Subgroups — C₆₇×#32983 #30712234

Order 17152.

1734 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#484×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2848	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1872	C₂	1	4	yes	maximal, complemented
5	C₆₇×#1852	C₂	1	4	yes	maximal, complemented
6	C₆₇×#1824	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1779	C₂	1	1	yes	maximal, characteristic
8	C₂⁴×C₄×C₆₇	—	2	1	no	—
9	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₆₇	—	2	2	no	—
14	C₂²×C₄⋊C₄×C₆₇	—	2	8	no	—
15	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
17	#484×C₆₇	—	2	8	no	—
18	C₂×#107×C₆₇	C₂²	1	4	yes	complemented
19	C₂×#103×C₆₇	C₂²	1	4	yes	complemented
20	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
22	#385×C₆₇	—	2	1	no	—
23	#385×C₆₇	—	2	2	no	—
24	#380×C₆₇	C₂²	1	1	yes	characteristic
25	#380×C₆₇	C₂²	1	2	yes	—
26	#379×C₆₇	—	2	1	no	—
27	#340×C₆₇	C₂²	1	8	yes	complemented
28	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
29	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₆₇	—	2	4	no	—
31	C₂³×C₄×C₆₇	—	2	8	no	—
32	C₂³×C₄×C₆₇	—	2	8	no	—
33	C₂³×C₄×C₆₇	—	2	4	no	—
34	C₂³×C₄×C₆₇	—	2	2	no	—
35	C₂³×C₄×C₆₇	—	4	8	no	—
36	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₆₇	D₄	1	2	yes	—
38	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
40	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
41	C₂²⋊Q₈×C₆₇	—	2	4	no	—
42	C₂²⋊Q₈×C₆₇	—	2	8	no	—
43	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
44	C₂×C₄⋊C₄×C₆₇	—	2	16	no	—
45	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₆₇	—	2	16	no	—
49	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₇	D₄	1	8	yes	—
52	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
55	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
59	#107×C₆₇	—	2	8	no	—
60	#103×C₆₇	—	2	8	no	—
61	C₂²⋊C₈×C₆₇	—	2	4	no	—
62	C₂²⋊C₈×C₆₇	—	2	8	no	—
63	#95×C₆₇	—	2	1	no	—
64	#95×C₆₇	—	2	2	no	—
65	C₂⁴×C₆₇	—	2	2	no	—
66	C₂⁴×C₆₇	—	2	4	no	—
67	C₂⁴×C₆₇	—	2	4	no	—
68	C₂⁴×C₆₇	—	2	2	no	—
69	C₂⁴×C₆₇	Q₁₆	1	4	yes	—
70	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
71	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
72	C₂×Q₈×C₆₇	—	2	2	no	—
73	C₂×Q₈×C₆₇	—	2	4	no	—
74	C₂²×C₄×C₆₇	—	2	32	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	—	2	4	no	—
79	C₂²×C₄×C₆₇	—	2	4	no	—
80	C₂²×C₄×C₆₇	—	2	4	no	—
81	C₂²×C₄×C₆₇	—	2	4	no	—
82	C₂²×C₄×C₆₇	—	2	4	no	—
83	C₂²×C₄×C₆₇	—	2	16	no	—
84	C₂²×C₄×C₆₇	—	2	8	no	—
85	C₂²×C₄×C₆₇	—	2	4	no	—
86	C₂²×C₄×C₆₇	—	2	1	no	—
87	C₂²×C₄×C₆₇	—	2	1	no	—
88	C₂²×C₄×C₆₇	—	2	2	no	—
89	C₂²×C₄×C₆₇	—	4	32	no	—
90	C₂²×C₄×C₆₇	—	4	8	no	—
91	C₂²×C₄×C₆₇	—	4	8	no	—
92	C₂²×C₄×C₆₇	—	4	8	no	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₆₇	#41	1	8	yes	—
97	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₆₇	—	2	4	no	—
99	C₂×C₈×C₆₇	—	2	8	no	—
100	C₄⋊C₄×C₆₇	—	2	16	no	—
101	C₄⋊C₄×C₆₇	—	2	8	no	—
102	C₄⋊C₄×C₆₇	—	2	4	no	—
103	C₄⋊C₄×C₆₇	—	2	2	no	—
104	C₄⋊C₄×C₆₇	—	2	4	no	—
105	C₄⋊C₄×C₆₇	—	4	2	no	—
106	C₄⋊C₄×C₆₇	—	4	4	no	—
107	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
108	C₂²⋊C₄×C₆₇	—	4	2	no	—
109	C₂²⋊C₄×C₆₇	—	4	4	no	—
110	C₂²⋊C₄×C₆₇	—	4	4	no	—
111	C₂²⋊C₄×C₆₇	—	4	2	no	—
112	C₂³×C₆₇	—	2	8	no	—
113	C₂³×C₆₇	—	2	8	no	—
114	C₂³×C₆₇	—	2	16	no	—
115	C₂³×C₆₇	—	2	2	no	—
116	C₂³×C₆₇	—	2	2	no	—
117	C₂³×C₆₇	—	2	2	no	—
118	C₂³×C₆₇	—	2	2	no	—
119	C₂³×C₆₇	—	2	2	no	—
120	C₂³×C₆₇	—	2	2	no	—
121	C₂³×C₆₇	—	2	8	no	—
122	C₂³×C₆₇	—	2	16	no	—
123	C₂³×C₆₇	#120	1	2	yes	—
124	C₂³×C₆₇	#123	1	4	yes	—
125	C₂³×C₆₇	C₂×Q₁₆	1	2	yes	—
126	C₂³×C₆₇	C₂×Q₁₆	1	4	yes	—
127	C₂³×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
128	C₂³×C₆₇	#137	1	2	yes	—
129	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₆₇	—	4	4	no	—
131	C₂×C₄×C₆₇	—	2	16	no	—
132	C₂×C₄×C₆₇	—	2	8	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	2	8	no	—
137	C₂×C₄×C₆₇	—	2	16	no	—
138	C₂×C₄×C₆₇	—	2	8	no	—
139	C₂×C₄×C₆₇	—	4	16	no	—
140	C₂×C₄×C₆₇	—	4	32	no	—
141	C₂×C₄×C₆₇	—	4	8	no	—
142	C₂×C₄×C₆₇	—	4	1	no	—
143	C₂×C₄×C₆₇	—	4	1	no	—
144	C₂×C₄×C₆₇	—	4	2	no	—
145	C₂×C₄×C₆₇	—	4	2	no	—
146	C₂×C₄×C₆₇	—	4	2	no	—
147	C₂×C₄×C₆₇	—	4	2	no	—
148	C₂×C₄×C₆₇	—	4	2	no	—
149	C₂×C₄×C₆₇	#120	1	2	yes	—
150	C₂×C₄×C₆₇	#123	1	4	yes	—
151	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
152	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
153	C₈×C₆₇	—	4	4	no	—
154	C₂²×C₆₇	—	2	32	no	—
155	C₂²×C₆₇	—	2	4	no	—
156	C₂²×C₆₇	—	2	4	no	—
157	C₂²×C₆₇	—	2	4	no	—
158	C₂²×C₆₇	—	2	4	no	—
159	C₂²×C₆₇	—	2	4	no	—
160	C₂²×C₆₇	—	2	2	no	—
161	C₂²×C₆₇	—	2	4	no	—
162	C₂²×C₆₇	—	2	4	no	—
163	C₂²×C₆₇	—	2	2	no	—
164	C₂²×C₆₇	—	2	4	no	—
165	C₂²×C₆₇	#451	1	4	yes	—
166	C₂²×C₆₇	#484	1	8	yes	complemented
167	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
168	C₂²×C₆₇	C₂×#123	1	2	yes	—
169	C₂²×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
170	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
171	C₂²×C₆₇	C₂×#137	1	1	yes	characteristic
172	C₄×C₆₇	—	2	2	no	—
173	C₄×C₆₇	—	2	4	no	—
174	C₄×C₆₇	—	4	8	no	—
175	C₄×C₆₇	—	8	2	no	—
176	C₄×C₆₇	—	8	1	no	—
177	C₄×C₆₇	—	8	1	no	—
178	C₄×C₆₇	#525	1	4	yes	—
179	#32983	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₆₇	—	2	4	no	—
181	C₂×C₆₇	—	2	8	no	—
182	C₂×C₆₇	#2849	1	1	yes	characteristic
183	C₂×C₆₇	C₂×#451	1	1	yes	characteristic
184	C₂×C₆₇	#3003	1	1	yes	characteristic
185	C₂×C₆₇	C₂×#484	1	2	yes	—
186	C₂×C₆₇	#3092	1	2	yes	—
187	C₂³×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic
188	C₂×#484	C₂×C₆₇	1	2	yes	complemented
189	#2848	C₂×C₆₇	1	1	yes	characteristic
190	#1872	C₂×C₆₇	1	4	yes	complemented
191	#1852	C₂×C₆₇	1	4	yes	complemented
192	#1824	C₂×C₆₇	1	2	yes	complemented
193	#1779	C₂×C₆₇	1	1	yes	characteristic
194	C₆₇	#32983	1	1	yes	characteristic, direct product factor, Sylow
195	C₂⁴×C₄	—	2	1	no	—
196	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
197	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
198	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
199	C₂²×C₄⋊C₄	—	2	1	no	—
200	C₂²×C₄⋊C₄	—	2	2	no	—
201	C₂²×C₄⋊C₄	—	2	8	no	—
202	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
203	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
204	#484	—	2	8	no	—
205	C₂×#107	C₂²×C₆₇	1	4	yes	complemented
206	C₂×#103	C₂²×C₆₇	1	4	yes	complemented
207	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
208	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
209	#385	—	2	2	no	—
210	#385	—	2	1	no	—
211	#380	C₂²×C₆₇	1	1	yes	characteristic
212	#380	C₂²×C₆₇	1	2	yes	—
213	#379	—	2	1	no	—
214	#340	C₂²×C₆₇	1	8	yes	complemented
215	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
216	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
217	C₂³×C₄	—	2	4	no	—
218	C₂³×C₄	—	2	8	no	—
219	C₂³×C₄	—	2	8	no	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	—	2	2	no	—
222	C₂³×C₄	—	4	8	no	—
223	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
224	C₂³×C₄	D₄×C₆₇	1	2	yes	—
225	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
226	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
227	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
228	C₂²⋊Q₈	—	2	4	no	—
229	C₂²⋊Q₈	—	2	8	no	—
230	C₂×C₄⋊C₄	—	2	8	no	—
231	C₂×C₄⋊C₄	—	2	16	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	16	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	D₄×C₆₇	1	8	yes	—
239	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	1	no	—
246	#107	—	2	8	no	—
247	#103	—	2	8	no	—
248	C₂²⋊C₈	—	2	4	no	—
249	C₂²⋊C₈	—	2	8	no	—
250	#95	—	2	1	no	—
251	#95	—	2	2	no	—
252	C₂⁴	—	2	2	no	—
253	C₂⁴	—	2	4	no	—
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	2	2	no	—
256	C₂⁴	Q₁₆×C₆₇	1	4	yes	—
257	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
258	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂²×C₄	—	2	32	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	16	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	4	32	no	—
277	C₂²×C₄	—	4	8	no	—
278	C₂²×C₄	—	4	8	no	—
279	C₂²×C₄	—	4	8	no	—
280	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
282	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
283	C₂²×C₄	#41×C₆₇	1	8	yes	—
284	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	8	no	—
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	8	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	—	4	4	no	—
294	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₂³	—	2	8	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	2	16	no	—
302	C₂³	—	2	8	no	—
303	C₂³	—	2	16	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	#120×C₆₇	1	2	yes	—
311	C₂³	#123×C₆₇	1	4	yes	—
312	C₂³	C₂×Q₁₆×C₆₇	1	2	yes	—
313	C₂³	C₂×Q₁₆×C₆₇	1	4	yes	—
314	C₂³	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
315	C₂³	#137×C₆₇	1	2	yes	—
316	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
317	Q₈	—	4	4	no	—
318	C₂×C₄	—	2	16	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	16	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	4	16	no	—
327	C₂×C₄	—	4	32	no	—
328	C₂×C₄	—	4	8	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	#120×C₆₇	1	2	yes	—
337	C₂×C₄	#123×C₆₇	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
339	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	32	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	4	no	—
352	C₂²	#451×C₆₇	1	4	yes	—
353	C₂²	#484×C₆₇	1	8	yes	complemented
354	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
355	C₂²	C₂×#123×C₆₇	1	2	yes	—
356	C₂²	C₂²×Q₁₆×C₆₇	1	1	yes	characteristic
357	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
358	C₂²	C₂×#137×C₆₇	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	2	4	no	—
361	C₄	—	4	8	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	1	no	—
365	C₄	#525×C₆₇	1	4	yes	—
366	C₂	—	2	4	no	—
367	C₂	—	2	8	no	—
368	C₂	C₆₇×#2849	1	1	yes	characteristic
369	C₂	C₂×#451×C₆₇	1	1	yes	characteristic
370	C₂	C₆₇×#3003	1	1	yes	characteristic
371	C₂	C₂×#484×C₆₇	1	2	yes	—
372	C₂	C₆₇×#3092	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂⁵×C₆₇	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂⁴×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#484×C₆₇	C₂	semidirect
4. C₆₇×#1872	C₂	semidirect
5. C₆₇×#1852	C₂	semidirect
6. C₆₇×#1824	C₂	semidirect
18. C₂×#107×C₆₇	C₂²	semidirect
19. C₂×#103×C₆₇	C₂²	semidirect
27. #340×C₆₇	C₂²	semidirect
166. C₂²×C₆₇	#484	semidirect
179. #32983	C₆₇	direct (N × H)
188. C₂×#484	C₂×C₆₇	semidirect
190. #1872	C₂×C₆₇	semidirect
191. #1852	C₂×C₆₇	semidirect
192. #1824	C₂×C₆₇	semidirect
194. C₆₇	#32983	direct (N × H)
205. C₂×#107	C₂²×C₆₇	semidirect
206. C₂×#103	C₂²×C₆₇	semidirect
214. #340	C₂²×C₆₇	semidirect
353. C₂²	#484×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₆₇	2
C₂×#484×C₆₇	2
C₆₇×#2848	2
C₆₇×#1872	2
C₆₇×#1852	2
C₆₇×#1824	2
C₆₇×#1779	2
#32983	67

Subgroups — C67×#32983 #30712234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#32983 #30712234