Subgroups — C₂×C₆₇×#2621 #30713877

Order 17152.

3046 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₆₇	C₂	1	2	yes	maximal
3	C₂²×#117×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2621	C₂	1	16	yes	maximal, direct product factor
5	C₂×#398×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#397×C₆₇	C₂	1	4	yes	maximal
7	C₂×#391×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₆₇	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₆₇	—	2	8	no	—
12	C₂×C₄⋊Q₈×C₆₇	C₂²	1	8	yes	complemented
13	C₂×C₂²⋊Q₈×C₆₇	—	2	16	no	—
14	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	16	yes	—
15	C₂×#117×C₆₇	—	2	8	no	—
16	C₂×#117×C₆₇	C₂²	1	8	yes	—
17	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
19	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
21	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
23	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
25	#398×C₆₇	C₂²	1	32	yes	complemented
26	#397×C₆₇	C₂²	1	32	yes	—
27	#391×C₆₇	C₂²	1	16	yes	complemented
28	#382×C₆₇	C₂²	1	8	yes	complemented
29	C₂×#95×C₆₇	C₂²	1	4	yes	—
30	C₂×#95×C₆₇	C₂²	1	8	yes	—
31	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
32	C₂²×Q₈×C₆₇	—	2	8	no	—
33	C₂²×Q₈×C₆₇	—	2	8	no	—
34	C₂²×Q₈×C₆₇	—	2	8	no	—
35	C₂²×Q₈×C₆₇	C₂³	1	8	yes	—
36	C₂³×C₄×C₆₇	—	2	4	no	—
37	C₂³×C₄×C₆₇	—	2	4	no	—
38	C₂³×C₄×C₆₇	D₄	1	8	yes	—
39	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
41	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
42	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
43	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	C₄⋊Q₈×C₆₇	—	2	32	no	—
47	C₂²⋊Q₈×C₆₇	—	2	64	no	—
48	#117×C₆₇	—	2	32	no	—
49	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	16	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	16	no	—
53	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
54	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
55	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
56	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
57	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
58	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
60	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
61	C₂×C₄²×C₆₇	—	2	4	no	—
62	C₂×C₄²×C₆₇	D₄	1	8	yes	—
63	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
64	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
65	#95×C₆₇	C₂³	1	16	yes	—
66	#95×C₆₇	C₂³	1	32	yes	—
67	C₂⁴×C₆₇	—	2	2	no	—
68	C₂⁴×C₆₇	—	2	2	no	—
69	C₂⁴×C₆₇	—	2	8	no	—
70	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
71	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
72	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
73	C₂×Q₈×C₆₇	—	2	16	no	—
74	C₂×Q₈×C₆₇	—	2	16	no	—
75	C₂×Q₈×C₆₇	—	2	16	no	—
76	C₂×Q₈×C₆₇	—	4	32	no	—
77	C₂²×C₄×C₆₇	—	2	2	no	—
78	C₂²×C₄×C₆₇	—	2	2	no	—
79	C₂²×C₄×C₆₇	—	2	8	no	—
80	C₂²×C₄×C₆₇	—	2	32	no	—
81	C₂²×C₄×C₆₇	—	2	8	no	—
82	C₂²×C₄×C₆₇	—	2	8	no	—
83	C₂²×C₄×C₆₇	—	2	4	no	—
84	C₂²×C₄×C₆₇	—	2	8	no	—
85	C₂²×C₄×C₆₇	—	2	8	no	—
86	C₂²×C₄×C₆₇	—	2	8	no	—
87	C₂²×C₄×C₆₇	—	2	8	no	—
88	C₂²×C₄×C₆₇	—	2	8	no	—
89	C₂²×C₄×C₆₇	—	2	16	no	—
90	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
91	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	16	yes	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₆₇	#41	1	4	yes	—
96	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
99	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
100	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
102	C₄⋊C₄×C₆₇	—	2	16	no	—
103	C₄⋊C₄×C₆₇	—	2	16	no	—
104	C₄⋊C₄×C₆₇	—	2	32	no	—
105	C₄⋊C₄×C₆₇	—	2	32	no	—
106	C₂²⋊C₄×C₆₇	—	2	32	no	—
107	C₂²⋊C₄×C₆₇	—	2	16	no	—
108	C₄²×C₆₇	—	2	8	no	—
109	C₄²×C₆₇	C₂×D₄	1	16	yes	—
110	C₂³×C₆₇	—	2	8	no	—
111	C₂³×C₆₇	—	2	16	no	—
112	C₂³×C₆₇	—	2	2	no	—
113	C₂³×C₆₇	—	2	2	no	—
114	C₂³×C₆₇	—	2	8	no	—
115	C₂³×C₆₇	—	4	8	no	—
116	C₂³×C₆₇	—	4	8	no	—
117	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
118	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
119	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
120	C₂³×C₆₇	C₂×#41	1	2	yes	—
121	C₂³×C₆₇	2₋¹⁺⁴	1	8	yes	—
122	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
123	Q₈×C₆₇	—	4	32	no	—
124	C₂×C₄×C₆₇	—	2	8	no	—
125	C₂×C₄×C₆₇	—	2	16	no	—
126	C₂×C₄×C₆₇	—	2	2	no	—
127	C₂×C₄×C₆₇	—	2	2	no	—
128	C₂×C₄×C₆₇	—	2	8	no	—
129	C₂×C₄×C₆₇	—	2	32	no	—
130	C₂×C₄×C₆₇	—	2	4	no	—
131	C₂×C₄×C₆₇	—	2	8	no	—
132	C₂×C₄×C₆₇	—	2	8	no	—
133	C₂×C₄×C₆₇	—	2	8	no	—
134	C₂×C₄×C₆₇	—	2	8	no	—
135	C₂×C₄×C₆₇	—	2	8	no	—
136	C₂×C₄×C₆₇	—	2	16	no	—
137	C₂×C₄×C₆₇	—	4	16	no	—
138	C₂×C₄×C₆₇	—	4	8	no	—
139	C₂×C₄×C₆₇	—	4	16	no	—
140	C₂×C₄×C₆₇	#121	1	16	yes	—
141	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
142	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
143	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
144	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
145	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
146	C₂²×C₆₇	—	2	4	no	—
147	C₂²×C₆₇	—	2	8	no	—
148	C₂²×C₆₇	—	4	16	no	—
149	C₂²×C₆₇	—	4	4	no	—
150	C₂²×C₆₇	—	4	4	no	—
151	C₂²×C₆₇	C₂×#121	1	4	yes	—
152	C₂²×C₆₇	#536	1	8	yes	—
153	C₂²×C₆₇	#536	1	8	yes	—
154	C₂²×C₆₇	#541	1	8	yes	—
155	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
156	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
157	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
158	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	4	yes	—
159	C₄×C₆₇	—	2	4	no	—
160	C₄×C₆₇	—	2	8	no	—
161	C₄×C₆₇	—	4	8	no	—
162	C₄×C₆₇	—	4	4	no	—
163	C₄×C₆₇	—	4	8	no	—
164	C₄×C₆₇	C₂×#121	1	8	yes	—
165	C₂×#2621	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂×C₆₇	—	4	4	no	—
167	C₂×C₆₇	#2621	1	8	yes	direct product factor
168	C₂×C₆₇	C₂²×#121	1	1	yes	characteristic
169	C₂×C₆₇	C₂×#536	1	2	yes	—
170	C₂×C₆₇	C₂×#536	1	2	yes	—
171	C₂×C₆₇	C₂×#541	1	2	yes	—
172	C₂²×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
173	C₂²×C₂²⋊Q₈	C₂×C₆₇	1	2	yes	—
174	C₂²×#117	C₂×C₆₇	1	1	yes	characteristic
175	#2621	C₂×C₆₇	1	16	yes	direct product factor
176	C₂×#398	C₂×C₆₇	1	4	yes	complemented
177	C₂×#397	C₂×C₆₇	1	4	yes	—
178	C₂×#391	C₂×C₆₇	1	2	yes	complemented
179	C₂×#382	C₂×C₆₇	1	1	yes	characteristic, complemented
180	C₆₇	C₂×#2621	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³×Q₈	C₂²×C₆₇	1	2	yes	—
182	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
183	C₂×C₄⋊Q₈	—	2	8	no	—
184	C₂×C₄⋊Q₈	C₂²×C₆₇	1	8	yes	complemented
185	C₂×C₂²⋊Q₈	—	2	16	no	—
186	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	16	yes	—
187	C₂×#117	—	2	8	no	—
188	C₂×#117	C₂²×C₆₇	1	8	yes	—
189	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
190	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
191	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
192	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
193	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
194	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
195	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
196	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
197	#398	C₂²×C₆₇	1	32	yes	complemented
198	#397	C₂²×C₆₇	1	32	yes	—
199	#391	C₂²×C₆₇	1	16	yes	complemented
200	#382	C₂²×C₆₇	1	8	yes	complemented
201	C₂×#95	C₂²×C₆₇	1	4	yes	—
202	C₂×#95	C₂²×C₆₇	1	8	yes	—
203	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
204	C₂²×Q₈	—	2	8	no	—
205	C₂²×Q₈	—	2	8	no	—
206	C₂²×Q₈	—	2	8	no	—
207	C₂²×Q₈	C₂³×C₆₇	1	8	yes	—
208	C₂³×C₄	—	2	4	no	—
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	D₄×C₆₇	1	8	yes	—
211	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
212	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
213	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
214	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
215	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
216	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
217	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
218	C₄⋊Q₈	—	2	32	no	—
219	C₂²⋊Q₈	—	2	64	no	—
220	#117	—	2	32	no	—
221	C₂×C₄⋊C₄	—	2	8	no	—
222	C₂×C₄⋊C₄	—	2	8	no	—
223	C₂×C₄⋊C₄	—	2	16	no	—
224	C₂×C₄⋊C₄	—	2	16	no	—
225	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
226	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
227	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
228	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
229	C₂×C₂²⋊C₄	—	2	16	no	—
230	C₂×C₂²⋊C₄	—	2	8	no	—
231	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
232	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
233	C₂×C₄²	—	2	4	no	—
234	C₂×C₄²	D₄×C₆₇	1	8	yes	—
235	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
236	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
237	#95	C₂³×C₆₇	1	16	yes	—
238	#95	C₂³×C₆₇	1	32	yes	—
239	C₂⁴	—	2	2	no	—
240	C₂⁴	—	2	2	no	—
241	C₂⁴	—	2	8	no	—
242	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
243	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
244	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
245	C₂×Q₈	—	2	16	no	—
246	C₂×Q₈	—	2	16	no	—
247	C₂×Q₈	—	2	16	no	—
248	C₂×Q₈	—	4	32	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	32	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	16	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
263	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
264	C₂²×C₄	C₂×D₄×C₆₇	1	16	yes	—
265	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
266	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
267	C₂²×C₄	#41×C₆₇	1	4	yes	—
268	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
269	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
270	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
271	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
272	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
273	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
274	C₄⋊C₄	—	2	16	no	—
275	C₄⋊C₄	—	2	16	no	—
276	C₄⋊C₄	—	2	32	no	—
277	C₄⋊C₄	—	2	32	no	—
278	C₂²⋊C₄	—	2	32	no	—
279	C₂²⋊C₄	—	2	16	no	—
280	C₄²	—	2	8	no	—
281	C₄²	C₂×D₄×C₆₇	1	16	yes	—
282	C₂³	—	2	8	no	—
283	C₂³	—	2	16	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	8	no	—
287	C₂³	—	4	8	no	—
288	C₂³	—	4	8	no	—
289	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
290	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
291	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
292	C₂³	C₂×#41×C₆₇	1	2	yes	—
293	C₂³	2₋¹⁺⁴×C₆₇	1	8	yes	—
294	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
295	Q₈	—	4	32	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	16	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	32	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	16	no	—
309	C₂×C₄	—	4	16	no	—
310	C₂×C₄	—	4	8	no	—
311	C₂×C₄	—	4	16	no	—
312	C₂×C₄	#121×C₆₇	1	16	yes	—
313	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
314	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
315	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
316	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
317	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	8	no	—
320	C₂²	—	4	16	no	—
321	C₂²	—	4	4	no	—
322	C₂²	—	4	4	no	—
323	C₂²	C₂×#121×C₆₇	1	4	yes	—
324	C₂²	#536×C₆₇	1	8	yes	—
325	C₂²	#536×C₆₇	1	8	yes	—
326	C₂²	#541×C₆₇	1	8	yes	—
327	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
328	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
329	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
330	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	4	yes	—
331	C₄	—	2	4	no	—
332	C₄	—	2	8	no	—
333	C₄	—	4	8	no	—
334	C₄	—	4	4	no	—
335	C₄	—	4	8	no	—
336	C₄	C₂×#121×C₆₇	1	8	yes	—
337	C₂	—	4	4	no	—
338	C₂	C₆₇×#2621	1	8	yes	direct product factor
339	C₂	C₂²×#121×C₆₇	1	1	yes	characteristic
340	C₂	C₂×#536×C₆₇	1	2	yes	—
341	C₂	C₂×#536×C₆₇	1	2	yes	—
342	C₂	C₂×#541×C₆₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊Q₈×C₆₇	C₂	semidirect
4. C₆₇×#2621	C₂	direct (N × H)
5. C₂×#398×C₆₇	C₂	semidirect
7. C₂×#391×C₆₇	C₂	semidirect
8. C₂×#382×C₆₇	C₂	semidirect
12. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
25. #398×C₆₇	C₂²	semidirect
27. #391×C₆₇	C₂²	semidirect
28. #382×C₆₇	C₂²	semidirect
165. C₂×#2621	C₆₇	direct (N × H)
167. C₂×C₆₇	#2621	direct (N × H)
172. C₂²×C₄⋊Q₈	C₂×C₆₇	semidirect
175. #2621	C₂×C₆₇	direct (N × H)
176. C₂×#398	C₂×C₆₇	semidirect
178. C₂×#391	C₂×C₆₇	semidirect
179. C₂×#382	C₂×C₆₇	semidirect
180. C₆₇	C₂×#2621	direct (N × H)
184. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
197. #398	C₂²×C₆₇	semidirect
199. #391	C₂²×C₆₇	semidirect
200. #382	C₂²×C₆₇	semidirect
338. C₂	C₆₇×#2621	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₆₇	2
C₂²×C₂²⋊Q₈×C₆₇	2
C₂²×#117×C₆₇	2
C₆₇×#2621	2
C₂×#398×C₆₇	2
C₂×#397×C₆₇	2
C₂×#391×C₆₇	2
C₂×#382×C₆₇	2
C₂×#2621	67

Subgroups — C2×C67×#2621 #30713877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2621 #30713877