C₄×D₆₇	#95	1	2	yes	—
152	C₄×D₆₇	C₄×C₈	1	2	yes	—
153	C₄×D₆₇	C₄×C₈	1	2	yes	—
154	C₄×D₆₇	C₂²⋊C₈	1	2	yes	—
155	C₄×D₆₇	C₂²⋊C₈	1	2	yes	—
156	C₄×D₆₇	C₄⋊C₈	1	2	yes	—
157	C₄×D₆₇	C₄⋊C₈	1	2	yes	—
158	C₈×C₆₇	—	2	2	no	—
159	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₆₇⋊C₈	—	2	2	no	—
164	C₆₇⋊C₈	#95	1	2	yes	—
165	C₆₇⋊C₈	#95	1	2	yes	—
166	C₂²×C₆₇	—	2	2	no	—
167	C₂²×C₆₇	C₂×#97	1	1	yes	characteristic
168	C₂²×C₆₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
169	C₂²×C₆₇	C₂×C₄⋊C₈	1	1	yes	characteristic
170	C₂×D₆₇	—	2	2	no	—
171	C₂×D₆₇	—	2	4	no	—
172	C₂×D₆₇	—	2	4	no	—
173	C₂×D₆₇	#336	1	2	yes	—
174	C₂×D₆₇	#336	1	2	yes	—
175	C₂×D₆₇	#350	1	4	yes	—
176	C₄×C₆₇	—	4	2	no	—
177	C₄×C₆₇	C₂×#95	1	1	yes	characteristic
178	C₄×C₆₇	C₂×C₄×C₈	1	1	yes	characteristic
179	C₄×C₆₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
180	C₄×C₆₇	C₂×C₄⋊C₈	1	1	yes	characteristic
181	Dic₆₇	—	4	2	no	—
182	Dic₆₇	#336	1	2	yes	—
183	Dic₆₇	#336	1	2	yes	—
184	C₂×#1379	—	67	1	no	maximal, Sylow
185	C₂×C₆₇	—	2	1	no	—
186	C₂×C₆₇	—	2	1	no	—
187	C₂×C₆₇	C₂×#336	1	1	yes	characteristic
188	C₂×C₆₇	C₂×#350	1	2	yes	—
189	D₆₇	—	2	2	no	—
190	D₆₇	#1379	1	4	yes	direct product factor
191	C₂²×M₃₂	—	67	1	no	—
192	C₂³×C₁₆	—	67	1	no	—
193	C₂×#405	—	67	1	no	—
194	#1379	—	67	1	no	—
195	#1379	—	67	1	no	—
196	#1379	—	67	1	no	—
197	#1379	D₆₇	1	1	yes	characteristic, direct product factor
198	C₆₇	C₂×#1379	1	1	yes	characteristic, complemented, Sylow
199	C₂²×M₁₆	—	67	1	no	—
200	C₂³×C₈	—	67	1	no	—
201	C₂×#117	—	67	1	no	—
202	C₂×M₃₂	—	67	1	no	—
203	C₂×M₃₂	—	67	4	no	—
204	C₂×M₃₂	—	134	1	no	—
205	C₂×M₃₂	—	134	2	no	—
206	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
207	C₂²×C₁₆	—	67	1	no	—
208	C₂²×C₁₆	—	67	4	no	—
209	C₂²×C₁₆	—	134	1	no	—
210	C₂²×C₁₆	—	134	1	no	—
211	C₂²×C₁₆	—	134	2	no	—
212	C₂²×C₁₆	—	134	1	no	—
213	C₂²×C₁₆	C₂×D₆₇	1	1	yes	characteristic
214	#405	—	67	1	no	—
215	#405	—	67	1	no	—
216	#405	—	67	1	no	—
217	#405	—	134	1	no	—
218	#405	—	134	1	no	—
219	#405	C₂×D₆₇	1	1	yes	characteristic
220	C₂×#97	—	134	1	no	—
221	C₂×C₄×C₈	—	134	1	no	—
222	C₂³×C₄	—	67	1	no	—
223	C₂×M₁₆	—	67	1	no	—
224	C₂×M₁₆	—	67	4	no	—
225	C₂×M₁₆	—	134	1	no	—
226	C₂×M₁₆	—	134	2	no	—
227	C₂×M₁₆	C₄×D₆₇	1	1	yes	characteristic
228	C₂²×C₈	—	67	1	no	—
229	C₂²×C₈	—	67	2	no	—
230	C₂²×C₈	—	67	2	no	—
231	C₂²×C₈	—	67	1	no	—
232	C₂²×C₈	—	67	1	no	—
233	C₂²×C₈	—	67	2	no	—
234	C₂²×C₈	—	67	1	no	—
235	C₂²×C₈	—	67	1	no	—
236	C₂²×C₈	—	67	2	no	—
237	C₂²×C₈	—	134	1	no	—
238	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
239	#117	—	67	1	no	—
240	#117	—	67	2	no	—
241	#117	—	134	1	no	—
242	#117	—	134	1	no	—
243	#117	C₄×D₆₇	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	67	2	no	—
245	C₂×C₂²⋊C₄	—	134	1	no	—
246	C₂×C₄²	—	134	1	no	—
247	M₃₂	—	2	1	no	—
248	M₃₂	—	67	2	no	—
249	M₃₂	—	134	4	no	—
250	M₃₂	—	134	1	no	—
251	M₃₂	C₄×D₆₇	1	2	yes	complemented
252	C₂×C₁₆	—	2	1	no	—
253	C₂×C₁₆	—	2	1	no	—
254	C₂×C₁₆	—	2	1	no	—
255	C₂×C₁₆	—	67	2	no	—
256	C₂×C₁₆	—	134	4	no	—
257	C₂×C₁₆	—	134	4	no	—
258	C₂×C₁₆	—	134	4	no	—
259	C₂×C₁₆	—	134	1	no	—
260	C₂×C₁₆	—	134	1	no	—
261	C₂×C₁₆	—	134	1	no	—
262	C₂×C₁₆	C₄×D₆₇	1	2	yes	complemented
263	#97	—	2	1	no	—
264	#97	—	134	1	no	—
265	#97	—	134	1	no	—
266	#97	—	134	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	134	1	no	—
269	C₄×C₈	—	134	1	no	—
270	C₄×C₈	—	134	1	no	—
271	C₂⁴	—	67	1	no	—
272	C₂²×C₄	—	67	1	no	—
273	C₂²×C₄	—	67	2	no	—
274	C₂²×C₄	—	67	1	no	—
275	C₂²×C₄	—	67	1	no	—
276	C₂²×C₄	—	67	2	no	—
277	C₂²×C₄	—	67	1	no	—
278	C₂²×C₄	—	67	1	no	—
279	C₂²×C₄	—	67	2	no	—
280	C₂²×C₄	—	67	2	no	—
281	C₂²×C₄	—	134	2	no	—
282	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
283	M₁₆	—	2	1	no	—
284	M₁₆	—	67	2	no	—
285	M₁₆	—	134	4	no	—
286	M₁₆	—	134	1	no	—
287	M₁₆	C₈×D₆₇	1	2	yes	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	67	2	no	—
290	C₂×C₈	—	67	1	no	—
291	C₂×C₈	—	67	1	no	—
292	C₂×C₈	—	67	2	no	—
293	C₂×C₈	—	67	2	no	—
294	C₂×C₈	—	67	2	no	—
295	C₂×C₈	—	67	2	no	—
296	C₂×C₈	—	67	2	no	—
297	C₂×C₈	—	67	2	no	—
298	C₂×C₈	—	67	2	no	—
299	C₂×C₈	—	67	2	no	—
300	C₂×C₈	—	67	2	no	—
301	C₂×C₈	—	134	4	no	—
302	C₂×C₈	—	134	1	no	—
303	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
304	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
305	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
306	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
307	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
308	C₂×C₈	Q₈×D₆₇	1	1	yes	characteristic
309	C₄⋊C₄	—	67	2	no	—
310	C₄⋊C₄	—	134	2	no	—
311	C₄⋊C₄	C₈×D₆₇	1	2	yes	—
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	134	2	no	—
314	C₂²⋊C₄	—	134	1	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	134	2	no	—
317	C₄²	—	134	1	no	—
318	C₁₆	—	2	2	no	—
319	C₁₆	—	2	2	no	—
320	C₁₆	—	134	2	no	—
321	C₁₆	—	134	2	no	—
322	C₂³	—	67	1	no	—
323	C₂³	—	67	2	no	—
324	C₂³	—	67	1	no	—
325	C₂³	—	67	2	no	—
326	C₂³	—	134	4	no	—
327	C₂³	M₁₆×D₆₇	1	1	yes	characteristic
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	268	4	no	—
330	C₂×C₄	—	67	2	no	—
331	C₂×C₄	—	67	1	no	—
332	C₂×C₄	—	67	1	no	—
333	C₂×C₄	—	67	2	no	—
334	C₂×C₄	—	67	2	no	—
335	C₂×C₄	—	67	2	no	—
336	C₂×C₄	—	67	2	no	—
337	C₂×C₄	—	67	2	no	—
338	C₂×C₄	—	67	2	no	—
339	C₂×C₄	—	67	2	no	—
340	C₂×C₄	—	67	2	no	—
341	C₂×C₄	—	67	2	no	—
342	C₂×C₄	—	134	2	no	—
343	C₂×C₄	C₄²×D₆₇	1	1	yes	characteristic
344	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
345	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
346	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
348	C₂×C₄	M₁₆×D₆₇	1	1	yes	characteristic
349	C₈	—	2	2	no	—
350	C₈	—	67	2	no	—
351	C₈	—	67	2	no	—
352	C₈	—	134	2	no	—
353	C₈	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
354	C₈	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
355	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
356	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
357	C₂²	—	2	2	no	—
358	C₂²	—	67	4	no	—
359	C₂²	—	67	2	no	—
360	C₂²	—	67	2	no	—
361	C₂²	—	134	4	no	—
362	C₂²	—	134	4	no	—
363	C₂²	—	134	2	no	—
364	C₂²	#97×D₆₇	1	1	yes	characteristic
365	C₂²	C₂²⋊C₈×D₆₇	1	1	yes	characteristic
366	C₂²	C₄⋊C₈×D₆₇	1	1	yes	characteristic
367	C₄	—	4	2	no	—
368	C₄	—	268	2	no	—
369	C₄	—	67	2	no	—
370	C₄	—	67	2	no	—
371	C₄	#95×D₆₇	1	1	yes	characteristic
372	C₄	C₄×C₈×D₆₇	1	1	yes	characteristic
373	C₄	C₂²⋊C₈×D₆₇	1	1	yes	characteristic
374	C₄	C₄⋊C₈×D₆₇	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	67	4	no	—
378	C₂	—	134	2	no	—
379	C₂	#336×D₆₇	1	1	yes	characteristic
380	C₂	#350×D₆₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₆₇
commutator	C₄×C₆₇	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₆₇×#1379	C₂
socle	C₂²×C₆₇	C₂×C₂²⋊C₈
prime radical	C₂³×D₆₇	M₁₆
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	#1379	D₆₇
hypocenter	C₆₇	C₂×#1379
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1379

Complements

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

N	H ≅ G/N	type
4. #22558299	C₂	semidirect
5. #22558298	C₂	semidirect
6. #22558297	C₂	semidirect
7. C₆₇×#1379	C₂	semidirect
14. M₃₂×D₆₇	C₄	semidirect
20. C₂×C₁₆×D₆₇	C₄	semidirect
54. #14523983	C₂×C₄	semidirect
59. C₂×C₆₇⋊C₁₆	C₂×C₄	semidirect
73. M₃₂×C₆₇	C₂×C₄	semidirect
77. C₂×C₁₆×C₆₇	C₂×C₄	semidirect
190. D₆₇	#1379	direct (N × H)
197. #1379	D₆₇	direct (N × H)
198. C₆₇	C₂×#1379	semidirect
251. M₃₂	C₄×D₆₇	semidirect
262. C₂×C₁₆	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₆₇	2
C₂²×C₁₆×D₆₇	2
#405×D₆₇	2
#22558299	2
#22558298	2
#22558297	2
C₆₇×#1379	2
C₂×#1379	67

Subgroups — #1379×D67 #30770698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1379×D₆₇ #30770698