Subgroups — C₆₇×#9732 #30688983

Order 17152.

586 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#492×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#1988	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#1982	C₂	1	1	yes	maximal, characteristic
4	C₈×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#334×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#332×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#331×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×SD₁₆×C₆₇	—	2	1	no	—
9	C₂²×SD₁₆×C₆₇	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
12	#492×C₆₇	—	2	2	no	—
13	#492×C₆₇	C₄	1	4	yes	complemented
14	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×#102×C₆₇	—	2	2	no	—
18	C₂×C₄×C₈×C₆₇	—	2	1	no	—
19	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
21	#340×C₆₇	—	2	2	no	—
22	#336×C₆₇	—	2	1	no	—
23	#334×C₆₇	—	2	2	no	—
24	#332×C₆₇	—	2	2	no	—
25	#331×C₆₇	—	2	2	no	—
26	C₂²×Q₈×C₆₇	—	2	1	no	—
27	C₂²×D₄×C₆₇	—	2	1	no	—
28	C₂²×D₄×C₆₇	—	2	1	no	—
29	C₂²×D₄×C₆₇	—	2	1	no	—
30	C₂×SD₁₆×C₆₇	—	2	4	no	—
31	C₂×SD₁₆×C₆₇	—	2	4	no	—
32	C₂×SD₁₆×C₆₇	—	4	2	no	—
33	C₂×SD₁₆×C₆₇	—	4	2	no	—
34	C₂×SD₁₆×C₆₇	—	4	2	no	—
35	C₂×SD₁₆×C₆₇	—	4	2	no	—
36	C₂²×C₈×C₆₇	—	2	1	no	—
37	C₂²×C₈×C₆₇	—	2	1	no	—
38	C₂²×C₈×C₆₇	—	2	1	no	—
39	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
41	C₄⋊Q₈×C₆₇	—	2	1	no	—
42	C₄⋊Q₈×C₆₇	—	2	1	no	—
43	C₄⋊Q₈×C₆₇	—	2	1	no	—
44	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
45	#127×C₆₇	—	2	1	no	—
46	#127×C₆₇	—	2	1	no	—
47	#127×C₆₇	—	2	1	no	—
48	#127×C₆₇	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
52	C₂×C₄²×C₆₇	—	2	1	no	—
53	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₆₇	—	2	1	no	—
55	C₄⋊C₈×C₆₇	—	2	1	no	—
56	C₄⋊C₈×C₆₇	—	2	1	no	—
57	C₄⋊C₈×C₆₇	—	2	1	no	—
58	C₄⋊C₈×C₆₇	—	2	1	no	—
59	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
60	#102×C₆₇	—	4	4	no	—
61	C₄×C₈×C₆₇	—	4	2	no	—
62	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
63	C₄×C₈×C₆₇	D₄	1	2	yes	—
64	#95×C₆₇	—	2	1	no	—
65	C₂⁴×C₆₇	—	4	1	no	—
66	C₂×Q₈×C₆₇	—	2	2	no	—
67	C₂×Q₈×C₆₇	—	4	1	no	—
68	C₂×Q₈×C₆₇	—	4	1	no	—
69	C₂×Q₈×C₆₇	—	4	1	no	—
70	C₂×Q₈×C₆₇	—	4	1	no	—
71	C₂×Q₈×C₆₇	—	4	1	no	—
72	C₂×D₄×C₆₇	—	2	2	no	—
73	C₂×D₄×C₆₇	—	2	2	no	—
74	C₂×D₄×C₆₇	—	2	2	no	—
75	C₂×D₄×C₆₇	—	4	1	no	—
76	C₂×D₄×C₆₇	—	4	1	no	—
77	C₂×D₄×C₆₇	—	4	1	no	—
78	C₂×D₄×C₆₇	—	4	1	no	—
79	C₂×D₄×C₆₇	—	4	2	no	—
80	C₂×D₄×C₆₇	—	4	1	no	—
81	C₂×D₄×C₆₇	—	4	2	no	—
82	C₂×D₄×C₆₇	—	4	1	no	—
83	C₂×D₄×C₆₇	—	4	1	no	—
84	C₂×D₄×C₆₇	—	8	2	no	—
85	C₂²×C₄×C₆₇	—	2	2	no	—
86	C₂²×C₄×C₆₇	—	4	1	no	—
87	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
90	SD₁₆×C₆₇	—	4	8	no	—
91	SD₁₆×C₆₇	—	4	8	no	—
92	C₂×C₈×C₆₇	—	2	1	no	—
93	C₂×C₈×C₆₇	—	2	1	no	—
94	C₂×C₈×C₆₇	—	2	2	no	—
95	C₂×C₈×C₆₇	—	4	1	no	—
96	C₂×C₈×C₆₇	—	4	1	no	—
97	C₂×C₈×C₆₇	—	4	1	no	—
98	C₂×C₈×C₆₇	—	4	1	no	—
99	C₂×C₈×C₆₇	—	4	2	no	—
100	C₂×C₈×C₆₇	—	4	2	no	—
101	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
102	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
103	C₂×C₈×C₆₇	D₈	1	2	yes	—
104	C₂×C₈×C₆₇	SD₁₆	1	2	yes	—
105	C₄⋊C₄×C₆₇	—	2	2	no	—
106	C₄⋊C₄×C₆₇	—	2	2	no	—
107	C₄⋊C₄×C₆₇	—	2	2	no	—
108	C₄⋊C₄×C₆₇	—	4	1	no	—
109	C₄⋊C₄×C₆₇	—	4	1	no	—
110	C₄⋊C₄×C₆₇	SD₁₆	1	4	yes	complemented
111	C₄²×C₆₇	—	4	1	no	—
112	C₄²×C₆₇	—	4	1	no	—
113	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₆₇	#41	1	1	yes	characteristic
117	C₂³×C₆₇	—	4	2	no	—
118	C₂³×C₆₇	—	8	1	no	—
119	C₂³×C₆₇	—	8	1	no	—
120	C₂³×C₆₇	—	8	2	no	—
121	C₂³×C₆₇	—	8	2	no	—
122	C₂³×C₆₇	#121	1	1	yes	characteristic
123	Q₈×C₆₇	—	4	2	no	—
124	Q₈×C₆₇	—	4	2	no	—
125	Q₈×C₆₇	—	8	1	no	—
126	Q₈×C₆₇	—	8	1	no	—
127	D₄×C₆₇	—	4	2	no	—
128	D₄×C₆₇	—	4	2	no	—
129	D₄×C₆₇	—	4	4	no	—
130	D₄×C₆₇	—	8	2	no	—
131	D₄×C₆₇	—	8	2	no	—
132	D₄×C₆₇	—	8	1	no	—
133	D₄×C₆₇	—	8	1	no	—
134	D₄×C₆₇	—	8	1	no	—
135	D₄×C₆₇	—	8	1	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	4	no	—
138	C₂×C₄×C₆₇	—	4	2	no	—
139	C₂×C₄×C₆₇	—	4	2	no	—
140	C₂×C₄×C₆₇	—	4	2	no	—
141	C₂×C₄×C₆₇	—	8	1	no	—
142	C₂×C₄×C₆₇	—	8	1	no	—
143	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
147	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
148	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₆₇	#135	1	2	yes	—
153	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₈×C₆₇	—	2	2	no	—
156	C₈×C₆₇	—	4	2	no	—
157	C₈×C₆₇	—	8	1	no	—
158	C₈×C₆₇	—	8	1	no	—
159	C₈×C₆₇	#102	1	4	yes	complemented
160	C₂²×C₆₇	—	8	2	no	—
161	C₂²×C₆₇	—	8	2	no	—
162	C₂²×C₆₇	—	8	2	no	—
163	C₂²×C₆₇	—	16	2	no	—
164	C₂²×C₆₇	—	16	2	no	—
165	C₂²×C₆₇	#390	1	1	yes	characteristic
166	C₂²×C₆₇	#459	1	1	yes	characteristic
167	C₂²×C₆₇	#460	1	1	yes	characteristic
168	C₂²×C₆₇	#465	1	2	yes	—
169	C₂²×C₆₇	#471	1	2	yes	—
170	C₄×C₆₇	—	2	1	no	—
171	C₄×C₆₇	—	2	1	no	—
172	C₄×C₆₇	—	4	4	no	—
173	C₄×C₆₇	—	8	2	no	—
174	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
175	C₄×C₆₇	#418	1	1	yes	characteristic
176	C₄×C₆₇	C₄×SD₁₆	1	2	yes	—
177	C₄×C₆₇	#459	1	1	yes	characteristic
178	C₄×C₆₇	#460	1	1	yes	characteristic
179	C₄×C₆₇	#492	1	1	yes	characteristic
180	C₄×C₆₇	#495	1	1	yes	characteristic
181	#9732	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂×C₆₇	—	16	2	no	—
183	C₂×C₆₇	#1665	1	2	yes	—
184	C₂×C₆₇	#1666	1	2	yes	—
185	C₂×C₆₇	#1968	1	1	yes	characteristic
186	C₂×C₆₇	#1977	1	1	yes	characteristic
187	C₂×C₆₇	#1982	1	1	yes	characteristic
188	C₂×#492	C₂×C₆₇	1	1	yes	characteristic
189	#1988	C₂×C₆₇	1	1	yes	characteristic, complemented
190	#1982	C₂×C₆₇	1	1	yes	characteristic
191	C₈×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
192	C₂×#334	C₂×C₆₇	1	1	yes	characteristic, complemented
193	C₂×#332	C₂×C₆₇	1	1	yes	characteristic, complemented
194	C₂×#331	C₂×C₆₇	1	1	yes	characteristic
195	C₆₇	#9732	1	1	yes	characteristic, direct product factor, Sylow
196	C₂²×SD₁₆	—	2	1	no	—
197	C₂²×SD₁₆	—	2	1	no	—
198	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
199	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
200	#492	—	2	2	no	—
201	#492	C₄×C₆₇	1	4	yes	complemented
202	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
205	C₂×#102	—	2	2	no	—
206	C₂×C₄×C₈	—	2	1	no	—
207	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
208	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
209	#340	—	2	2	no	—
210	#336	—	2	1	no	—
211	#334	—	2	2	no	—
212	#332	—	2	2	no	—
213	#331	—	2	2	no	—
214	C₂²×Q₈	—	2	1	no	—
215	C₂²×D₄	—	2	1	no	—
216	C₂²×D₄	—	2	1	no	—
217	C₂²×D₄	—	2	1	no	—
218	C₂×SD₁₆	—	2	4	no	—
219	C₂×SD₁₆	—	2	4	no	—
220	C₂×SD₁₆	—	4	2	no	—
221	C₂×SD₁₆	—	4	2	no	—
222	C₂×SD₁₆	—	4	2	no	—
223	C₂×SD₁₆	—	4	2	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
228	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
233	#127	—	2	1	no	—
234	#127	—	2	1	no	—
235	#127	—	2	1	no	—
236	#127	C₂×C₄×C₆₇	1	2	yes	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	D₄×C₆₇	1	2	yes	—
248	#102	—	4	4	no	—
249	C₄×C₈	—	4	2	no	—
250	C₄×C₈	C₂×C₄×C₆₇	1	2	yes	—
251	C₄×C₈	D₄×C₆₇	1	2	yes	—
252	#95	—	2	1	no	—
253	C₂⁴	—	4	1	no	—
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	—	4	1	no	—
256	C₂×Q₈	—	4	1	no	—
257	C₂×Q₈	—	4	1	no	—
258	C₂×Q₈	—	4	1	no	—
259	C₂×Q₈	—	4	1	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂×D₄	—	4	1	no	—
265	C₂×D₄	—	4	1	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	8	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
277	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
278	SD₁₆	—	4	8	no	—
279	SD₁₆	—	4	8	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	4	1	no	—
286	C₂×C₈	—	4	1	no	—
287	C₂×C₈	—	4	2	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	C₂²⋊C₄×C₆₇	1	2	yes	—
290	C₂×C₈	C₂²⋊C₄×C₆₇	1	2	yes	—
291	C₂×C₈	D₈×C₆₇	1	2	yes	—
292	C₂×C₈	SD₁₆×C₆₇	1	2	yes	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	SD₁₆×C₆₇	1	4	yes	complemented
299	C₄²	—	4	1	no	—
300	C₄²	—	4	1	no	—
301	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
302	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
303	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
304	C₄²	#41×C₆₇	1	1	yes	characteristic
305	C₂³	—	4	2	no	—
306	C₂³	—	8	1	no	—
307	C₂³	—	8	1	no	—
308	C₂³	—	8	2	no	—
309	C₂³	—	8	2	no	—
310	C₂³	#121×C₆₇	1	1	yes	characteristic
311	Q₈	—	4	2	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	8	1	no	—
314	Q₈	—	8	1	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	4	no	—
318	D₄	—	8	2	no	—
319	D₄	—	8	2	no	—
320	D₄	—	8	1	no	—
321	D₄	—	8	1	no	—
322	D₄	—	8	1	no	—
323	D₄	—	8	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	8	1	no	—
330	C₂×C₄	—	8	1	no	—
331	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
332	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
333	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
334	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
335	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
336	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
337	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
338	C₂×C₄	C₂×SD₁₆×C₆₇	1	1	yes	characteristic
339	C₂×C₄	C₂×SD₁₆×C₆₇	1	2	yes	—
340	C₂×C₄	#135×C₆₇	1	2	yes	—
341	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
342	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
343	C₈	—	2	2	no	—
344	C₈	—	4	2	no	—
345	C₈	—	8	1	no	—
346	C₈	—	8	1	no	—
347	C₈	#102×C₆₇	1	4	yes	complemented
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	16	2	no	—
352	C₂²	—	16	2	no	—
353	C₂²	#390×C₆₇	1	1	yes	characteristic
354	C₂²	#459×C₆₇	1	1	yes	characteristic
355	C₂²	#460×C₆₇	1	1	yes	characteristic
356	C₂²	#465×C₆₇	1	2	yes	—
357	C₂²	#471×C₆₇	1	2	yes	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	4	4	no	—
361	C₄	—	8	2	no	—
362	C₄	C₂×#102×C₆₇	1	1	yes	characteristic
363	C₄	#418×C₆₇	1	1	yes	characteristic
364	C₄	C₄×SD₁₆×C₆₇	1	2	yes	—
365	C₄	#459×C₆₇	1	1	yes	characteristic
366	C₄	#460×C₆₇	1	1	yes	characteristic
367	C₄	#492×C₆₇	1	1	yes	characteristic
368	C₄	#495×C₆₇	1	1	yes	characteristic
369	C₂	—	16	2	no	—
370	C₂	C₆₇×#1665	1	2	yes	—
371	C₂	C₆₇×#1666	1	2	yes	—
372	C₂	C₆₇×#1968	1	1	yes	characteristic
373	C₂	C₆₇×#1977	1	1	yes	characteristic
374	C₂	C₆₇×#1982	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	#121
commutator	C₄²	C₂²×C₄×C₆₇
Frattini, cosocle	C₂×C₄²	C₂³×C₆₇
prime radical	C₂×#127×C₆₇	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#1988	C₂	semidirect
4. C₈×C₄⋊C₄×C₆₇	C₂	semidirect
5. C₂×#334×C₆₇	C₂	semidirect
6. C₂×#332×C₆₇	C₂	semidirect
13. #492×C₆₇	C₄	semidirect
110. C₄⋊C₄×C₆₇	SD₁₆	semidirect
159. C₈×C₆₇	#102	semidirect
181. #9732	C₆₇	direct (N × H)
189. #1988	C₂×C₆₇	semidirect
191. C₈×C₄⋊C₄	C₂×C₆₇	semidirect
192. C₂×#334	C₂×C₆₇	semidirect
193. C₂×#332	C₂×C₆₇	semidirect
195. C₆₇	#9732	direct (N × H)
201. #492	C₄×C₆₇	semidirect
298. C₄⋊C₄	SD₁₆×C₆₇	semidirect
347. C₈	#102×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#492×C₆₇	2
C₆₇×#1988	2
C₆₇×#1982	2
C₈×C₄⋊C₄×C₆₇	2
C₂×#334×C₆₇	2
C₂×#332×C₆₇	2
C₂×#331×C₆₇	2
#9732	67

Subgroups — C67×#9732 #30688983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#9732 #30688983