Subgroups — C₆₇×#20741 #30699992

Order 17152.

1306 conjugacy classes of subgroups.

The subgroup lattice has 366 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
2	C₂×#432×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2283	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1824	C₂	1	2	yes	maximal
5	C₆₇×#1805	C₂	1	4	yes	maximal, complemented
6	C₆₇×#1787	C₂	1	2	yes	maximal
7	C₆₇×#1763	C₂	1	4	yes	maximal, complemented
8	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₆₇	—	2	4	no	—
10	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
11	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
12	C₂×C₄×Q₈×C₆₇	C₄	1	8	yes	complemented
13	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₆₇	—	2	1	no	—
18	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
19	#432×C₆₇	—	2	4	no	—
20	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
21	C₂×#103×C₆₇	C₂²	1	8	yes	—
22	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
23	C₂×#97×C₆₇	C₂²	1	2	yes	—
24	#383×C₆₇	—	2	1	no	—
25	#382×C₆₇	C₂²	1	2	yes	—
26	#381×C₆₇	—	2	1	no	—
27	#380×C₆₇	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
30	#376×C₆₇	—	2	1	no	—
31	#340×C₆₇	C₂²	1	8	yes	—
32	C₂²×Q₈×C₆₇	—	2	8	no	—
33	C₂²×Q₈×C₆₇	—	2	2	no	—
34	C₂²×Q₈×C₆₇	—	2	1	no	—
35	C₂²×Q₈×C₆₇	C₂×C₄	1	4	yes	—
36	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₆₇	—	2	1	no	—
38	C₂³×C₄×C₆₇	—	2	1	no	—
39	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
43	C₄×Q₈×C₆₇	—	2	8	no	—
44	C₄×Q₈×C₆₇	—	2	8	no	—
45	C₄×Q₈×C₆₇	—	2	4	no	—
46	C₄×Q₈×C₆₇	—	2	4	no	—
47	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	—
49	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
56	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
58	C₂×C₄²×C₆₇	—	2	8	no	—
59	C₂×C₄²×C₆₇	—	2	2	no	—
60	C₂×C₄²×C₆₇	—	2	2	no	—
61	C₂×C₄²×C₆₇	—	2	2	no	—
62	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₆₇	D₄	1	4	yes	—
66	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₆₇	—	2	4	no	—
69	#103×C₆₇	—	2	16	no	—
70	C₂²⋊C₈×C₆₇	—	2	4	no	—
71	#97×C₆₇	—	2	4	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	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₆₇	—	2	16	no	—
78	C₂×Q₈×C₆₇	—	2	8	no	—
79	C₂×Q₈×C₆₇	—	2	16	no	—
80	C₂×Q₈×C₆₇	—	2	4	no	—
81	C₂×Q₈×C₆₇	—	2	2	no	—
82	C₂×Q₈×C₆₇	—	2	4	no	—
83	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
84	C₂×Q₈×C₆₇	#41	1	8	yes	—
85	C₂²×C₄×C₆₇	—	2	8	no	—
86	C₂²×C₄×C₆₇	—	2	4	no	—
87	C₂²×C₄×C₆₇	—	2	4	no	—
88	C₂²×C₄×C₆₇	—	2	2	no	—
89	C₂²×C₄×C₆₇	—	2	4	no	—
90	C₂²×C₄×C₆₇	—	2	4	no	—
91	C₂²×C₄×C₆₇	—	2	2	no	—
92	C₂²×C₄×C₆₇	—	2	4	no	—
93	C₂²×C₄×C₆₇	—	4	2	no	—
94	C₂²×C₄×C₆₇	—	4	4	no	—
95	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
97	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₆₇	—	2	4	no	—
106	C₂×C₈×C₆₇	—	2	8	no	—
107	C₄⋊C₄×C₆₇	—	2	8	no	—
108	C₄⋊C₄×C₆₇	—	2	8	no	—
109	C₄⋊C₄×C₆₇	—	2	4	no	—
110	C₄⋊C₄×C₆₇	—	2	2	no	—
111	C₄⋊C₄×C₆₇	—	2	8	no	—
112	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
113	C₂²⋊C₄×C₆₇	—	4	4	no	—
114	C₄²×C₆₇	—	2	8	no	—
115	C₄²×C₆₇	—	2	8	no	—
116	C₄²×C₆₇	—	4	4	no	—
117	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
118	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
119	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
121	C₄²×C₆₇	C₂×D₄	1	2	yes	—
122	C₄²×C₆₇	C₂×D₄	1	2	yes	—
123	C₂³×C₆₇	—	2	2	no	—
124	C₂³×C₆₇	—	2	2	no	—
125	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
126	C₂³×C₆₇	#137	1	4	yes	—
127	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₆₇	—	2	16	no	—
129	Q₈×C₆₇	—	2	4	no	—
130	Q₈×C₆₇	—	2	8	no	—
131	Q₈×C₆₇	#117	1	8	yes	—
132	C₂×C₄×C₆₇	—	2	16	no	—
133	C₂×C₄×C₆₇	—	2	4	no	—
134	C₂×C₄×C₆₇	—	2	8	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	—	2	2	no	—
139	C₂×C₄×C₆₇	—	2	2	no	—
140	C₂×C₄×C₆₇	—	2	8	no	—
141	C₂×C₄×C₆₇	—	2	4	no	—
142	C₂×C₄×C₆₇	—	2	4	no	—
143	C₂×C₄×C₆₇	—	2	4	no	—
144	C₂×C₄×C₆₇	—	4	4	no	—
145	C₂×C₄×C₆₇	—	4	8	no	—
146	C₂×C₄×C₆₇	—	4	4	no	—
147	C₂×C₄×C₆₇	—	4	4	no	—
148	C₂×C₄×C₆₇	—	4	4	no	—
149	C₂×C₄×C₆₇	—	4	4	no	—
150	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
158	C₈×C₆₇	—	4	4	no	—
159	C₂²×C₆₇	—	2	8	no	—
160	C₂²×C₆₇	—	2	2	no	—
161	C₂²×C₆₇	—	2	2	no	—
162	C₂²×C₆₇	#419	1	4	yes	—
163	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₆₇	#525	1	2	yes	—
165	C₂²×C₆₇	C₂×#137	1	2	yes	—
166	C₂²×C₆₇	#575	1	2	yes	—
167	C₄×C₆₇	—	2	2	no	—
168	C₄×C₆₇	—	2	2	no	—
169	C₄×C₆₇	—	2	2	no	—
170	C₄×C₆₇	—	2	2	no	—
171	C₄×C₆₇	—	2	8	no	—
172	C₄×C₆₇	—	2	2	no	—
173	C₄×C₆₇	—	4	4	no	—
174	C₄×C₆₇	—	8	4	no	—
175	C₄×C₆₇	C₂×#117	1	2	yes	—
176	C₄×C₆₇	#525	1	2	yes	—
177	#20741	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₆₇	—	2	4	no	—
179	C₂×C₆₇	#2280	1	1	yes	characteristic
180	C₂×C₆₇	C₂×#419	1	1	yes	characteristic
181	C₂×C₆₇	#2896	1	1	yes	characteristic
182	C₂×C₆₇	#3117	1	4	yes	—
183	C₂²×C₄×Q₈	C₂×C₆₇	1	1	yes	characteristic
184	C₂×#432	C₂×C₆₇	1	1	yes	characteristic
185	#2283	C₂×C₆₇	1	1	yes	characteristic
186	#1824	C₂×C₆₇	1	2	yes	—
187	#1805	C₂×C₆₇	1	4	yes	complemented
188	#1787	C₂×C₆₇	1	2	yes	—
189	#1763	C₂×C₆₇	1	4	yes	complemented
190	C₆₇	#20741	1	1	yes	characteristic, direct product factor, Sylow
191	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
192	C₂×C₄×Q₈	—	2	4	no	—
193	C₂×C₄×Q₈	—	2	1	no	—
194	C₂×C₄×Q₈	—	2	1	no	—
195	C₂×C₄×Q₈	C₄×C₆₇	1	8	yes	complemented
196	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
197	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
198	C₂²×C₄⋊C₄	—	2	1	no	—
199	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
200	C₂²×C₄²	—	2	1	no	—
201	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
202	#432	—	2	4	no	—
203	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
204	C₂×#103	C₂²×C₆₇	1	8	yes	—
205	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
206	C₂×#97	C₂²×C₆₇	1	2	yes	—
207	#383	—	2	1	no	—
208	#382	C₂²×C₆₇	1	2	yes	—
209	#381	—	2	1	no	—
210	#380	C₂²×C₆₇	1	2	yes	—
211	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
212	C₄×C₂²⋊C₄	—	2	1	no	—
213	#376	—	2	1	no	—
214	#340	C₂²×C₆₇	1	8	yes	—
215	C₂²×Q₈	—	2	8	no	—
216	C₂²×Q₈	—	2	2	no	—
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×Q₈	C₂×C₄×C₆₇	1	4	yes	—
219	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
220	C₂³×C₄	—	2	1	no	—
221	C₂³×C₄	—	2	1	no	—
222	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
223	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
224	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
226	C₄×Q₈	—	2	8	no	—
227	C₄×Q₈	—	2	8	no	—
228	C₄×Q₈	—	2	4	no	—
229	C₄×Q₈	—	2	4	no	—
230	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	—
231	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	—
232	C₂×C₄⋊C₄	—	2	8	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
238	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
239	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₄²	—	2	8	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
246	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
248	C₂×C₄²	D₄×C₆₇	1	4	yes	—
249	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
251	C₄⋊C₈	—	2	4	no	—
252	#103	—	2	16	no	—
253	C₂²⋊C₈	—	2	4	no	—
254	#97	—	2	4	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
260	C₂×Q₈	—	2	16	no	—
261	C₂×Q₈	—	2	8	no	—
262	C₂×Q₈	—	2	16	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
267	C₂×Q₈	#41×C₆₇	1	8	yes	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
279	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
280	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
287	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	8	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	8	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₄²	—	2	8	no	—
298	C₄²	—	2	8	no	—
299	C₄²	—	4	4	no	—
300	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
301	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
302	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
303	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
304	C₄²	C₂×D₄×C₆₇	1	2	yes	—
305	C₄²	C₂×D₄×C₆₇	1	2	yes	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	2	no	—
308	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
309	C₂³	#137×C₆₇	1	4	yes	—
310	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
311	Q₈	—	2	16	no	—
312	Q₈	—	2	4	no	—
313	Q₈	—	2	8	no	—
314	Q₈	#117×C₆₇	1	8	yes	—
315	C₂×C₄	—	2	16	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	8	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
338	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
341	C₈	—	4	4	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	2	2	no	—
345	C₂²	#419×C₆₇	1	4	yes	—
346	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
347	C₂²	#525×C₆₇	1	2	yes	—
348	C₂²	C₂×#137×C₆₇	1	2	yes	—
349	C₂²	#575×C₆₇	1	2	yes	—
350	C₄	—	2	8	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	4	4	no	—
357	C₄	—	8	4	no	—
358	C₄	C₂×#117×C₆₇	1	2	yes	—
359	C₄	#525×C₆₇	1	2	yes	—
360	C₂	—	2	4	no	—
361	C₂	C₆₇×#2280	1	1	yes	characteristic
362	C₂	C₂×#419×C₆₇	1	1	yes	characteristic
363	C₂	C₆₇×#2896	1	1	yes	characteristic
364	C₂	C₆₇×#3117	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂⁴×C₆₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₆₇×#1805	C₂	semidirect
7. C₆₇×#1763	C₂	semidirect
12. C₂×C₄×Q₈×C₆₇	C₄	semidirect
177. #20741	C₆₇	direct (N × H)
187. #1805	C₂×C₆₇	semidirect
189. #1763	C₂×C₆₇	semidirect
190. C₆₇	#20741	direct (N × H)
195. C₂×C₄×Q₈	C₄×C₆₇	semidirect

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
C₂×#432×C₆₇	2
C₆₇×#2283	2
C₆₇×#1824	2
C₆₇×#1805	2
C₆₇×#1787	2
C₆₇×#1763	2
#20741	67

Subgroups — C67×#20741 #30699992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#20741 #30699992