Subgroups — C₆₇×#21271 #30700522

Order 17152.

962 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#432×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#1955	C₂	1	2	yes	maximal
4	C₆₇×#1940	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1923	C₂	1	4	yes	maximal, complemented
6	C₆₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1749	C₂	1	2	yes	maximal, complemented
8	C₄×#97×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₄×C₆₇	C₄	1	2	yes	—
10	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
12	#432×C₆₇	—	2	8	no	—
13	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	—
15	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
16	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
17	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×#97×C₆₇	C₂²	1	2	yes	—
19	C₂×#97×C₆₇	C₂²	1	2	yes	—
20	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
22	C₄×C₄⋊C₄×C₆₇	C₄	1	2	yes	—
23	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₆₇	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₆₇	C₄	1	2	yes	—
26	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
27	C₄³×C₆₇	C₂²	1	1	yes	characteristic
28	#336×C₆₇	C₂²	1	4	yes	—
29	#336×C₆₇	C₂²	1	2	yes	—
30	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
34	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
35	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
36	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
37	C₄×D₄×C₆₇	—	2	8	no	—
38	C₄×D₄×C₆₇	—	2	4	no	—
39	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
43	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₆₇	—	2	4	no	—
45	C₂×C₄²×C₆₇	—	2	4	no	—
46	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
51	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₆₇	—	2	8	no	—
55	C₄⋊C₈×C₆₇	—	2	4	no	—
56	C₂²⋊C₈×C₆₇	—	2	8	no	—
57	C₂²⋊C₈×C₆₇	—	2	8	no	—
58	#97×C₆₇	—	2	4	no	—
59	#97×C₆₇	—	2	4	no	—
60	#97×C₆₇	—	2	2	no	—
61	#97×C₆₇	D₄	1	4	yes	complemented
62	C₄×C₈×C₆₇	—	2	4	no	—
63	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
64	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
65	#95×C₆₇	C₂×C₄	1	2	yes	—
66	#95×C₆₇	C₂×C₄	1	2	yes	—
67	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
68	C₂×D₄×C₆₇	—	2	4	no	—
69	C₂×D₄×C₆₇	—	2	2	no	—
70	C₂²×C₄×C₆₇	—	2	4	no	—
71	C₂²×C₄×C₆₇	—	2	4	no	—
72	C₂²×C₄×C₆₇	—	2	4	no	—
73	C₂²×C₄×C₆₇	—	2	4	no	—
74	C₂²×C₄×C₆₇	—	2	2	no	—
75	C₂²×C₄×C₆₇	—	2	2	no	—
76	C₂²×C₄×C₆₇	—	2	4	no	—
77	C₂²×C₄×C₆₇	—	2	4	no	—
78	C₂²×C₄×C₆₇	—	4	2	no	—
79	C₂²×C₄×C₆₇	—	4	2	no	—
80	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
88	C₂×C₈×C₆₇	—	2	2	no	—
89	C₂×C₈×C₆₇	—	2	2	no	—
90	C₂×C₈×C₆₇	—	2	2	no	—
91	C₂×C₈×C₆₇	—	2	2	no	—
92	C₂×C₈×C₆₇	—	2	4	no	—
93	C₂×C₈×C₆₇	—	2	4	no	—
94	C₂×C₈×C₆₇	—	2	4	no	—
95	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
96	C₂×C₈×C₆₇	#41	1	4	yes	—
97	C₄⋊C₄×C₆₇	—	2	2	no	—
98	C₄⋊C₄×C₆₇	—	2	4	no	—
99	C₂²⋊C₄×C₆₇	—	2	4	no	—
100	C₂²⋊C₄×C₆₇	—	2	4	no	—
101	C₂²⋊C₄×C₆₇	M₁₆	1	8	yes	—
102	C₄²×C₆₇	—	2	4	no	—
103	C₄²×C₆₇	—	2	4	no	—
104	C₄²×C₆₇	—	2	4	no	—
105	C₄²×C₆₇	—	2	2	no	—
106	C₄²×C₆₇	—	2	2	no	—
107	C₄²×C₆₇	—	2	2	no	—
108	C₄²×C₆₇	—	4	2	no	—
109	C₄²×C₆₇	C₂×D₄	1	2	yes	—
110	C₄²×C₆₇	#41	1	4	yes	—
111	C₄²×C₆₇	#41	1	2	yes	—
112	C₂³×C₆₇	—	2	2	no	—
113	C₂³×C₆₇	—	2	2	no	—
114	C₂³×C₆₇	—	2	2	no	—
115	C₂³×C₆₇	—	2	2	no	—
116	C₂³×C₆₇	—	2	2	no	—
117	C₂³×C₆₇	—	2	2	no	—
118	C₂³×C₆₇	C₂×M₁₆	1	4	yes	—
119	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
120	D₄×C₆₇	—	2	8	no	—
121	C₂×C₄×C₆₇	—	2	2	no	—
122	C₂×C₄×C₆₇	—	2	2	no	—
123	C₂×C₄×C₆₇	—	2	2	no	—
124	C₂×C₄×C₆₇	—	2	2	no	—
125	C₂×C₄×C₆₇	—	2	2	no	—
126	C₂×C₄×C₆₇	—	2	2	no	—
127	C₂×C₄×C₆₇	—	2	2	no	—
128	C₂×C₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	2	no	—
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	4	8	no	—
136	C₂×C₄×C₆₇	—	4	8	no	—
137	C₂×C₄×C₆₇	—	4	4	no	—
138	C₂×C₄×C₆₇	—	4	4	no	—
139	C₂×C₄×C₆₇	#117	1	2	yes	—
140	C₂×C₄×C₆₇	#117	1	2	yes	—
141	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
142	C₂×C₄×C₆₇	C₂×M₁₆	1	4	yes	—
143	C₂×C₄×C₆₇	C₂×M₁₆	1	4	yes	—
144	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
147	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
148	C₈×C₆₇	—	2	4	no	—
149	C₈×C₆₇	—	2	4	no	—
150	C₈×C₆₇	—	4	4	no	—
151	C₂²×C₆₇	—	2	4	no	—
152	C₂²×C₆₇	—	2	4	no	—
153	C₂²×C₆₇	—	2	4	no	—
154	C₂²×C₆₇	—	4	2	no	—
155	C₂²×C₆₇	—	4	2	no	—
156	C₂²×C₆₇	—	4	2	no	—
157	C₂²×C₆₇	—	4	2	no	—
158	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
159	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
160	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
161	C₂²×C₆₇	C₂²×M₁₆	1	2	yes	—
162	C₂²×C₆₇	#568	1	2	yes	—
163	C₄×C₆₇	—	2	2	no	—
164	C₄×C₆₇	—	2	2	no	—
165	C₄×C₆₇	—	2	4	no	—
166	C₄×C₆₇	—	2	4	no	—
167	C₄×C₆₇	—	2	4	no	—
168	C₄×C₆₇	—	4	2	no	—
169	C₄×C₆₇	—	4	2	no	—
170	C₄×C₆₇	#529	1	2	yes	—
171	C₄×C₆₇	#532	1	2	yes	—
172	#21271	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂×C₆₇	—	4	4	no	—
174	C₂×C₆₇	#2293	1	1	yes	characteristic
175	C₂×C₆₇	#2920	1	1	yes	characteristic
176	C₂×C₆₇	#2923	1	1	yes	characteristic
177	C₂×C₆₇	D₄×M₁₆	1	2	yes	—
178	C₂×C₆₇	#2970	1	2	yes	—
179	C₂×#432	C₂×C₆₇	1	2	yes	complemented
180	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic
181	#1955	C₂×C₆₇	1	2	yes	—
182	#1940	C₂×C₆₇	1	2	yes	complemented
183	#1923	C₂×C₆₇	1	4	yes	complemented
184	#1767	C₂×C₆₇	1	1	yes	characteristic, complemented
185	#1749	C₂×C₆₇	1	2	yes	complemented
186	C₄×#97	C₂×C₆₇	1	1	yes	characteristic, complemented
187	C₆₇	#21271	1	1	yes	characteristic, direct product factor, Sylow
188	C₂×C₄×D₄	C₄×C₆₇	1	2	yes	—
189	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
190	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
191	#432	—	2	8	no	—
192	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	—
193	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
194	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
195	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
196	C₂×#97	C₂²×C₆₇	1	2	yes	—
197	C₂×#97	C₂²×C₆₇	1	2	yes	—
198	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
199	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
201	C₄×C₄⋊C₄	C₄×C₆₇	1	2	yes	—
202	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
203	C₄×C₂²⋊C₄	C₄×C₆₇	1	2	yes	—
204	C₄×C₂²⋊C₄	C₄×C₆₇	1	2	yes	—
205	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
206	C₄³	C₂²×C₆₇	1	1	yes	characteristic
207	#336	C₂²×C₆₇	1	2	yes	—
208	#336	C₂²×C₆₇	1	4	yes	—
209	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
210	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
211	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
212	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
213	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
214	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
215	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
216	C₄×D₄	—	2	8	no	—
217	C₄×D₄	—	2	4	no	—
218	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
220	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
221	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
222	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
223	C₂×C₄²	—	2	4	no	—
224	C₂×C₄²	—	2	4	no	—
225	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
227	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
228	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
229	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
231	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
233	C₄⋊C₈	—	2	8	no	—
234	C₄⋊C₈	—	2	4	no	—
235	C₂²⋊C₈	—	2	8	no	—
236	C₂²⋊C₈	—	2	8	no	—
237	#97	—	2	4	no	—
238	#97	—	2	4	no	—
239	#97	—	2	2	no	—
240	#97	D₄×C₆₇	1	4	yes	complemented
241	C₄×C₈	—	2	4	no	—
242	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
243	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
244	#95	C₂×C₄×C₆₇	1	2	yes	—
245	#95	C₂×C₄×C₆₇	1	2	yes	—
246	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
247	C₂×D₄	—	2	4	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
266	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
275	C₂×C₈	#41×C₆₇	1	4	yes	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₂²⋊C₄	—	2	4	no	—
279	C₂²⋊C₄	—	2	4	no	—
280	C₂²⋊C₄	M₁₆×C₆₇	1	8	yes	—
281	C₄²	—	2	4	no	—
282	C₄²	—	2	4	no	—
283	C₄²	—	2	4	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	4	2	no	—
288	C₄²	C₂×D₄×C₆₇	1	2	yes	—
289	C₄²	#41×C₆₇	1	4	yes	—
290	C₄²	#41×C₆₇	1	2	yes	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	C₂×M₁₆×C₆₇	1	4	yes	—
298	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
299	D₄	—	2	8	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	8	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	#117×C₆₇	1	2	yes	—
319	C₂×C₄	#117×C₆₇	1	2	yes	—
320	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
321	C₂×C₄	C₂×M₁₆×C₆₇	1	4	yes	—
322	C₂×C₄	C₂×M₁₆×C₆₇	1	4	yes	—
323	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
324	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
325	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
326	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
327	C₈	—	2	4	no	—
328	C₈	—	2	4	no	—
329	C₈	—	4	4	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	C₂×#117×C₆₇	1	1	yes	characteristic
338	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
339	C₂²	C₄×#41×C₆₇	1	1	yes	characteristic
340	C₂²	C₂²×M₁₆×C₆₇	1	2	yes	—
341	C₂²	#568×C₆₇	1	2	yes	—
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	4	no	—
345	C₄	—	2	4	no	—
346	C₄	—	2	4	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	2	no	—
349	C₄	#529×C₆₇	1	2	yes	—
350	C₄	#532×C₆₇	1	2	yes	—
351	C₂	—	4	4	no	—
352	C₂	C₆₇×#2293	1	1	yes	characteristic
353	C₂	C₆₇×#2920	1	1	yes	characteristic
354	C₂	C₆₇×#2923	1	1	yes	characteristic
355	C₂	D₄×M₁₆×C₆₇	1	2	yes	—
356	C₂	C₆₇×#2970	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×#432×C₆₇	C₂	semidirect
4. C₆₇×#1940	C₂	semidirect
5. C₆₇×#1923	C₂	semidirect
6. C₆₇×#1767	C₂	semidirect
7. C₆₇×#1749	C₂	semidirect
8. C₄×#97×C₆₇	C₂	semidirect
61. #97×C₆₇	D₄	semidirect
172. #21271	C₆₇	direct (N × H)
179. C₂×#432	C₂×C₆₇	semidirect
182. #1940	C₂×C₆₇	semidirect
183. #1923	C₂×C₆₇	semidirect
184. #1767	C₂×C₆₇	semidirect
185. #1749	C₂×C₆₇	semidirect
186. C₄×#97	C₂×C₆₇	semidirect
187. C₆₇	#21271	direct (N × H)
240. #97	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#432×C₆₇	2
C₄²×D₄×C₆₇	2
C₆₇×#1955	2
C₆₇×#1940	2
C₆₇×#1923	2
C₆₇×#1767	2
C₆₇×#1749	2
C₄×#97×C₆₇	2
#21271	67

Subgroups — C67×#21271 #30700522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#21271 #30700522