Subgroups — C₆₇×#21392 #30700643

Order 17152.

1150 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1987	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1981	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1873	C₂	1	4	yes	maximal
7	C₆₇×#1763	C₂	1	4	yes	maximal, complemented
8	#533×C₆₇	—	2	4	no	—
9	#533×C₆₇	C₄	1	8	yes	complemented
10	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
12	C₂×#125×C₆₇	—	2	1	no	—
13	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
16	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
17	C₂×#117×C₆₇	—	2	1	no	—
18	C₂×#117×C₆₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
20	#432×C₆₇	—	2	4	no	—
21	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
22	C₂×#103×C₆₇	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
24	C₂×#97×C₆₇	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
28	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
29	#376×C₆₇	—	2	1	no	—
30	C₄³×C₆₇	—	2	1	no	—
31	#340×C₆₇	C₂²	1	8	yes	—
32	C₂²×Q₈×C₆₇	—	2	1	no	—
33	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
38	C₄⋊Q₈×C₆₇	—	2	2	no	—
39	C₄⋊Q₈×C₆₇	—	2	2	no	—
40	C₄⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
41	C₄⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
42	#125×C₆₇	—	2	8	no	—
43	C₂²⋊Q₈×C₆₇	—	2	8	no	—
44	C₂²⋊Q₈×C₆₇	—	2	4	no	—
45	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	—
46	C₄×Q₈×C₆₇	—	2	8	no	—
47	C₄×Q₈×C₆₇	—	2	4	no	—
48	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	—
49	#117×C₆₇	—	2	8	no	—
50	#117×C₆₇	—	2	8	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
60	C₂×C₄²×C₆₇	—	2	2	no	—
61	C₂×C₄²×C₆₇	—	2	2	no	—
62	C₂×C₄²×C₆₇	—	2	2	no	—
63	C₂×C₄²×C₆₇	—	2	2	no	—
64	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₆₇	D₄	1	4	yes	—
68	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₆₇	—	2	4	no	—
71	#103×C₆₇	—	2	16	no	—
72	C₂²⋊C₈×C₆₇	—	2	4	no	—
73	#97×C₆₇	—	2	4	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	4	no	—
78	C₂×Q₈×C₆₇	—	2	2	no	—
79	C₂×Q₈×C₆₇	—	2	8	no	—
80	C₂×Q₈×C₆₇	—	4	4	no	—
81	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₆₇	—	2	4	no	—
83	C₂²×C₄×C₆₇	—	2	4	no	—
84	C₂²×C₄×C₆₇	—	2	4	no	—
85	C₂²×C₄×C₆₇	—	2	2	no	—
86	C₂²×C₄×C₆₇	—	2	2	no	—
87	C₂²×C₄×C₆₇	—	4	2	no	—
88	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
90	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₆₇	—	2	4	no	—
99	C₂×C₈×C₆₇	—	2	8	no	—
100	C₄⋊C₄×C₆₇	—	2	4	no	—
101	C₄⋊C₄×C₆₇	—	2	4	no	—
102	C₄⋊C₄×C₆₇	—	2	4	no	—
103	C₄⋊C₄×C₆₇	—	2	8	no	—
104	C₄⋊C₄×C₆₇	—	2	8	no	—
105	C₄⋊C₄×C₆₇	—	2	2	no	—
106	C₄⋊C₄×C₆₇	—	2	4	no	—
107	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
108	C₄⋊C₄×C₆₇	#41	1	8	yes	—
109	C₂²⋊C₄×C₆₇	—	2	8	no	—
110	C₂²⋊C₄×C₆₇	—	2	8	no	—
111	C₄²×C₆₇	—	2	8	no	—
112	C₄²×C₆₇	—	2	8	no	—
113	C₄²×C₆₇	—	4	4	no	—
114	C₄²×C₆₇	—	4	4	no	—
115	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
116	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
117	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₆₇	C₂×D₄	1	2	yes	—
120	C₄²×C₆₇	C₂×D₄	1	2	yes	—
121	C₂³×C₆₇	—	2	2	no	—
122	C₂³×C₆₇	—	2	2	no	—
123	C₂³×C₆₇	—	2	2	no	—
124	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
125	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₆₇	—	2	8	no	—
127	Q₈×C₆₇	—	4	8	no	—
128	Q₈×C₆₇	—	4	4	no	—
129	C₂×C₄×C₆₇	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	2	no	—
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	4	no	—
134	C₂×C₄×C₆₇	—	2	4	no	—
135	C₂×C₄×C₆₇	—	2	8	no	—
136	C₂×C₄×C₆₇	—	2	4	no	—
137	C₂×C₄×C₆₇	—	2	4	no	—
138	C₂×C₄×C₆₇	—	2	8	no	—
139	C₂×C₄×C₆₇	—	4	4	no	—
140	C₂×C₄×C₆₇	—	4	4	no	—
141	C₂×C₄×C₆₇	—	4	4	no	—
142	C₂×C₄×C₆₇	—	4	4	no	—
143	C₂×C₄×C₆₇	—	4	4	no	—
144	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₆₇	#137	1	4	yes	—
150	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
153	C₈×C₆₇	—	4	4	no	—
154	C₂²×C₆₇	—	2	2	no	—
155	C₂²×C₆₇	—	2	2	no	—
156	C₂²×C₆₇	—	2	2	no	—
157	C₂²×C₆₇	—	4	4	no	—
158	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₆₇	#525	1	2	yes	—
160	C₂²×C₆₇	C₂×#137	1	2	yes	—
161	C₂²×C₆₇	#575	1	2	yes	—
162	C₄×C₆₇	—	2	2	no	—
163	C₄×C₆₇	—	2	2	no	—
164	C₄×C₆₇	—	2	2	no	—
165	C₄×C₆₇	—	2	2	no	—
166	C₄×C₆₇	—	4	8	no	—
167	C₄×C₆₇	—	4	4	no	—
168	C₄×C₆₇	—	4	4	no	—
169	C₄×C₆₇	#419	1	4	yes	—
170	C₄×C₆₇	C₄×#41	1	2	yes	—
171	C₄×C₆₇	#532	1	2	yes	—
172	#21392	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂×C₆₇	—	4	2	no	—
174	C₂×C₆₇	#2297	1	1	yes	characteristic
175	C₂×C₆₇	C₂×#419	1	1	yes	characteristic
176	C₂×C₆₇	#2896	1	1	yes	characteristic
177	C₂×C₆₇	#3116	1	4	yes	—
178	C₂×#533	C₂×C₆₇	1	1	yes	characteristic
179	C₂×#432	C₂×C₆₇	1	1	yes	characteristic
180	C₄×#117	C₂×C₆₇	1	1	yes	characteristic
181	#1987	C₂×C₆₇	1	2	yes	complemented
182	#1981	C₂×C₆₇	1	2	yes	complemented
183	#1873	C₂×C₆₇	1	4	yes	—
184	#1763	C₂×C₆₇	1	4	yes	complemented
185	C₆₇	#21392	1	1	yes	characteristic, direct product factor, Sylow
186	#533	—	2	4	no	—
187	#533	C₄×C₆₇	1	8	yes	complemented
188	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
189	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
190	C₂×#125	—	2	1	no	—
191	C₂×C₂²⋊Q₈	—	2	1	no	—
192	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
193	C₂×C₄×Q₈	—	2	1	no	—
194	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
195	C₂×#117	—	2	1	no	—
196	C₂×#117	C₂²×C₆₇	1	2	yes	—
197	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
198	#432	—	2	4	no	—
199	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
200	C₂×#103	C₂²×C₆₇	1	8	yes	—
201	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
202	C₂×#97	C₂²×C₆₇	1	2	yes	—
203	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
204	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
205	C₄×C₂²⋊C₄	—	2	1	no	—
206	C₄×C₂²⋊C₄	—	2	1	no	—
207	#376	—	2	1	no	—
208	C₄³	—	2	1	no	—
209	#340	C₂²×C₆₇	1	8	yes	—
210	C₂²×Q₈	—	2	1	no	—
211	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
212	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
213	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
216	C₄⋊Q₈	—	2	2	no	—
217	C₄⋊Q₈	—	2	2	no	—
218	C₄⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
219	C₄⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
220	#125	—	2	8	no	—
221	C₂²⋊Q₈	—	2	8	no	—
222	C₂²⋊Q₈	—	2	4	no	—
223	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	—
224	C₄×Q₈	—	2	8	no	—
225	C₄×Q₈	—	2	4	no	—
226	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	—
227	#117	—	2	8	no	—
228	#117	—	2	8	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
243	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
244	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₆₇	1	4	yes	—
246	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
248	C₄⋊C₈	—	2	4	no	—
249	#103	—	2	16	no	—
250	C₂²⋊C₈	—	2	4	no	—
251	#97	—	2	4	no	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	8	no	—
258	C₂×Q₈	—	4	4	no	—
259	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
267	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
268	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	8	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	8	no	—
282	C₄⋊C₄	—	2	8	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
286	C₄⋊C₄	#41×C₆₇	1	8	yes	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	—	2	8	no	—
289	C₄²	—	2	8	no	—
290	C₄²	—	2	8	no	—
291	C₄²	—	4	4	no	—
292	C₄²	—	4	4	no	—
293	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
294	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
295	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
296	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
297	C₄²	C₂×D₄×C₆₇	1	2	yes	—
298	C₄²	C₂×D₄×C₆₇	1	2	yes	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
303	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
304	Q₈	—	2	8	no	—
305	Q₈	—	4	8	no	—
306	Q₈	—	4	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
323	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
324	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
325	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
327	C₂×C₄	#137×C₆₇	1	4	yes	—
328	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
331	C₈	—	4	4	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	4	4	no	—
336	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
337	C₂²	#525×C₆₇	1	2	yes	—
338	C₂²	C₂×#137×C₆₇	1	2	yes	—
339	C₂²	#575×C₆₇	1	2	yes	—
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	8	no	—
346	C₄	—	4	4	no	—
347	C₄	#419×C₆₇	1	4	yes	—
348	C₄	C₄×#41×C₆₇	1	2	yes	—
349	C₄	#532×C₆₇	1	2	yes	—
350	C₂	—	4	2	no	—
351	C₂	C₆₇×#2297	1	1	yes	characteristic
352	C₂	C₂×#419×C₆₇	1	1	yes	characteristic
353	C₂	C₆₇×#2896	1	1	yes	characteristic
354	C₂	C₆₇×#3116	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
4. C₆₇×#1987	C₂	semidirect
5. C₆₇×#1981	C₂	semidirect
7. C₆₇×#1763	C₂	semidirect
9. #533×C₆₇	C₄	semidirect
172. #21392	C₆₇	direct (N × H)
181. #1987	C₂×C₆₇	semidirect
182. #1981	C₂×C₆₇	semidirect
184. #1763	C₂×C₆₇	semidirect
185. C₆₇	#21392	direct (N × H)
187. #533	C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₆₇	2
C₂×#432×C₆₇	2
C₄×#117×C₆₇	2
C₆₇×#1987	2
C₆₇×#1981	2
C₆₇×#1873	2
C₆₇×#1763	2
#21392	67

Subgroups — C67×#21392 #30700643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#21392 #30700643