Subgroups — C₆₇×#19749 #30699000

Order 17152.

822 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3185	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3182	C₂	1	2	yes	maximal, complemented
3	C₆₇×#3151	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#3138	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1722	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1719	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1717	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1715	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1709	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1708	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1455	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
13	#533×C₆₇	C₂²	1	2	yes	—
14	#532×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
16	#500×C₆₇	C₂²	1	2	yes	complemented
17	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
18	#496×C₆₇	—	2	2	no	—
19	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
20	#493×C₆₇	C₂²	1	1	yes	characteristic
21	#493×C₆₇	C₂²	1	1	yes	characteristic
22	#492×C₆₇	C₂²	1	1	yes	characteristic
23	#492×C₆₇	C₂²	1	1	yes	characteristic
24	#492×C₆₇	C₂²	1	2	yes	complemented
25	#490×C₆₇	—	2	4	no	—
26	#487×C₆₇	C₂²	1	2	yes	complemented
27	#487×C₆₇	C₂²	1	2	yes	complemented
28	#486×C₆₇	C₂²	1	2	yes	—
29	#486×C₆₇	C₂²	1	2	yes	—
30	#486×C₆₇	C₂²	1	2	yes	—
31	#486×C₆₇	C₂²	1	2	yes	—
32	#486×C₆₇	C₂²	1	2	yes	complemented
33	#470×C₆₇	—	2	2	no	—
34	#468×C₆₇	—	2	4	no	—
35	#441×C₆₇	—	2	2	no	—
36	#440×C₆₇	—	2	4	no	—
37	#418×C₆₇	—	2	4	no	—
38	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
39	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
40	#322×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#322×C₆₇	C₂²	1	2	yes	complemented
42	C₈²×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₆₇	—	2	1	no	—
44	C₂²×D₄×C₆₇	—	2	1	no	—
45	C₂²×D₄×C₆₇	—	2	2	no	—
46	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
47	C₂×Q₁₆×C₆₇	—	2	2	no	—
48	C₂×SD₁₆×C₆₇	—	2	4	no	—
49	C₂×SD₁₆×C₆₇	—	2	2	no	—
50	C₂×SD₁₆×C₆₇	—	2	2	no	—
51	C₂×D₈×C₆₇	—	2	2	no	—
52	C₂×D₈×C₆₇	—	2	2	no	—
53	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
54	C₂×M₁₆×C₆₇	D₄	1	4	yes	—
55	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
58	#127×C₆₇	—	2	2	no	—
59	#127×C₆₇	—	2	1	no	—
60	#127×C₆₇	C₂³	1	1	yes	characteristic
61	#127×C₆₇	C₂³	1	1	yes	characteristic
62	#127×C₆₇	C₂³	1	1	yes	characteristic
63	#125×C₆₇	—	2	2	no	—
64	#124×C₆₇	—	2	1	no	—
65	C₂²⋊Q₈×C₆₇	—	2	2	no	—
66	C₂²⋊Q₈×C₆₇	—	2	2	no	—
67	#121×C₆₇	—	2	2	no	—
68	C₄×Q₈×C₆₇	—	2	2	no	—
69	C₄×Q₈×C₆₇	—	2	2	no	—
70	C₄×D₄×C₆₇	—	2	2	no	—
71	#117×C₆₇	—	2	2	no	—
72	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
73	#107×C₆₇	—	2	4	no	—
74	#106×C₆₇	—	2	2	no	—
75	#103×C₆₇	—	2	4	no	—
76	#103×C₆₇	—	2	4	no	—
77	#102×C₆₇	—	2	4	no	—
78	#102×C₆₇	—	2	4	no	—
79	#102×C₆₇	—	2	4	no	—
80	#102×C₆₇	—	2	4	no	—
81	#102×C₆₇	—	2	4	no	—
82	#97×C₆₇	D₄	1	4	yes	—
83	#97×C₆₇	D₄	1	2	yes	—
84	C₄×C₈×C₆₇	C₂³	1	2	yes	—
85	C₄×C₈×C₆₇	C₂³	1	2	yes	—
86	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂⁴×C₆₇	—	4	1	no	—
89	#41×C₆₇	—	4	4	no	—
90	C₂×Q₈×C₆₇	—	2	2	no	—
91	C₂×Q₈×C₆₇	—	2	2	no	—
92	C₂×Q₈×C₆₇	—	2	1	no	—
93	C₂×D₄×C₆₇	—	2	2	no	—
94	C₂×D₄×C₆₇	—	2	2	no	—
95	C₂×D₄×C₆₇	—	2	2	no	—
96	C₂×D₄×C₆₇	—	2	1	no	—
97	C₂×D₄×C₆₇	—	2	1	no	—
98	C₂×D₄×C₆₇	—	2	1	no	—
99	C₂×D₄×C₆₇	—	4	4	no	—
100	C₂×D₄×C₆₇	—	4	8	no	—
101	C₂×D₄×C₆₇	—	4	1	no	—
102	C₂×D₄×C₆₇	—	4	2	no	—
103	C₂×D₄×C₆₇	—	4	1	no	—
104	C₂²×C₄×C₆₇	—	4	1	no	—
105	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
107	Q₁₆×C₆₇	—	4	4	no	—
108	SD₁₆×C₆₇	—	4	8	no	—
109	SD₁₆×C₆₇	—	4	4	no	—
110	SD₁₆×C₆₇	—	4	4	no	—
111	D₈×C₆₇	—	4	4	no	—
112	D₈×C₆₇	—	4	4	no	—
113	M₁₆×C₆₇	—	2	4	no	—
114	M₁₆×C₆₇	—	4	4	no	—
115	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
116	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
117	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	2	2	no	—
122	C₄⋊C₄×C₆₇	—	2	2	no	—
123	C₄⋊C₄×C₆₇	—	2	2	no	—
124	C₄⋊C₄×C₆₇	—	4	2	no	—
125	C₄⋊C₄×C₆₇	—	4	2	no	—
126	C₂²⋊C₄×C₆₇	—	4	2	no	—
127	C₂²⋊C₄×C₆₇	—	4	2	no	—
128	C₄²×C₆₇	—	4	2	no	—
129	C₄²×C₆₇	C₂×D₄	1	2	yes	—
130	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
132	C₂³×C₆₇	—	4	1	no	—
133	C₂³×C₆₇	—	4	1	no	—
134	C₂³×C₆₇	—	4	1	no	—
135	C₂³×C₆₇	—	8	2	no	—
136	C₂³×C₆₇	—	8	4	no	—
137	C₂³×C₆₇	#127	1	1	yes	characteristic
138	Q₈×C₆₇	—	4	2	no	—
139	Q₈×C₆₇	—	4	4	no	—
140	Q₈×C₆₇	—	4	4	no	—
141	D₄×C₆₇	—	4	2	no	—
142	D₄×C₆₇	—	4	2	no	—
143	D₄×C₆₇	—	4	2	no	—
144	D₄×C₆₇	—	4	4	no	—
145	D₄×C₆₇	—	4	4	no	—
146	D₄×C₆₇	—	4	4	no	—
147	D₄×C₆₇	—	8	2	no	—
148	D₄×C₆₇	—	8	4	no	—
149	D₄×C₆₇	—	8	2	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	2	4	no	—
152	C₂×C₄×C₆₇	—	4	2	no	—
153	C₂×C₄×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	—	4	1	no	—
155	C₂×C₄×C₆₇	—	8	2	no	—
156	C₂×C₄×C₆₇	#127	1	2	yes	—
157	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
160	C₈×C₆₇	—	2	2	no	—
161	C₈×C₆₇	—	2	4	no	—
162	C₈×C₆₇	—	2	4	no	—
163	C₈×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
164	C₂²×C₆₇	—	2	1	no	—
165	C₂²×C₆₇	—	2	2	no	—
166	C₂²×C₆₇	—	8	1	no	—
167	C₂²×C₆₇	—	8	1	no	—
168	C₂²×C₆₇	—	8	1	no	—
169	C₂²×C₆₇	—	8	2	no	—
170	C₂²×C₆₇	—	8	2	no	—
171	C₂²×C₆₇	—	8	2	no	—
172	C₂²×C₆₇	—	16	4	no	—
173	C₂²×C₆₇	C₂×#127	1	1	yes	characteristic
174	C₄×C₆₇	—	2	1	no	—
175	C₄×C₆₇	—	2	2	no	—
176	C₄×C₆₇	—	8	1	no	—
177	C₄×C₆₇	—	8	2	no	—
178	C₄×C₆₇	—	8	2	no	—
179	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
180	C₄×C₆₇	#575	1	4	yes	—
181	#19749	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂×C₆₇	—	4	1	no	—
183	C₂×C₆₇	—	16	1	no	—
184	C₂×C₆₇	—	16	1	no	—
185	C₂×C₆₇	—	16	1	no	—
186	C₂×C₆₇	#3151	1	1	yes	characteristic
187	C₂×C₆₇	#3153	1	2	yes	—
188	#3185	C₂×C₆₇	1	1	yes	characteristic, complemented
189	#3182	C₂×C₆₇	1	2	yes	complemented
190	#3151	C₂×C₆₇	1	1	yes	characteristic
191	#3138	C₂×C₆₇	1	2	yes	complemented
192	#1722	C₂×C₆₇	1	1	yes	characteristic, complemented
193	#1719	C₂×C₆₇	1	2	yes	complemented
194	#1717	C₂×C₆₇	1	2	yes	complemented
195	#1715	C₂×C₆₇	1	1	yes	characteristic, complemented
196	#1709	C₂×C₆₇	1	1	yes	characteristic, complemented
197	#1708	C₂×C₆₇	1	1	yes	characteristic, complemented
198	#1455	C₂×C₆₇	1	1	yes	characteristic, complemented
199	C₆₇	#19749	1	1	yes	characteristic, direct product factor, Sylow
200	C₂×AGL(1,ℤ/8)	—	2	2	no	—
201	#533	C₂²×C₆₇	1	2	yes	—
202	#532	C₂²×C₆₇	1	1	yes	characteristic
203	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
204	#500	C₂²×C₆₇	1	2	yes	complemented
205	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
206	#496	—	2	2	no	—
207	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
208	#493	C₂²×C₆₇	1	1	yes	characteristic
209	#493	C₂²×C₆₇	1	1	yes	characteristic
210	#492	C₂²×C₆₇	1	1	yes	characteristic
211	#492	C₂²×C₆₇	1	1	yes	characteristic
212	#492	C₂²×C₆₇	1	2	yes	complemented
213	#490	—	2	4	no	—
214	#487	C₂²×C₆₇	1	2	yes	complemented
215	#487	C₂²×C₆₇	1	2	yes	complemented
216	#486	C₂²×C₆₇	1	2	yes	—
217	#486	C₂²×C₆₇	1	2	yes	—
218	#486	C₂²×C₆₇	1	2	yes	—
219	#486	C₂²×C₆₇	1	2	yes	—
220	#486	C₂²×C₆₇	1	2	yes	complemented
221	#470	—	2	2	no	—
222	#468	—	2	4	no	—
223	#441	—	2	2	no	—
224	#440	—	2	4	no	—
225	#418	—	2	4	no	—
226	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
227	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
228	#322	C₂²×C₆₇	1	1	yes	characteristic, complemented
229	#322	C₂²×C₆₇	1	2	yes	complemented
230	C₈²	C₂²×C₆₇	1	1	yes	characteristic, complemented
231	C₂×#41	—	2	1	no	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	2	no	—
234	AGL(1,ℤ/8)	—	4	8	no	—
235	C₂×Q₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×SD₁₆	—	2	4	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×M₁₆	D₄×C₆₇	1	2	yes	—
242	C₂×M₁₆	D₄×C₆₇	1	4	yes	—
243	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
244	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
245	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
246	#127	—	2	2	no	—
247	#127	—	2	1	no	—
248	#127	C₂³×C₆₇	1	1	yes	characteristic
249	#127	C₂³×C₆₇	1	1	yes	characteristic
250	#127	C₂³×C₆₇	1	1	yes	characteristic
251	#125	—	2	2	no	—
252	#124	—	2	1	no	—
253	C₂²⋊Q₈	—	2	2	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	#121	—	2	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	#117	—	2	2	no	—
260	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
261	#107	—	2	4	no	—
262	#106	—	2	2	no	—
263	#103	—	2	4	no	—
264	#103	—	2	4	no	—
265	#102	—	2	4	no	—
266	#102	—	2	4	no	—
267	#102	—	2	4	no	—
268	#102	—	2	4	no	—
269	#102	—	2	4	no	—
270	#97	D₄×C₆₇	1	4	yes	—
271	#97	D₄×C₆₇	1	2	yes	—
272	C₄×C₈	C₂³×C₆₇	1	2	yes	—
273	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₆₇	1	2	yes	—
275	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
276	C₂⁴	—	4	1	no	—
277	#41	—	4	4	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	—	4	8	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
295	Q₁₆	—	4	4	no	—
296	SD₁₆	—	4	4	no	—
297	SD₁₆	—	4	8	no	—
298	SD₁₆	—	4	4	no	—
299	D₈	—	4	4	no	—
300	D₈	—	4	4	no	—
301	M₁₆	—	2	4	no	—
302	M₁₆	—	4	4	no	—
303	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
304	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
305	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
306	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₄²	—	4	2	no	—
317	C₄²	C₂×D₄×C₆₇	1	2	yes	—
318	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
319	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
320	C₂³	—	4	1	no	—
321	C₂³	—	4	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	8	2	no	—
324	C₂³	—	8	4	no	—
325	C₂³	#127×C₆₇	1	1	yes	characteristic
326	Q₈	—	4	2	no	—
327	Q₈	—	4	4	no	—
328	Q₈	—	4	4	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	4	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	8	2	no	—
336	D₄	—	8	4	no	—
337	D₄	—	8	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	#127×C₆₇	1	2	yes	—
345	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
348	C₈	—	2	2	no	—
349	C₈	—	2	4	no	—
350	C₈	—	2	4	no	—
351	C₈	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	16	4	no	—
361	C₂²	C₂×#127×C₆₇	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	2	2	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	2	no	—
367	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
368	C₄	#575×C₆₇	1	4	yes	—
369	C₂	—	4	1	no	—
370	C₂	—	16	1	no	—
371	C₂	—	16	1	no	—
372	C₂	—	16	1	no	—
373	C₂	C₆₇×#3151	1	1	yes	characteristic
374	C₂	C₆₇×#3153	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₇
prime radical	C₆₇×#3151	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3185	C₂	semidirect
2. C₆₇×#3182	C₂	semidirect
4. C₆₇×#3138	C₂	semidirect
5. C₆₇×#1722	C₂	semidirect
6. C₆₇×#1719	C₂	semidirect
7. C₆₇×#1717	C₂	semidirect
8. C₆₇×#1715	C₂	semidirect
9. C₆₇×#1709	C₂	semidirect
10. C₆₇×#1708	C₂	semidirect
11. C₆₇×#1455	C₂	semidirect
16. #500×C₆₇	C₂²	semidirect
17. #498×C₆₇	C₂²	semidirect
19. #494×C₆₇	C₂²	semidirect
24. #492×C₆₇	C₂²	semidirect
26. #487×C₆₇	C₂²	semidirect
27. #487×C₆₇	C₂²	semidirect
32. #486×C₆₇	C₂²	semidirect
40. #322×C₆₇	C₂²	semidirect
41. #322×C₆₇	C₂²	semidirect
42. C₈²×C₆₇	C₂²	semidirect
181. #19749	C₆₇	direct (N × H)
188. #3185	C₂×C₆₇	semidirect
189. #3182	C₂×C₆₇	semidirect
191. #3138	C₂×C₆₇	semidirect
192. #1722	C₂×C₆₇	semidirect
193. #1719	C₂×C₆₇	semidirect
194. #1717	C₂×C₆₇	semidirect
195. #1715	C₂×C₆₇	semidirect
196. #1709	C₂×C₆₇	semidirect
197. #1708	C₂×C₆₇	semidirect
198. #1455	C₂×C₆₇	semidirect
199. C₆₇	#19749	direct (N × H)
204. #500	C₂²×C₆₇	semidirect
205. #498	C₂²×C₆₇	semidirect
207. #494	C₂²×C₆₇	semidirect
212. #492	C₂²×C₆₇	semidirect
214. #487	C₂²×C₆₇	semidirect
215. #487	C₂²×C₆₇	semidirect
220. #486	C₂²×C₆₇	semidirect
228. #322	C₂²×C₆₇	semidirect
229. #322	C₂²×C₆₇	semidirect
230. C₈²	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3185	2
C₆₇×#3182	2
C₆₇×#3151	2
C₆₇×#3138	2
C₆₇×#1722	2
C₆₇×#1719	2
C₆₇×#1717	2
C₆₇×#1715	2
C₆₇×#1709	2
C₆₇×#1708	2
C₆₇×#1455	2
#19749	67

Subgroups — C67×#19749 #30699000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#19749 #30699000