Subgroups — C₂×C₆₇×#3292 #30740354

Order 17152.

2766 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#576×C₆₇	C₂	1	4	yes	maximal, complemented
2	C₆₇×#3292	C₂	1	16	yes	maximal, direct product factor
3	C₂×#493×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#472×C₆₇	C₂	1	4	yes	maximal, complemented
5	C₂×#453×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#443×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	4	yes	complemented
8	#576×C₆₇	—	2	16	no	—
9	#576×C₆₇	C₂²	1	32	yes	complemented
10	C₂×AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
11	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	8	yes	complemented
12	C₂×#135×C₆₇	—	2	4	no	—
13	C₂×#135×C₆₇	C₂²	1	2	yes	—
14	C₂²×D₈×C₆₇	—	2	4	no	—
15	C₂²×D₈×C₆₇	C₂²	1	4	yes	complemented
16	C₂×#131×C₆₇	C₂²	1	4	yes	complemented
17	C₂×#127×C₆₇	C₂²	1	2	yes	complemented
18	#493×C₆₇	C₂²	1	8	yes	complemented
19	#472×C₆₇	C₂²	1	32	yes	complemented
20	#453×C₆₇	C₂²	1	32	yes	complemented
21	#443×C₆₇	C₂²	1	16	yes	complemented
22	C₂×#108×C₆₇	C₂²	1	2	yes	complemented
23	C₂×#104×C₆₇	C₂²	1	4	yes	complemented
24	C₂×#100×C₆₇	C₂²	1	4	yes	complemented
25	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	H(5,𝔽₂)×C₆₇	—	2	16	no	—
27	H(5,𝔽₂)×C₆₇	—	4	4	no	—
28	H(5,𝔽₂)×C₆₇	C₂³	1	16	yes	complemented
29	C₂×#41×C₆₇	—	2	8	no	—
30	C₂×#41×C₆₇	C₂³	1	4	yes	—
31	C₂²×D₄×C₆₇	—	2	8	no	—
32	C₂²×D₄×C₆₇	—	4	2	no	—
33	C₂²×D₄×C₆₇	—	4	4	no	—
34	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
35	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
36	AGL(1,ℤ/8)×C₆₇	—	2	64	no	—
37	AGL(1,ℤ/8)×C₆₇	C₂³	1	32	yes	complemented
38	#135×C₆₇	—	2	32	no	—
39	#135×C₆₇	D₄	1	8	yes	complemented
40	#135×C₆₇	C₂³	1	8	yes	—
41	C₂×Q₁₆×C₆₇	D₄	1	2	yes	complemented
42	C₂×SD₁₆×C₆₇	—	2	8	no	—
43	C₂×SD₁₆×C₆₇	D₄	1	4	yes	complemented
44	C₂×D₈×C₆₇	—	2	8	no	—
45	C₂×D₈×C₆₇	—	2	32	no	—
46	C₂×D₈×C₆₇	—	2	4	no	—
47	C₂×D₈×C₆₇	—	2	4	no	—
48	C₂×D₈×C₆₇	—	2	8	no	—
49	C₂×D₈×C₆₇	D₄	1	2	yes	complemented
50	C₂×D₈×C₆₇	C₂³	1	16	yes	complemented
51	#131×C₆₇	—	2	8	no	—
52	#131×C₆₇	C₂³	1	16	yes	complemented
53	C₂×M₁₆×C₆₇	—	2	4	no	—
54	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
55	C₂²×C₈×C₆₇	—	2	4	no	—
56	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
57	#127×C₆₇	—	4	2	no	—
58	#127×C₆₇	C₂³	1	8	yes	complemented
59	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
60	#108×C₆₇	C₂³	1	8	yes	complemented
61	#104×C₆₇	C₂³	1	16	yes	complemented
62	#100×C₆₇	C₂³	1	16	yes	complemented
63	C₄×C₈×C₆₇	C₂³	1	4	yes	complemented
64	C₂⁴×C₆₇	—	2	4	no	—
65	C₂⁴×C₆₇	—	4	4	no	—
66	#41×C₆₇	—	2	4	no	—
67	#41×C₆₇	—	2	4	no	—
68	#41×C₆₇	—	2	32	no	—
69	#41×C₆₇	—	4	16	no	—
70	#41×C₆₇	C₂×D₄	1	8	yes	—
71	#41×C₆₇	C₂⁴	1	8	yes	—
72	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
73	C₂×D₄×C₆₇	—	2	4	no	—
74	C₂×D₄×C₆₇	—	2	32	no	—
75	C₂×D₄×C₆₇	—	2	8	no	—
76	C₂×D₄×C₆₇	—	2	8	no	—
77	C₂×D₄×C₆₇	—	2	4	no	—
78	C₂×D₄×C₆₇	—	4	16	no	—
79	C₂×D₄×C₆₇	—	4	8	no	—
80	C₂×D₄×C₆₇	—	4	8	no	—
81	C₂×D₄×C₆₇	—	4	16	no	—
82	C₂×D₄×C₆₇	—	4	16	no	—
83	C₂×D₄×C₆₇	—	8	8	no	—
84	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
85	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
86	C₂²×C₄×C₆₇	—	2	1	no	—
87	C₂²×C₄×C₆₇	—	2	4	no	—
88	C₂²×C₄×C₆₇	—	4	4	no	—
89	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
90	Q₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
91	SD₁₆×C₆₇	—	2	32	no	—
92	SD₁₆×C₆₇	C₂×D₄	1	16	yes	complemented
93	D₈×C₆₇	—	2	32	no	—
94	D₈×C₆₇	—	2	16	no	—
95	D₈×C₆₇	—	2	16	no	—
96	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
97	M₁₆×C₆₇	—	2	4	no	—
98	M₁₆×C₆₇	—	2	16	no	—
99	M₁₆×C₆₇	C₂⁴	1	8	yes	—
100	C₂×C₈×C₆₇	—	2	4	no	—
101	C₂×C₈×C₆₇	—	2	16	no	—
102	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
105	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
106	C₄²×C₆₇	—	2	1	no	—
107	C₄²×C₆₇	C₂⁴	1	2	yes	—
108	C₂³×C₆₇	—	2	4	no	—
109	C₂³×C₆₇	—	2	8	no	—
110	C₂³×C₆₇	—	4	16	no	—
111	C₂³×C₆₇	—	4	4	no	—
112	C₂³×C₆₇	—	4	4	no	—
113	C₂³×C₆₇	—	8	8	no	—
114	C₂³×C₆₇	—	16	8	no	—
115	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
116	Q₈×C₆₇	—	2	4	no	—
117	Q₈×C₆₇	C₂²×D₄	1	8	yes	—
118	D₄×C₆₇	—	2	8	no	—
119	D₄×C₆₇	—	2	8	no	—
120	D₄×C₆₇	—	2	4	no	—
121	D₄×C₆₇	—	2	16	no	—
122	D₄×C₆₇	—	4	32	no	—
123	D₄×C₆₇	—	4	8	no	—
124	D₄×C₆₇	—	8	16	no	—
125	D₄×C₆₇	C₂²×D₄	1	8	yes	—
126	C₂×C₄×C₆₇	—	2	4	no	—
127	C₂×C₄×C₆₇	—	2	4	no	—
128	C₂×C₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	—	2	8	no	—
130	C₂×C₄×C₆₇	—	2	8	no	—
131	C₂×C₄×C₆₇	—	4	16	no	—
132	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
133	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
134	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
136	C₈×C₆₇	—	2	8	no	—
137	C₈×C₆₇	C₂²×D₄	1	4	yes	—
138	C₈×C₆₇	C₂²×D₄	1	4	yes	—
139	C₂²×C₆₇	—	2	2	no	—
140	C₂²×C₆₇	—	2	8	no	—
141	C₂²×C₆₇	—	4	8	no	—
142	C₂²×C₆₇	—	4	8	no	—
143	C₂²×C₆₇	—	8	8	no	—
144	C₂²×C₆₇	—	8	8	no	—
145	C₂²×C₆₇	—	16	4	no	—
146	C₂²×C₆₇	—	16	16	no	—
147	C₂²×C₆₇	D₄²	1	1	yes	characteristic
148	C₂²×C₆₇	D₄²	1	1	yes	characteristic
149	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
150	C₄×C₆₇	—	2	4	no	—
151	C₄×C₆₇	—	2	8	no	—
152	C₄×C₆₇	D₄²	1	2	yes	—
153	C₄×C₆₇	C₂³×D₄	1	2	yes	—
154	C₂×#3292	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂×C₆₇	—	2	1	no	—
156	C₂×C₆₇	—	2	1	no	—
157	C₂×C₆₇	—	4	8	no	—
158	C₂×C₆₇	—	8	8	no	—
159	C₂×C₆₇	#3292	1	2	yes	direct product factor
160	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
161	C₂×#576	C₂×C₆₇	1	4	yes	complemented
162	#3292	C₂×C₆₇	1	16	yes	direct product factor
163	C₂×#493	C₂×C₆₇	1	1	yes	characteristic, complemented
164	C₂×#472	C₂×C₆₇	1	4	yes	complemented
165	C₂×#453	C₂×C₆₇	1	4	yes	complemented
166	C₂×#443	C₂×C₆₇	1	2	yes	complemented
167	C₆₇	C₂×#3292	1	1	yes	characteristic, direct product factor, Sylow
168	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	4	yes	complemented
169	#576	—	2	16	no	—
170	#576	C₂²×C₆₇	1	32	yes	complemented
171	C₂×AGL(1,ℤ/8)	—	2	8	no	—
172	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	8	yes	complemented
173	C₂×#135	—	2	4	no	—
174	C₂×#135	C₂²×C₆₇	1	2	yes	—
175	C₂²×D₈	—	2	4	no	—
176	C₂²×D₈	C₂²×C₆₇	1	4	yes	complemented
177	C₂×#131	C₂²×C₆₇	1	4	yes	complemented
178	C₂×#127	C₂²×C₆₇	1	2	yes	complemented
179	#493	C₂²×C₆₇	1	8	yes	complemented
180	#472	C₂²×C₆₇	1	32	yes	complemented
181	#453	C₂²×C₆₇	1	32	yes	complemented
182	#443	C₂²×C₆₇	1	16	yes	complemented
183	C₂×#108	C₂²×C₆₇	1	2	yes	complemented
184	C₂×#104	C₂²×C₆₇	1	4	yes	complemented
185	C₂×#100	C₂²×C₆₇	1	4	yes	complemented
186	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
187	H(5,𝔽₂)	—	2	16	no	—
188	H(5,𝔽₂)	—	4	4	no	—
189	H(5,𝔽₂)	C₂³×C₆₇	1	16	yes	complemented
190	C₂×#41	—	2	8	no	—
191	C₂×#41	C₂³×C₆₇	1	4	yes	—
192	C₂²×D₄	—	2	8	no	—
193	C₂²×D₄	—	4	2	no	—
194	C₂²×D₄	—	4	4	no	—
195	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
196	AGL(1,ℤ/8)	—	2	16	no	—
197	AGL(1,ℤ/8)	—	2	64	no	—
198	AGL(1,ℤ/8)	C₂³×C₆₇	1	32	yes	complemented
199	#135	—	2	32	no	—
200	#135	D₄×C₆₇	1	8	yes	complemented
201	#135	C₂³×C₆₇	1	8	yes	—
202	C₂×Q₁₆	D₄×C₆₇	1	2	yes	complemented
203	C₂×SD₁₆	—	2	8	no	—
204	C₂×SD₁₆	D₄×C₆₇	1	4	yes	complemented
205	C₂×D₈	—	2	8	no	—
206	C₂×D₈	—	2	32	no	—
207	C₂×D₈	—	2	4	no	—
208	C₂×D₈	—	2	4	no	—
209	C₂×D₈	—	2	8	no	—
210	C₂×D₈	D₄×C₆₇	1	2	yes	complemented
211	C₂×D₈	C₂³×C₆₇	1	16	yes	complemented
212	#131	—	2	8	no	—
213	#131	C₂³×C₆₇	1	16	yes	complemented
214	C₂×M₁₆	—	2	4	no	—
215	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
216	C₂²×C₈	—	2	4	no	—
217	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
218	#127	—	4	2	no	—
219	#127	C₂³×C₆₇	1	8	yes	complemented
220	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
221	#108	C₂³×C₆₇	1	8	yes	complemented
222	#104	C₂³×C₆₇	1	16	yes	complemented
223	#100	C₂³×C₆₇	1	16	yes	complemented
224	C₄×C₈	C₂³×C₆₇	1	4	yes	complemented
225	C₂⁴	—	2	4	no	—
226	C₂⁴	—	4	4	no	—
227	#41	—	2	4	no	—
228	#41	—	2	4	no	—
229	#41	—	2	32	no	—
230	#41	—	4	16	no	—
231	#41	C₂×D₄×C₆₇	1	8	yes	—
232	#41	C₂⁴×C₆₇	1	8	yes	—
233	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
234	C₂×D₄	—	2	4	no	—
235	C₂×D₄	—	2	32	no	—
236	C₂×D₄	—	2	8	no	—
237	C₂×D₄	—	2	8	no	—
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	—	4	16	no	—
240	C₂×D₄	—	4	8	no	—
241	C₂×D₄	—	4	8	no	—
242	C₂×D₄	—	4	16	no	—
243	C₂×D₄	—	4	16	no	—
244	C₂×D₄	—	8	8	no	—
245	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
246	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	4	no	—
250	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
251	Q₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
252	SD₁₆	—	2	32	no	—
253	SD₁₆	C₂×D₄×C₆₇	1	16	yes	complemented
254	D₈	—	2	32	no	—
255	D₈	—	2	16	no	—
256	D₈	—	2	16	no	—
257	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
258	M₁₆	—	2	4	no	—
259	M₁₆	—	2	16	no	—
260	M₁₆	C₂⁴×C₆₇	1	8	yes	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	16	no	—
263	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
264	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
265	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
266	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
267	C₄²	—	2	1	no	—
268	C₄²	C₂⁴×C₆₇	1	2	yes	—
269	C₂³	—	2	4	no	—
270	C₂³	—	2	8	no	—
271	C₂³	—	4	16	no	—
272	C₂³	—	4	4	no	—
273	C₂³	—	4	4	no	—
274	C₂³	—	8	8	no	—
275	C₂³	—	16	8	no	—
276	C₂³	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
277	Q₈	—	2	4	no	—
278	Q₈	C₂²×D₄×C₆₇	1	8	yes	—
279	D₄	—	2	8	no	—
280	D₄	—	2	8	no	—
281	D₄	—	2	4	no	—
282	D₄	—	2	16	no	—
283	D₄	—	4	32	no	—
284	D₄	—	4	8	no	—
285	D₄	—	8	16	no	—
286	D₄	C₂²×D₄×C₆₇	1	8	yes	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	4	16	no	—
293	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
294	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
295	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
296	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
297	C₈	—	2	8	no	—
298	C₈	C₂²×D₄×C₆₇	1	4	yes	—
299	C₈	C₂²×D₄×C₆₇	1	4	yes	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	8	no	—
302	C₂²	—	4	8	no	—
303	C₂²	—	4	8	no	—
304	C₂²	—	8	8	no	—
305	C₂²	—	8	8	no	—
306	C₂²	—	16	4	no	—
307	C₂²	—	16	16	no	—
308	C₂²	D₄²×C₆₇	1	1	yes	characteristic
309	C₂²	D₄²×C₆₇	1	1	yes	characteristic
310	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
311	C₄	—	2	4	no	—
312	C₄	—	2	8	no	—
313	C₄	D₄²×C₆₇	1	2	yes	—
314	C₄	C₂³×D₄×C₆₇	1	2	yes	—
315	C₂	—	2	1	no	—
316	C₂	—	2	1	no	—
317	C₂	—	4	8	no	—
318	C₂	—	8	8	no	—
319	C₂	C₆₇×#3292	1	2	yes	direct product factor
320	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#576×C₆₇	C₂	semidirect
2. C₆₇×#3292	C₂	direct (N × H)
3. C₂×#493×C₆₇	C₂	semidirect
4. C₂×#472×C₆₇	C₂	semidirect
5. C₂×#453×C₆₇	C₂	semidirect
6. C₂×#443×C₆₇	C₂	semidirect
7. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
9. #576×C₆₇	C₂²	semidirect
11. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
15. C₂²×D₈×C₆₇	C₂²	semidirect
16. C₂×#131×C₆₇	C₂²	semidirect
17. C₂×#127×C₆₇	C₂²	semidirect
18. #493×C₆₇	C₂²	semidirect
19. #472×C₆₇	C₂²	semidirect
20. #453×C₆₇	C₂²	semidirect
21. #443×C₆₇	C₂²	semidirect
22. C₂×#108×C₆₇	C₂²	semidirect
23. C₂×#104×C₆₇	C₂²	semidirect
24. C₂×#100×C₆₇	C₂²	semidirect
25. C₂×C₄×C₈×C₆₇	C₂²	semidirect
28. H(5,𝔽₂)×C₆₇	C₂³	semidirect
37. AGL(1,ℤ/8)×C₆₇	C₂³	semidirect
39. #135×C₆₇	D₄	semidirect
41. C₂×Q₁₆×C₆₇	D₄	semidirect
43. C₂×SD₁₆×C₆₇	D₄	semidirect
49. C₂×D₈×C₆₇	D₄	semidirect
50. C₂×D₈×C₆₇	C₂³	semidirect
52. #131×C₆₇	C₂³	semidirect
58. #127×C₆₇	C₂³	semidirect
60. #108×C₆₇	C₂³	semidirect
61. #104×C₆₇	C₂³	semidirect
62. #100×C₆₇	C₂³	semidirect
63. C₄×C₈×C₆₇	C₂³	semidirect
90. Q₁₆×C₆₇	C₂×D₄	semidirect
92. SD₁₆×C₆₇	C₂×D₄	semidirect
96. D₈×C₆₇	C₂×D₄	semidirect
154. C₂×#3292	C₆₇	direct (N × H)
159. C₂×C₆₇	#3292	direct (N × H)
161. C₂×#576	C₂×C₆₇	semidirect
162. #3292	C₂×C₆₇	direct (N × H)
163. C₂×#493	C₂×C₆₇	semidirect
164. C₂×#472	C₂×C₆₇	semidirect
165. C₂×#453	C₂×C₆₇	semidirect
166. C₂×#443	C₂×C₆₇	semidirect
167. C₆₇	C₂×#3292	direct (N × H)
168. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
170. #576	C₂²×C₆₇	semidirect
172. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
176. C₂²×D₈	C₂²×C₆₇	semidirect
177. C₂×#131	C₂²×C₆₇	semidirect
178. C₂×#127	C₂²×C₆₇	semidirect
179. #493	C₂²×C₆₇	semidirect
180. #472	C₂²×C₆₇	semidirect
181. #453	C₂²×C₆₇	semidirect
182. #443	C₂²×C₆₇	semidirect
183. C₂×#108	C₂²×C₆₇	semidirect
184. C₂×#104	C₂²×C₆₇	semidirect
185. C₂×#100	C₂²×C₆₇	semidirect
186. C₂×C₄×C₈	C₂²×C₆₇	semidirect
189. H(5,𝔽₂)	C₂³×C₆₇	semidirect
198. AGL(1,ℤ/8)	C₂³×C₆₇	semidirect
200. #135	D₄×C₆₇	semidirect
202. C₂×Q₁₆	D₄×C₆₇	semidirect
204. C₂×SD₁₆	D₄×C₆₇	semidirect
210. C₂×D₈	D₄×C₆₇	semidirect
211. C₂×D₈	C₂³×C₆₇	semidirect
213. #131	C₂³×C₆₇	semidirect
219. #127	C₂³×C₆₇	semidirect
221. #108	C₂³×C₆₇	semidirect
222. #104	C₂³×C₆₇	semidirect
223. #100	C₂³×C₆₇	semidirect
224. C₄×C₈	C₂³×C₆₇	semidirect
251. Q₁₆	C₂×D₄×C₆₇	semidirect
253. SD₁₆	C₂×D₄×C₆₇	semidirect
257. D₈	C₂×D₄×C₆₇	semidirect
319. C₂	C₆₇×#3292	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#576×C₆₇	2
C₆₇×#3292	2
C₂×#493×C₆₇	2
C₂×#472×C₆₇	2
C₂×#453×C₆₇	2
C₂×#443×C₆₇	2
C₂×#3292	67

Subgroups — C2×C67×#3292 #30740354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3292 #30740354