Subgroups — C₂×C₆₇×#2180 #30712717

Order 17152.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#510×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#444×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#441×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2180	C₂	1	8	yes	maximal, direct product factor
5	C₂×#365×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#362×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#360×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#347×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×#131×C₆₇	—	2	1	no	—
12	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
13	#510×C₆₇	C₄	1	4	yes	complemented
14	#510×C₆₇	C₂²	1	4	yes	—
15	C₂×Q₃₂×C₆₇	C₄	1	2	yes	complemented
16	C₂×SD₃₂×C₆₇	C₄	1	2	yes	complemented
17	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
19	#444×C₆₇	—	2	2	no	—
20	#444×C₆₇	C₂²	1	4	yes	—
21	#441×C₆₇	—	2	2	no	—
22	#441×C₆₇	C₂²	1	4	yes	complemented
23	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#104×C₆₇	—	2	1	no	—
26	C₂×#103×C₆₇	—	2	1	no	—
27	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
28	#365×C₆₇	C₂²	1	4	yes	complemented
29	#362×C₆₇	C₂²	1	4	yes	complemented
30	#360×C₆₇	C₂²	1	4	yes	—
31	#347×C₆₇	C₂²	1	4	yes	complemented
32	C₂×#41×C₆₇	—	2	1	no	—
33	C₂²×Q₈×C₆₇	—	2	1	no	—
34	#135×C₆₇	—	2	1	no	—
35	#135×C₆₇	—	2	1	no	—
36	#135×C₆₇	C₂×C₄	1	2	yes	—
37	#135×C₆₇	C₂³	1	2	yes	—
38	C₂×Q₁₆×C₆₇	—	2	1	no	—
39	C₂×Q₁₆×C₆₇	—	2	1	no	—
40	C₂×Q₁₆×C₆₇	—	2	1	no	—
41	C₂×Q₁₆×C₆₇	C₂×C₄	1	2	yes	—
42	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂×Q₁₆×C₆₇	C₂×C₄	1	2	yes	—
44	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
45	C₂×SD₁₆×C₆₇	—	2	1	no	—
46	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
47	#131×C₆₇	—	2	4	no	—
48	#131×C₆₇	—	4	2	no	—
49	C₂×M₁₆×C₆₇	—	2	1	no	—
50	C₂×M₁₆×C₆₇	—	4	1	no	—
51	C₂²×C₈×C₆₇	—	4	1	no	—
52	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
54	C₄×Q₈×C₆₇	—	2	4	no	—
55	C₄×Q₈×C₆₇	—	4	2	no	—
56	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₆₇	—	4	1	no	—
58	C₂×C₄²×C₆₇	—	4	1	no	—
59	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
60	Q₃₂×C₆₇	C₂×C₄	1	8	yes	complemented
61	SD₃₂×C₆₇	C₂×C₄	1	8	yes	complemented
62	M₃₂×C₆₇	—	2	1	no	—
63	M₃₂×C₆₇	C₂×C₄	1	2	yes	—
64	M₃₂×C₆₇	C₂³	1	2	yes	—
65	M₃₂×C₆₇	C₂³	1	2	yes	—
66	C₂×C₁₆×C₆₇	—	2	1	no	—
67	C₂×C₁₆×C₆₇	C₂×C₄	1	2	yes	—
68	#108×C₆₇	—	2	1	no	—
69	#108×C₆₇	C₂³	1	2	yes	—
70	#106×C₆₇	—	2	1	no	—
71	#106×C₆₇	C₂³	1	2	yes	—
72	#104×C₆₇	—	2	4	no	—
73	#103×C₆₇	—	2	4	no	—
74	#97×C₆₇	D₄	1	2	yes	—
75	#97×C₆₇	C₂³	1	2	yes	—
76	#41×C₆₇	—	2	2	no	—
77	#41×C₆₇	—	2	2	no	—
78	#41×C₆₇	—	4	1	no	—
79	#41×C₆₇	—	4	1	no	—
80	C₂×Q₈×C₆₇	—	2	1	no	—
81	C₂×Q₈×C₆₇	—	2	2	no	—
82	C₂×Q₈×C₆₇	—	2	2	no	—
83	C₂×Q₈×C₆₇	—	2	2	no	—
84	C₂×Q₈×C₆₇	—	4	1	no	—
85	C₂×Q₈×C₆₇	—	4	1	no	—
86	C₂×Q₈×C₆₇	—	4	1	no	—
87	C₂×D₄×C₆₇	—	2	1	no	—
88	C₂×D₄×C₆₇	—	4	1	no	—
89	C₂²×C₄×C₆₇	—	2	1	no	—
90	C₂²×C₄×C₆₇	—	4	1	no	—
91	C₂²×C₄×C₆₇	—	4	1	no	—
92	C₂²×C₄×C₆₇	—	4	1	no	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	Q₁₆×C₆₇	—	2	2	no	—
95	Q₁₆×C₆₇	—	2	2	no	—
96	Q₁₆×C₆₇	—	2	1	no	—
97	Q₁₆×C₆₇	—	2	2	no	—
98	Q₁₆×C₆₇	C₂²×C₄	1	4	yes	—
99	Q₁₆×C₆₇	C₂²×C₄	1	2	yes	—
100	SD₁₆×C₆₇	—	2	2	no	—
101	SD₁₆×C₆₇	—	2	2	no	—
102	D₈×C₆₇	—	2	1	no	—
103	D₈×C₆₇	C₂²×C₄	1	2	yes	—
104	M₁₆×C₆₇	—	2	2	no	—
105	M₁₆×C₆₇	—	4	4	no	—
106	M₁₆×C₆₇	—	4	1	no	—
107	C₂×C₈×C₆₇	—	2	1	no	—
108	C₂×C₈×C₆₇	—	2	1	no	—
109	C₂×C₈×C₆₇	—	4	4	no	—
110	C₂×C₈×C₆₇	—	4	1	no	—
111	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
116	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
117	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₆₇	—	2	2	no	—
119	C₄⋊C₄×C₆₇	—	4	4	no	—
120	C₄⋊C₄×C₆₇	—	4	1	no	—
121	C₄²×C₆₇	—	2	1	no	—
122	C₄²×C₆₇	—	4	4	no	—
123	C₄²×C₆₇	C₂×D₄	1	2	yes	—
124	C₁₆×C₆₇	—	2	2	no	—
125	C₁₆×C₆₇	C₂²×C₄	1	4	yes	—
126	C₂³×C₆₇	—	4	1	no	—
127	C₂³×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
128	Q₈×C₆₇	—	2	2	no	—
129	Q₈×C₆₇	—	2	4	no	—
130	Q₈×C₆₇	—	4	2	no	—
131	Q₈×C₆₇	—	4	2	no	—
132	Q₈×C₆₇	—	4	2	no	—
133	Q₈×C₆₇	—	4	1	no	—
134	D₄×C₆₇	—	2	2	no	—
135	D₄×C₆₇	—	4	2	no	—
136	D₄×C₆₇	—	4	2	no	—
137	D₄×C₆₇	—	4	1	no	—
138	C₂×C₄×C₆₇	—	2	2	no	—
139	C₂×C₄×C₆₇	—	4	2	no	—
140	C₂×C₄×C₆₇	—	4	2	no	—
141	C₂×C₄×C₆₇	—	4	2	no	—
142	C₂×C₄×C₆₇	—	4	1	no	—
143	C₂×C₄×C₆₇	—	4	2	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	—	8	2	no	—
148	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
154	C₈×C₆₇	—	2	2	no	—
155	C₈×C₆₇	—	4	2	no	—
156	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
157	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
158	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
159	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
160	C₂²×C₆₇	—	2	2	no	—
161	C₂²×C₆₇	—	4	2	no	—
162	C₂²×C₆₇	—	8	2	no	—
163	C₂²×C₆₇	#442	1	1	yes	characteristic
164	C₂²×C₆₇	#442	1	1	yes	characteristic
165	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₄×C₆₇	—	4	2	no	—
167	C₄×C₆₇	—	4	2	no	—
168	C₄×C₆₇	—	4	4	no	—
169	C₄×C₆₇	—	8	2	no	—
170	C₄×C₆₇	#442	1	1	yes	characteristic
171	C₄×C₆₇	#442	1	1	yes	characteristic
172	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
173	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂×#2180	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂×C₆₇	—	2	1	no	—
176	C₂×C₆₇	—	2	1	no	—
177	C₂×C₆₇	—	8	2	no	—
178	C₂×C₆₇	#2180	1	2	yes	direct product factor
179	C₂×C₆₇	C₂×#442	1	1	yes	characteristic
180	C₂×#510	C₂×C₆₇	1	1	yes	characteristic
181	C₂×#444	C₂×C₆₇	1	1	yes	characteristic
182	C₂×#441	C₂×C₆₇	1	1	yes	characteristic, complemented
183	#2180	C₂×C₆₇	1	8	yes	direct product factor
184	C₂×#365	C₂×C₆₇	1	1	yes	characteristic, complemented
185	C₂×#362	C₂×C₆₇	1	1	yes	characteristic, complemented
186	C₂×#360	C₂×C₆₇	1	1	yes	characteristic
187	C₂×#347	C₂×C₆₇	1	1	yes	characteristic, complemented
188	C₆₇	C₂×#2180	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
190	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
191	C₂×#131	—	2	1	no	—
192	C₂×C₄×Q₈	—	2	1	no	—
193	#510	C₄×C₆₇	1	4	yes	complemented
194	#510	C₂²×C₆₇	1	4	yes	—
195	C₂×Q₃₂	C₄×C₆₇	1	2	yes	complemented
196	C₂×SD₃₂	C₄×C₆₇	1	2	yes	complemented
197	C₂×M₃₂	C₂²×C₆₇	1	1	yes	characteristic
198	C₂×M₃₂	C₂²×C₆₇	1	1	yes	characteristic
199	#444	—	2	2	no	—
200	#444	C₂²×C₆₇	1	4	yes	—
201	#441	—	2	2	no	—
202	#441	C₂²×C₆₇	1	4	yes	complemented
203	C₂×#108	C₂²×C₆₇	1	1	yes	characteristic
204	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
205	C₂×#104	—	2	1	no	—
206	C₂×#103	—	2	1	no	—
207	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
208	#365	C₂²×C₆₇	1	4	yes	complemented
209	#362	C₂²×C₆₇	1	4	yes	complemented
210	#360	C₂²×C₆₇	1	4	yes	—
211	#347	C₂²×C₆₇	1	4	yes	complemented
212	C₂×#41	—	2	1	no	—
213	C₂²×Q₈	—	2	1	no	—
214	#135	—	2	1	no	—
215	#135	—	2	1	no	—
216	#135	C₂×C₄×C₆₇	1	2	yes	—
217	#135	C₂³×C₆₇	1	2	yes	—
218	C₂×Q₁₆	—	2	1	no	—
219	C₂×Q₁₆	—	2	1	no	—
220	C₂×Q₁₆	—	2	1	no	—
221	C₂×Q₁₆	C₂×C₄×C₆₇	1	2	yes	—
222	C₂×Q₁₆	C₂×C₄×C₆₇	1	2	yes	—
223	C₂×Q₁₆	C₂×C₄×C₆₇	1	1	yes	characteristic
224	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
225	C₂×SD₁₆	—	2	1	no	—
226	C₂×D₈	C₂×C₄×C₆₇	1	1	yes	characteristic
227	#131	—	2	4	no	—
228	#131	—	4	2	no	—
229	C₂×M₁₆	—	2	1	no	—
230	C₂×M₁₆	—	4	1	no	—
231	C₂²×C₈	—	4	1	no	—
232	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
234	C₄×Q₈	—	2	4	no	—
235	C₄×Q₈	—	4	2	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	4	1	no	—
238	C₂×C₄²	—	4	1	no	—
239	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
240	Q₃₂	C₂×C₄×C₆₇	1	8	yes	complemented
241	SD₃₂	C₂×C₄×C₆₇	1	8	yes	complemented
242	M₃₂	—	2	1	no	—
243	M₃₂	C₂×C₄×C₆₇	1	2	yes	—
244	M₃₂	C₂³×C₆₇	1	2	yes	—
245	M₃₂	C₂³×C₆₇	1	2	yes	—
246	C₂×C₁₆	—	2	1	no	—
247	C₂×C₁₆	C₂×C₄×C₆₇	1	2	yes	—
248	#108	—	2	1	no	—
249	#108	C₂³×C₆₇	1	2	yes	—
250	#106	—	2	1	no	—
251	#106	C₂³×C₆₇	1	2	yes	—
252	#104	—	2	4	no	—
253	#103	—	2	4	no	—
254	#97	D₄×C₆₇	1	2	yes	—
255	#97	C₂³×C₆₇	1	2	yes	—
256	#41	—	2	2	no	—
257	#41	—	2	2	no	—
258	#41	—	4	1	no	—
259	#41	—	4	1	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×Q₈	—	4	1	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
274	Q₁₆	—	2	2	no	—
275	Q₁₆	—	2	2	no	—
276	Q₁₆	—	2	1	no	—
277	Q₁₆	—	2	2	no	—
278	Q₁₆	C₂²×C₄×C₆₇	1	4	yes	—
279	Q₁₆	C₂²×C₄×C₆₇	1	2	yes	—
280	SD₁₆	—	2	2	no	—
281	SD₁₆	—	2	2	no	—
282	D₈	—	2	1	no	—
283	D₈	C₂²×C₄×C₆₇	1	2	yes	—
284	M₁₆	—	2	2	no	—
285	M₁₆	—	4	4	no	—
286	M₁₆	—	4	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
292	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
294	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
295	C₂×C₈	#41×C₆₇	1	1	yes	characteristic
296	C₂×C₈	#41×C₆₇	1	1	yes	characteristic
297	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	4	4	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	4	4	no	—
303	C₄²	C₂×D₄×C₆₇	1	2	yes	—
304	C₁₆	—	2	2	no	—
305	C₁₆	C₂²×C₄×C₆₇	1	4	yes	—
306	C₂³	—	4	1	no	—
307	C₂³	AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
308	Q₈	—	2	2	no	—
309	Q₈	—	2	4	no	—
310	Q₈	—	4	2	no	—
311	Q₈	—	4	2	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	4	1	no	—
314	D₄	—	2	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	8	2	no	—
328	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
329	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
330	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
331	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
332	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
334	C₈	—	2	2	no	—
335	C₈	—	4	2	no	—
336	C₈	C₄×D₄×C₆₇	1	1	yes	characteristic
337	C₈	C₄×D₄×C₆₇	1	1	yes	characteristic
338	C₈	C₂³×C₄×C₆₇	1	1	yes	characteristic
339	C₈	C₂×#41×C₆₇	1	1	yes	characteristic
340	C₂²	—	2	2	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	8	2	no	—
343	C₂²	#442×C₆₇	1	1	yes	characteristic
344	C₂²	#442×C₆₇	1	1	yes	characteristic
345	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
346	C₄	—	4	2	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	4	no	—
349	C₄	—	8	2	no	—
350	C₄	#442×C₆₇	1	1	yes	characteristic
351	C₄	#442×C₆₇	1	1	yes	characteristic
352	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
353	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
354	C₂	—	2	1	no	—
355	C₂	—	2	1	no	—
356	C₂	—	8	2	no	—
357	C₂	C₆₇×#2180	1	2	yes	direct product factor
358	C₂	C₂×#442×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	#442
commutator	C₈	C₂³×C₄×C₆₇
Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
prime radical	C₂×#135×C₆₇	C₂²
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ C₂×#97×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#441×C₆₇	C₂	semidirect
4. C₆₇×#2180	C₂	direct (N × H)
5. C₂×#365×C₆₇	C₂	semidirect
6. C₂×#362×C₆₇	C₂	semidirect
8. C₂×#347×C₆₇	C₂	semidirect
13. #510×C₆₇	C₄	semidirect
15. C₂×Q₃₂×C₆₇	C₄	semidirect
16. C₂×SD₃₂×C₆₇	C₄	semidirect
22. #441×C₆₇	C₂²	semidirect
28. #365×C₆₇	C₂²	semidirect
29. #362×C₆₇	C₂²	semidirect
31. #347×C₆₇	C₂²	semidirect
60. Q₃₂×C₆₇	C₂×C₄	semidirect
61. SD₃₂×C₆₇	C₂×C₄	semidirect
174. C₂×#2180	C₆₇	direct (N × H)
178. C₂×C₆₇	#2180	direct (N × H)
182. C₂×#441	C₂×C₆₇	semidirect
183. #2180	C₂×C₆₇	direct (N × H)
184. C₂×#365	C₂×C₆₇	semidirect
185. C₂×#362	C₂×C₆₇	semidirect
187. C₂×#347	C₂×C₆₇	semidirect
188. C₆₇	C₂×#2180	direct (N × H)
193. #510	C₄×C₆₇	semidirect
195. C₂×Q₃₂	C₄×C₆₇	semidirect
196. C₂×SD₃₂	C₄×C₆₇	semidirect
202. #441	C₂²×C₆₇	semidirect
208. #365	C₂²×C₆₇	semidirect
209. #362	C₂²×C₆₇	semidirect
211. #347	C₂²×C₆₇	semidirect
240. Q₃₂	C₂×C₄×C₆₇	semidirect
241. SD₃₂	C₂×C₄×C₆₇	semidirect
357. C₂	C₆₇×#2180	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×#510×C₆₇	2
C₂×#444×C₆₇	2
C₂×#441×C₆₇	2
C₆₇×#2180	2
C₂×#365×C₆₇	2
C₂×#362×C₆₇	2
C₂×#360×C₆₇	2
C₂×#347×C₆₇	2
C₂×#2180	67

Subgroups — C2×C67×#2180 #30712717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2180 #30712717