Subgroups — C₆₇×#32831 #30712082

Order 17152.

654 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2641	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2073	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2073	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2067	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2065	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2059	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2041	C₂	1	2	yes	maximal
11	C₆₇×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#107×C₆₇	C₂²	1	2	yes	—
15	C₂×#106×C₆₇	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
17	C₂×#102×C₆₇	C₂²	1	2	yes	—
18	C₂×#102×C₆₇	C₂²	1	2	yes	—
19	C₂×#102×C₆₇	C₂²	1	2	yes	—
20	C₂×#102×C₆₇	C₂²	1	2	yes	—
21	#400×C₆₇	—	2	2	no	—
22	#398×C₆₇	—	2	2	no	—
23	#394×C₆₇	—	2	2	no	—
24	#394×C₆₇	—	2	2	no	—
25	#390×C₆₇	C₂²	1	1	yes	characteristic
26	#390×C₆₇	C₂²	1	1	yes	characteristic
27	#390×C₆₇	C₂²	1	1	yes	characteristic
28	#390×C₆₇	C₂²	1	1	yes	characteristic
29	#389×C₆₇	C₂²	1	2	yes	—
30	#389×C₆₇	C₂²	1	2	yes	—
31	#384×C₆₇	C₂²	1	1	yes	characteristic
32	#382×C₆₇	C₂²	1	1	yes	characteristic
33	#376×C₆₇	C₂²	1	1	yes	characteristic
34	#340×C₆₇	C₂²	1	2	yes	—
35	#340×C₆₇	C₂²	1	2	yes	—
36	#336×C₆₇	C₂²	1	2	yes	—
37	#336×C₆₇	C₂²	1	1	yes	characteristic
38	#336×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×D₄×C₆₇	—	2	1	no	—
40	C₂²×D₄×C₆₇	—	2	1	no	—
41	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
44	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
45	#127×C₆₇	—	4	2	no	—
46	#125×C₆₇	—	4	2	no	—
47	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
48	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
49	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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×C₄²×C₆₇	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
63	#107×C₆₇	—	4	2	no	—
64	#106×C₆₇	—	4	2	no	—
65	C₄⋊C₈×C₆₇	—	4	2	no	—
66	#102×C₆₇	—	4	2	no	—
67	#102×C₆₇	—	4	2	no	—
68	#102×C₆₇	—	4	2	no	—
69	#102×C₆₇	—	4	2	no	—
70	#95×C₆₇	—	2	2	no	—
71	#95×C₆₇	—	2	2	no	—
72	#95×C₆₇	—	2	2	no	—
73	#95×C₆₇	D₄	1	2	yes	—
74	#95×C₆₇	D₄	1	2	yes	—
75	C₂⁴×C₆₇	—	2	1	no	—
76	C₂⁴×C₆₇	—	2	1	no	—
77	C₂×D₄×C₆₇	—	2	1	no	—
78	C₂×D₄×C₆₇	—	2	1	no	—
79	C₂×D₄×C₆₇	—	2	2	no	—
80	C₂×D₄×C₆₇	—	2	2	no	—
81	C₂×D₄×C₆₇	—	2	2	no	—
82	C₂×D₄×C₆₇	—	2	2	no	—
83	C₂×D₄×C₆₇	—	2	1	no	—
84	C₂×D₄×C₆₇	—	2	1	no	—
85	C₂×D₄×C₆₇	—	4	2	no	—
86	C₂×D₄×C₆₇	—	4	2	no	—
87	C₂×D₄×C₆₇	—	8	2	no	—
88	C₂×D₄×C₆₇	—	8	2	no	—
89	C₂²×C₄×C₆₇	—	2	1	no	—
90	C₂²×C₄×C₆₇	—	2	1	no	—
91	C₂²×C₄×C₆₇	—	2	2	no	—
92	C₂²×C₄×C₆₇	—	2	2	no	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₆₇	—	2	2	no	—
99	C₂×C₈×C₆₇	—	2	2	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	C₄⋊C₄×C₆₇	—	2	2	no	—
105	C₄⋊C₄×C₆₇	—	2	2	no	—
106	C₄⋊C₄×C₆₇	—	2	2	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	—	4	2	no	—
111	C₄⋊C₄×C₆₇	—	4	2	no	—
112	C₄⋊C₄×C₆₇	—	8	2	no	—
113	C₄⋊C₄×C₆₇	—	8	2	no	—
114	C₄⋊C₄×C₆₇	—	8	2	no	—
115	C₂²⋊C₄×C₆₇	—	8	2	no	—
116	C₂²⋊C₄×C₆₇	—	8	2	no	—
117	C₂²⋊C₄×C₆₇	—	8	2	no	—
118	C₂²⋊C₄×C₆₇	—	8	2	no	—
119	C₄²×C₆₇	—	2	1	no	—
120	C₄²×C₆₇	—	2	2	no	—
121	C₄²×C₆₇	—	2	2	no	—
122	C₄²×C₆₇	—	2	1	no	—
123	C₂³×C₆₇	—	4	1	no	—
124	C₂³×C₆₇	—	4	1	no	—
125	C₂³×C₆₇	—	4	1	no	—
126	C₂³×C₆₇	—	4	1	no	—
127	C₂³×C₆₇	—	4	1	no	—
128	C₂³×C₆₇	—	4	1	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	D₄×C₆₇	—	4	2	no	—
135	D₄×C₆₇	—	4	2	no	—
136	D₄×C₆₇	—	4	2	no	—
137	D₄×C₆₇	—	4	2	no	—
138	D₄×C₆₇	—	8	4	no	—
139	D₄×C₆₇	—	8	4	no	—
140	C₂×C₄×C₆₇	—	2	1	no	—
141	C₂×C₄×C₆₇	—	2	1	no	—
142	C₂×C₄×C₆₇	—	2	2	no	—
143	C₂×C₄×C₆₇	—	2	2	no	—
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	—	2	2	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	—	4	1	no	—
151	C₂×C₄×C₆₇	—	4	1	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	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
162	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
163	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
164	C₈×C₆₇	—	4	2	no	—
165	C₈×C₆₇	—	4	2	no	—
166	C₂²×C₆₇	—	8	1	no	—
167	C₂²×C₆₇	—	8	1	no	—
168	C₂²×C₆₇	—	8	1	no	—
169	C₂²×C₆₇	—	8	1	no	—
170	C₂²×C₆₇	—	8	1	no	—
171	C₂²×C₆₇	—	8	1	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	1	yes	characteristic
177	C₂²×C₆₇	#536	1	1	yes	characteristic
178	C₂²×C₆₇	#537	1	1	yes	characteristic
179	C₂²×C₆₇	#576	1	2	yes	—
180	C₂²×C₆₇	#577	1	2	yes	—
181	C₄×C₆₇	—	4	1	no	—
182	C₄×C₆₇	—	4	1	no	—
183	C₄×C₆₇	—	4	2	no	—
184	C₄×C₆₇	—	4	2	no	—
185	C₄×C₆₇	—	8	1	no	—
186	C₄×C₆₇	—	8	2	no	—
187	C₄×C₆₇	—	8	1	no	—
188	C₄×C₆₇	—	8	2	no	—
189	C₄×C₆₇	#562	1	2	yes	—
190	C₄×C₆₇	#563	1	2	yes	—
191	#32831	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₆₇	—	16	1	no	—
193	C₂×C₆₇	—	16	1	no	—
194	C₂×C₆₇	#2820	1	1	yes	characteristic
195	C₂×C₆₇	#3220	1	1	yes	characteristic
196	C₂×C₆₇	#3222	1	1	yes	characteristic
197	C₂×C₆₇	#3241	1	2	yes	—
198	C₂×C₆₇	#3257	1	2	yes	—
199	#2647	C₂×C₆₇	1	1	yes	characteristic, complemented
200	#2641	C₂×C₆₇	1	1	yes	characteristic
201	#2094	C₂×C₆₇	1	1	yes	characteristic, complemented
202	#2093	C₂×C₆₇	1	1	yes	characteristic, complemented
203	#2073	C₂×C₆₇	1	1	yes	characteristic, complemented
204	#2073	C₂×C₆₇	1	1	yes	characteristic, complemented
205	#2067	C₂×C₆₇	1	2	yes	complemented
206	#2065	C₂×C₆₇	1	2	yes	complemented
207	#2059	C₂×C₆₇	1	2	yes	complemented
208	#2041	C₂×C₆₇	1	2	yes	—
209	#1832	C₂×C₆₇	1	1	yes	characteristic, complemented
210	C₆₇	#32831	1	1	yes	characteristic, direct product factor, Sylow
211	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
212	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
213	C₂×#107	C₂²×C₆₇	1	2	yes	—
214	C₂×#106	C₂²×C₆₇	1	2	yes	—
215	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
216	C₂×#102	C₂²×C₆₇	1	2	yes	—
217	C₂×#102	C₂²×C₆₇	1	2	yes	—
218	C₂×#102	C₂²×C₆₇	1	2	yes	—
219	C₂×#102	C₂²×C₆₇	1	2	yes	—
220	#400	—	2	2	no	—
221	#398	—	2	2	no	—
222	#394	—	2	2	no	—
223	#394	—	2	2	no	—
224	#390	C₂²×C₆₇	1	1	yes	characteristic
225	#390	C₂²×C₆₇	1	1	yes	characteristic
226	#390	C₂²×C₆₇	1	1	yes	characteristic
227	#390	C₂²×C₆₇	1	1	yes	characteristic
228	#389	C₂²×C₆₇	1	2	yes	—
229	#389	C₂²×C₆₇	1	2	yes	—
230	#384	C₂²×C₆₇	1	1	yes	characteristic
231	#382	C₂²×C₆₇	1	1	yes	characteristic
232	#376	C₂²×C₆₇	1	1	yes	characteristic
233	#340	C₂²×C₆₇	1	2	yes	—
234	#340	C₂²×C₆₇	1	2	yes	—
235	#336	C₂²×C₆₇	1	2	yes	—
236	#336	C₂²×C₆₇	1	1	yes	characteristic
237	#336	C₂²×C₆₇	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
241	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
243	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
244	#127	—	4	2	no	—
245	#125	—	4	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	C₂³×C₆₇	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
262	#107	—	4	2	no	—
263	#106	—	4	2	no	—
264	C₄⋊C₈	—	4	2	no	—
265	#102	—	4	2	no	—
266	#102	—	4	2	no	—
267	#102	—	4	2	no	—
268	#102	—	4	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	#95	D₄×C₆₇	1	2	yes	—
273	#95	D₄×C₆₇	1	2	yes	—
274	C₂⁴	—	2	1	no	—
275	C₂⁴	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	8	2	no	—
287	C₂×D₄	—	8	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
297	C₂×C₈	—	2	2	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	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	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	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	8	2	no	—
312	C₄⋊C₄	—	8	2	no	—
313	C₄⋊C₄	—	8	2	no	—
314	C₂²⋊C₄	—	8	2	no	—
315	C₂²⋊C₄	—	8	2	no	—
316	C₂²⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	—	8	2	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	8	4	no	—
338	D₄	—	8	4	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	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	—	4	1	no	—
350	C₂×C₄	—	4	1	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	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
360	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
361	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
362	C₂×C₄	2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	1	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	#535×C₆₇	1	1	yes	characteristic
376	C₂²	#536×C₆₇	1	1	yes	characteristic
377	C₂²	#537×C₆₇	1	1	yes	characteristic
378	C₂²	#576×C₆₇	1	2	yes	—
379	C₂²	#577×C₆₇	1	2	yes	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	1	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	2	no	—
388	C₄	#562×C₆₇	1	2	yes	—
389	C₄	#563×C₆₇	1	2	yes	—
390	C₂	—	16	1	no	—
391	C₂	—	16	1	no	—
392	C₂	C₆₇×#2820	1	1	yes	characteristic
393	C₂	C₆₇×#3220	1	1	yes	characteristic
394	C₂	C₆₇×#3222	1	1	yes	characteristic
395	C₂	C₆₇×#3241	1	2	yes	—
396	C₂	C₆₇×#3257	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#127×C₆₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ #376×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2647	C₂	semidirect
3. C₆₇×#2094	C₂	semidirect
4. C₆₇×#2093	C₂	semidirect
5. C₆₇×#2073	C₂	semidirect
6. C₆₇×#2073	C₂	semidirect
7. C₆₇×#2067	C₂	semidirect
8. C₆₇×#2065	C₂	semidirect
9. C₆₇×#2059	C₂	semidirect
11. C₆₇×#1832	C₂	semidirect
191. #32831	C₆₇	direct (N × H)
199. #2647	C₂×C₆₇	semidirect
201. #2094	C₂×C₆₇	semidirect
202. #2093	C₂×C₆₇	semidirect
203. #2073	C₂×C₆₇	semidirect
204. #2073	C₂×C₆₇	semidirect
205. #2067	C₂×C₆₇	semidirect
206. #2065	C₂×C₆₇	semidirect
207. #2059	C₂×C₆₇	semidirect
209. #1832	C₂×C₆₇	semidirect
210. C₆₇	#32831	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×#2647	2
C₆₇×#2641	2
C₆₇×#2094	2
C₆₇×#2093	2
C₆₇×#2073	2
C₆₇×#2067	2
C₆₇×#2065	2
C₆₇×#2059	2
C₆₇×#2041	2
C₆₇×#1832	2
#32831	67

Subgroups — C67×#32831 #30712082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#32831 #30712082