Subgroups — C₆₇×#32809 #30712060

Order 17152.

752 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2861	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2055	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2054	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2026	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2025	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2015	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2012	C₂	1	2	yes	maximal
9	C₆₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
12	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₆₇	C₂²	1	2	yes	—
14	C₂×#124×C₆₇	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×#103×C₆₇	C₂²	1	2	yes	—
18	C₂×#103×C₆₇	C₂²	1	2	yes	—
19	C₂×#102×C₆₇	C₂²	1	2	yes	—
20	C₂×#102×C₆₇	C₂²	1	2	yes	—
21	#391×C₆₇	C₂²	1	2	yes	—
22	#391×C₆₇	C₂²	1	2	yes	—
23	#390×C₆₇	C₂²	1	2	yes	—
24	#390×C₆₇	C₂²	1	2	yes	—
25	#388×C₆₇	—	2	2	no	—
26	#388×C₆₇	—	2	2	no	—
27	#388×C₆₇	—	2	2	no	—
28	#388×C₆₇	—	2	2	no	—
29	C₄³×C₆₇	C₂²	1	1	yes	characteristic
30	#340×C₆₇	C₂²	1	1	yes	characteristic
31	#340×C₆₇	C₂²	1	2	yes	—
32	#340×C₆₇	C₂²	1	1	yes	characteristic
33	#336×C₆₇	C₂²	1	2	yes	—
34	#336×C₆₇	C₂²	1	2	yes	—
35	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
36	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
37	C₂×Q₁₆×C₆₇	—	4	2	no	—
38	C₂×Q₁₆×C₆₇	—	4	1	no	—
39	C₂×SD₁₆×C₆₇	—	4	2	no	—
40	C₂×SD₁₆×C₆₇	—	4	2	no	—
41	C₂×SD₁₆×C₆₇	—	4	2	no	—
42	C₂×D₈×C₆₇	—	4	2	no	—
43	C₂×D₈×C₆₇	—	4	1	no	—
44	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
47	#125×C₆₇	—	4	2	no	—
48	#125×C₆₇	—	4	2	no	—
49	#124×C₆₇	—	4	2	no	—
50	#124×C₆₇	—	4	2	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
61	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₆₇	D₄	1	2	yes	—
63	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
65	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₆₇	—	4	1	no	—
67	C₄⋊C₈×C₆₇	—	4	1	no	—
68	#103×C₆₇	—	4	2	no	—
69	#103×C₆₇	—	4	2	no	—
70	#102×C₆₇	—	4	2	no	—
71	#102×C₆₇	—	4	2	no	—
72	#95×C₆₇	—	2	2	no	—
73	#95×C₆₇	—	2	2	no	—
74	#95×C₆₇	—	2	2	no	—
75	#95×C₆₇	—	2	2	no	—
76	C₂⁴×C₆₇	—	2	2	no	—
77	C₂×Q₈×C₆₇	—	2	2	no	—
78	C₂×Q₈×C₆₇	—	2	2	no	—
79	C₂×Q₈×C₆₇	—	2	2	no	—
80	C₂×Q₈×C₆₇	—	2	2	no	—
81	C₂×Q₈×C₆₇	—	2	2	no	—
82	C₂×Q₈×C₆₇	—	2	2	no	—
83	C₂×D₄×C₆₇	—	2	2	no	—
84	C₂×D₄×C₆₇	—	2	2	no	—
85	C₂×D₄×C₆₇	—	2	2	no	—
86	C₂×D₄×C₆₇	—	2	2	no	—
87	C₂×D₄×C₆₇	—	2	2	no	—
88	C₂×D₄×C₆₇	—	2	2	no	—
89	C₂²×C₄×C₆₇	—	2	2	no	—
90	C₂²×C₄×C₆₇	—	2	2	no	—
91	C₂²×C₄×C₆₇	—	2	2	no	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
97	Q₁₆×C₆₇	—	4	4	no	—
98	SD₁₆×C₆₇	—	4	8	no	—
99	D₈×C₆₇	—	4	4	no	—
100	C₂×C₈×C₆₇	—	2	2	no	—
101	C₂×C₈×C₆₇	—	2	2	no	—
102	C₂×C₈×C₆₇	—	2	2	no	—
103	C₂×C₈×C₆₇	—	2	2	no	—
104	C₂×C₈×C₆₇	—	2	1	no	—
105	C₂×C₈×C₆₇	—	2	2	no	—
106	C₂×C₈×C₆₇	—	2	1	no	—
107	C₄⋊C₄×C₆₇	—	2	2	no	—
108	C₄⋊C₄×C₆₇	—	2	2	no	—
109	C₄⋊C₄×C₆₇	—	2	2	no	—
110	C₄⋊C₄×C₆₇	—	2	2	no	—
111	C₄⋊C₄×C₆₇	—	4	4	no	—
112	C₄⋊C₄×C₆₇	—	4	4	no	—
113	C₂²⋊C₄×C₆₇	—	4	4	no	—
114	C₂²⋊C₄×C₆₇	—	4	4	no	—
115	C₂²⋊C₄×C₆₇	—	4	4	no	—
116	C₂²⋊C₄×C₆₇	—	4	4	no	—
117	C₂²⋊C₄×C₆₇	—	4	4	no	—
118	C₂²⋊C₄×C₆₇	—	4	4	no	—
119	C₄²×C₆₇	—	2	2	no	—
120	C₄²×C₆₇	—	2	1	no	—
121	C₄²×C₆₇	—	2	2	no	—
122	C₄²×C₆₇	—	2	2	no	—
123	C₄²×C₆₇	—	2	1	no	—
124	C₄²×C₆₇	—	4	1	no	—
125	C₄²×C₆₇	—	4	2	no	—
126	C₂³×C₆₇	—	4	2	no	—
127	C₂³×C₆₇	—	4	2	no	—
128	C₂³×C₆₇	—	4	2	no	—
129	C₂³×C₆₇	—	4	2	no	—
130	C₂³×C₆₇	—	4	2	no	—
131	C₂³×C₆₇	—	4	2	no	—
132	C₂³×C₆₇	—	4	2	no	—
133	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₆₇	—	4	2	no	—
135	Q₈×C₆₇	—	4	2	no	—
136	Q₈×C₆₇	—	4	2	no	—
137	Q₈×C₆₇	—	4	2	no	—
138	D₄×C₆₇	—	4	2	no	—
139	D₄×C₆₇	—	4	2	no	—
140	D₄×C₆₇	—	4	2	no	—
141	D₄×C₆₇	—	4	2	no	—
142	C₂×C₄×C₆₇	—	2	1	no	—
143	C₂×C₄×C₆₇	—	2	1	no	—
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	—	2	1	no	—
147	C₂×C₄×C₆₇	—	2	2	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	2	2	no	—
152	C₂×C₄×C₆₇	—	4	2	no	—
153	C₂×C₄×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	—	4	2	no	—
155	C₂×C₄×C₆₇	—	4	2	no	—
156	C₂×C₄×C₆₇	—	4	2	no	—
157	C₂×C₄×C₆₇	—	4	2	no	—
158	C₂×C₄×C₆₇	—	4	2	no	—
159	C₂×C₄×C₆₇	—	4	2	no	—
160	C₂×C₄×C₆₇	—	4	2	no	—
161	C₂×C₄×C₆₇	#135	1	2	yes	—
162	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
164	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
165	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
166	C₈×C₆₇	—	4	1	no	—
167	C₈×C₆₇	—	4	2	no	—
168	C₈×C₆₇	—	4	1	no	—
169	C₂²×C₆₇	—	8	2	no	—
170	C₂²×C₆₇	—	8	2	no	—
171	C₂²×C₆₇	—	8	2	no	—
172	C₂²×C₆₇	—	8	2	no	—
173	C₂²×C₆₇	—	8	2	no	—
174	C₂²×C₆₇	—	8	2	no	—
175	C₂²×C₆₇	—	8	2	no	—
176	C₂²×C₆₇	#535	1	2	yes	—
177	C₂²×C₆₇	#537	1	1	yes	characteristic
178	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
179	C₂²×C₆₇	#575	1	2	yes	—
180	C₂²×C₆₇	#575	1	1	yes	characteristic
181	C₄×C₆₇	—	2	2	no	—
182	C₄×C₆₇	—	4	2	no	—
183	C₄×C₆₇	—	4	2	no	—
184	C₄×C₆₇	—	4	1	no	—
185	C₄×C₆₇	—	8	2	no	—
186	C₄×C₆₇	—	8	2	no	—
187	C₄×C₆₇	—	8	2	no	—
188	C₄×C₆₇	H(3,𝔽₄)	1	1	yes	characteristic
189	C₄×C₆₇	H(3,𝔽₄)	1	1	yes	characteristic
190	C₄×C₆₇	#562	1	2	yes	—
191	#32809	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₆₇	—	16	2	no	—
193	C₂×C₆₇	#2819	1	1	yes	characteristic
194	C₂×C₆₇	#3212	1	2	yes	—
195	C₂×C₆₇	#3219	1	2	yes	—
196	C₂×C₆₇	#3250	1	1	yes	characteristic
197	C₂×C₆₇	#3256	1	1	yes	characteristic
198	#2861	C₂×C₆₇	1	2	yes	complemented
199	#2056	C₂×C₆₇	1	1	yes	characteristic, complemented
200	#2055	C₂×C₆₇	1	2	yes	complemented
201	#2054	C₂×C₆₇	1	1	yes	characteristic
202	#2026	C₂×C₆₇	1	2	yes	complemented
203	#2025	C₂×C₆₇	1	2	yes	complemented
204	#2015	C₂×C₆₇	1	2	yes	complemented
205	#2012	C₂×C₆₇	1	2	yes	—
206	#1831	C₂×C₆₇	1	1	yes	characteristic, complemented
207	C₆₇	#32809	1	1	yes	characteristic, direct product factor, Sylow
208	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
209	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
210	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
211	C₂×#125	C₂²×C₆₇	1	2	yes	—
212	C₂×#124	C₂²×C₆₇	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
215	C₂×#103	C₂²×C₆₇	1	2	yes	—
216	C₂×#103	C₂²×C₆₇	1	2	yes	—
217	C₂×#102	C₂²×C₆₇	1	2	yes	—
218	C₂×#102	C₂²×C₆₇	1	2	yes	—
219	#391	C₂²×C₆₇	1	2	yes	—
220	#391	C₂²×C₆₇	1	2	yes	—
221	#390	C₂²×C₆₇	1	2	yes	—
222	#390	C₂²×C₆₇	1	2	yes	—
223	#388	—	2	2	no	—
224	#388	—	2	2	no	—
225	#388	—	2	2	no	—
226	#388	—	2	2	no	—
227	C₄³	C₂²×C₆₇	1	1	yes	characteristic
228	#340	C₂²×C₆₇	1	1	yes	characteristic
229	#340	C₂²×C₆₇	1	2	yes	—
230	#340	C₂²×C₆₇	1	1	yes	characteristic
231	#336	C₂²×C₆₇	1	2	yes	—
232	#336	C₂²×C₆₇	1	2	yes	—
233	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
234	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
235	C₂×Q₁₆	—	4	2	no	—
236	C₂×Q₁₆	—	4	1	no	—
237	C₂×SD₁₆	—	4	2	no	—
238	C₂×SD₁₆	—	4	2	no	—
239	C₂×SD₁₆	—	4	2	no	—
240	C₂×D₈	—	4	2	no	—
241	C₂×D₈	—	4	1	no	—
242	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
244	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
245	#125	—	4	2	no	—
246	#125	—	4	2	no	—
247	#124	—	4	2	no	—
248	#124	—	4	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₆₇	1	2	yes	—
261	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
263	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
264	C₄⋊C₈	—	4	1	no	—
265	C₄⋊C₈	—	4	1	no	—
266	#103	—	4	2	no	—
267	#103	—	4	2	no	—
268	#102	—	4	2	no	—
269	#102	—	4	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	C₂⁴	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
295	Q₁₆	—	4	4	no	—
296	SD₁₆	—	4	8	no	—
297	D₈	—	4	4	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	4	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₂²⋊C₄	—	4	4	no	—
313	C₂²⋊C₄	—	4	4	no	—
314	C₂²⋊C₄	—	4	4	no	—
315	C₂²⋊C₄	—	4	4	no	—
316	C₂²⋊C₄	—	4	4	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	4	1	no	—
323	C₄²	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
332	Q₈	—	4	2	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	#135×C₆₇	1	2	yes	—
360	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
361	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
362	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
363	C₂×C₄	2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	1	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	#535×C₆₇	1	2	yes	—
375	C₂²	#537×C₆₇	1	1	yes	characteristic
376	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
377	C₂²	#575×C₆₇	1	2	yes	—
378	C₂²	#575×C₆₇	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	1	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	H(3,𝔽₄)×C₆₇	1	1	yes	characteristic
387	C₄	H(3,𝔽₄)×C₆₇	1	1	yes	characteristic
388	C₄	#562×C₆₇	1	2	yes	—
389	C₂	—	16	2	no	—
390	C₂	C₆₇×#2819	1	1	yes	characteristic
391	C₂	C₆₇×#3212	1	2	yes	—
392	C₂	C₆₇×#3219	1	2	yes	—
393	C₂	C₆₇×#3250	1	1	yes	characteristic
394	C₂	C₆₇×#3256	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂²×D₈×C₆₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₄³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2861	C₂	semidirect
2. C₆₇×#2056	C₂	semidirect
3. C₆₇×#2055	C₂	semidirect
5. C₆₇×#2026	C₂	semidirect
6. C₆₇×#2025	C₂	semidirect
7. C₆₇×#2015	C₂	semidirect
9. C₆₇×#1831	C₂	semidirect
191. #32809	C₆₇	direct (N × H)
198. #2861	C₂×C₆₇	semidirect
199. #2056	C₂×C₆₇	semidirect
200. #2055	C₂×C₆₇	semidirect
202. #2026	C₂×C₆₇	semidirect
203. #2025	C₂×C₆₇	semidirect
204. #2015	C₂×C₆₇	semidirect
206. #1831	C₂×C₆₇	semidirect
207. C₆₇	#32809	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2861	2
C₆₇×#2056	2
C₆₇×#2055	2
C₆₇×#2054	2
C₆₇×#2026	2
C₆₇×#2025	2
C₆₇×#2015	2
C₆₇×#2012	2
C₆₇×#1831	2
#32809	67

Subgroups — C67×#32809 #30712060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#32809 #30712060