Subgroups — C₂×C₆₇×#3383 #30740607

Order 17152.

1766 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₆₇	C₂	1	2	yes	maximal
2	C₆₇×#3383	C₂	1	16	yes	maximal, direct product factor
3	C₂×#500×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#499×C₆₇	C₂	1	2	yes	maximal
5	C₂×#479×C₆₇	C₂	1	4	yes	maximal
6	C₂×#475×C₆₇	C₂	1	2	yes	maximal
7	C₂×C₈×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Q₁₆×C₆₇	C₂	1	2	yes	maximal
10	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
11	#557×C₆₇	—	2	8	no	—
12	#557×C₆₇	C₂²	1	16	yes	—
13	C₂×C₄⋊Q₈×C₆₇	—	2	2	no	—
14	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
15	C₂×#125×C₆₇	—	2	4	no	—
16	C₂×#125×C₆₇	C₂²	1	4	yes	—
17	C₂×C₄×Q₈×C₆₇	—	2	2	no	—
18	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
21	#500×C₆₇	C₂²	1	8	yes	—
22	#499×C₆₇	C₂²	1	16	yes	—
23	#479×C₆₇	C₂²	1	32	yes	—
24	#475×C₆₇	C₂²	1	16	yes	—
25	C₈×Q₈×C₆₇	C₂²	1	8	yes	—
26	C₄×Q₁₆×C₆₇	C₂²	1	16	yes	—
27	C₄×Q₁₆×C₆₇	C₂²	1	8	yes	—
28	C₂×#107×C₆₇	C₂²	1	2	yes	—
29	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#107×C₆₇	C₂²	1	2	yes	—
31	C₂×#106×C₆₇	C₂²	1	4	yes	—
32	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
34	C₂×#103×C₆₇	C₂²	1	4	yes	—
35	C₂×#103×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₆₇	—	2	2	no	—
39	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
41	C₂×Q₁₆×C₆₇	Q₈	1	8	yes	complemented
42	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
43	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
44	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
46	C₄⋊Q₈×C₆₇	—	2	16	no	—
47	C₄⋊Q₈×C₆₇	—	2	4	no	—
48	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
49	#125×C₆₇	—	2	32	no	—
50	#125×C₆₇	—	2	8	no	—
51	#125×C₆₇	C₂³	1	16	yes	—
52	C₄×Q₈×C₆₇	—	2	16	no	—
53	C₄×Q₈×C₆₇	—	2	8	no	—
54	C₄×Q₈×C₆₇	—	2	4	no	—
55	C₄×Q₈×C₆₇	D₄	1	4	yes	—
56	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
57	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
58	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
60	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
62	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
64	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
68	C₂×C₄²×C₆₇	—	2	4	no	—
69	C₂×C₄²×C₆₇	—	2	2	no	—
70	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
71	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
72	#107×C₆₇	C₂³	1	8	yes	—
73	#107×C₆₇	C₂³	1	4	yes	—
74	#107×C₆₇	C₂³	1	8	yes	—
75	#106×C₆₇	C₂³	1	16	yes	—
76	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
77	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
78	#103×C₆₇	C₂³	1	16	yes	—
79	#103×C₆₇	C₂³	1	8	yes	—
80	C₄×C₈×C₆₇	C₂³	1	8	yes	—
81	C₄×C₈×C₆₇	C₂³	1	4	yes	—
82	C₂×Q₈×C₆₇	—	2	4	no	—
83	C₂×Q₈×C₆₇	—	2	2	no	—
84	C₂×Q₈×C₆₇	—	2	8	no	—
85	C₂×Q₈×C₆₇	—	2	4	no	—
86	C₂×Q₈×C₆₇	—	4	8	no	—
87	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
88	C₂×Q₈×C₆₇	C₂×Q₈	1	8	yes	—
89	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
90	C₂²×C₄×C₆₇	—	2	2	no	—
91	C₂²×C₄×C₆₇	—	2	2	no	—
92	C₂²×C₄×C₆₇	—	2	4	no	—
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	2	yes	—
96	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
98	Q₁₆×C₆₇	C₂×Q₈	1	16	yes	complemented
99	C₂×C₈×C₆₇	—	2	4	no	—
100	C₂×C₈×C₆₇	—	2	2	no	—
101	C₂×C₈×C₆₇	C₂×Q₈	1	4	yes	—
102	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
103	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
104	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
105	C₄⋊C₄×C₆₇	—	2	16	no	—
106	C₄⋊C₄×C₆₇	—	2	8	no	—
107	C₄⋊C₄×C₆₇	—	2	16	no	—
108	C₄⋊C₄×C₆₇	—	2	8	no	—
109	C₄⋊C₄×C₆₇	—	2	16	no	—
110	C₄⋊C₄×C₆₇	—	2	2	no	—
111	C₄⋊C₄×C₆₇	—	2	4	no	—
112	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
113	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
114	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
115	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
116	C₄²×C₆₇	—	2	16	no	—
117	C₄²×C₆₇	—	2	8	no	—
118	C₄²×C₆₇	C₂×D₄	1	4	yes	—
119	C₄²×C₆₇	C₂×D₄	1	2	yes	—
120	C₄²×C₆₇	C₂⁴	1	4	yes	—
121	C₄²×C₆₇	C₂⁴	1	2	yes	—
122	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
123	Q₈×C₆₇	—	2	8	no	—
124	Q₈×C₆₇	—	2	8	no	—
125	Q₈×C₆₇	—	2	4	no	—
126	Q₈×C₆₇	—	4	16	no	—
127	Q₈×C₆₇	C₂²×Q₈	1	8	yes	—
128	C₂×C₄×C₆₇	—	2	8	no	—
129	C₂×C₄×C₆₇	—	2	4	no	—
130	C₂×C₄×C₆₇	—	2	4	no	—
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	2	4	no	—
133	C₂×C₄×C₆₇	—	2	4	no	—
134	C₂×C₄×C₆₇	—	2	8	no	—
135	C₂×C₄×C₆₇	—	4	8	no	—
136	C₂×C₄×C₆₇	—	4	4	no	—
137	C₂×C₄×C₆₇	#135	1	4	yes	—
138	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
139	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
140	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
141	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
143	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
144	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
145	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
146	C₈×C₆₇	—	2	4	no	—
147	C₈×C₆₇	—	2	2	no	—
148	C₈×C₆₇	C₂²×Q₈	1	4	yes	—
149	C₂²×C₆₇	D₄×Q₈	1	2	yes	—
150	C₂²×C₆₇	C₂×#135	1	2	yes	—
151	C₂²×C₆₇	#578	1	2	yes	—
152	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
153	C₄×C₆₇	—	2	8	no	—
154	C₄×C₆₇	—	2	4	no	—
155	C₄×C₆₇	—	2	4	no	—
156	C₄×C₆₇	—	2	2	no	—
157	C₄×C₆₇	—	4	8	no	—
158	C₄×C₆₇	—	4	4	no	—
159	C₄×C₆₇	D₄×Q₈	1	2	yes	—
160	C₄×C₆₇	C₂×#135	1	4	yes	—
161	C₄×C₆₇	C₂³×Q₈	1	1	yes	characteristic
162	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
163	C₂×#3383	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂×C₆₇	#3383	1	4	yes	direct product factor
165	C₂×C₆₇	C₂×D₄×Q₈	1	1	yes	characteristic
166	C₂×C₆₇	C₂²×#135	1	1	yes	characteristic
167	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
168	C₂×#557	C₂×C₆₇	1	2	yes	—
169	#3383	C₂×C₆₇	1	16	yes	direct product factor
170	C₂×#500	C₂×C₆₇	1	1	yes	characteristic
171	C₂×#499	C₂×C₆₇	1	2	yes	—
172	C₂×#479	C₂×C₆₇	1	4	yes	—
173	C₂×#475	C₂×C₆₇	1	2	yes	—
174	C₂×C₈×Q₈	C₂×C₆₇	1	1	yes	characteristic
175	C₂×C₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic
176	C₂×C₄×Q₁₆	C₂×C₆₇	1	2	yes	—
177	C₆₇	C₂×#3383	1	1	yes	characteristic, direct product factor, Sylow
178	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
179	#557	—	2	8	no	—
180	#557	C₂²×C₆₇	1	16	yes	—
181	C₂×C₄⋊Q₈	—	2	2	no	—
182	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
183	C₂×#125	—	2	4	no	—
184	C₂×#125	C₂²×C₆₇	1	4	yes	—
185	C₂×C₄×Q₈	—	2	2	no	—
186	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
187	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	—
188	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
189	#500	C₂²×C₆₇	1	8	yes	—
190	#499	C₂²×C₆₇	1	16	yes	—
191	#479	C₂²×C₆₇	1	32	yes	—
192	#475	C₂²×C₆₇	1	16	yes	—
193	C₈×Q₈	C₂²×C₆₇	1	8	yes	—
194	C₄×Q₁₆	C₂²×C₆₇	1	16	yes	—
195	C₄×Q₁₆	C₂²×C₆₇	1	8	yes	—
196	C₂×#107	C₂²×C₆₇	1	2	yes	—
197	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
198	C₂×#107	C₂²×C₆₇	1	2	yes	—
199	C₂×#106	C₂²×C₆₇	1	4	yes	—
200	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
201	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
202	C₂×#103	C₂²×C₆₇	1	4	yes	—
203	C₂×#103	C₂²×C₆₇	1	2	yes	—
204	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
205	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
206	C₂²×Q₈	—	2	2	no	—
207	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
208	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
209	C₂×Q₁₆	Q₈×C₆₇	1	8	yes	complemented
210	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
211	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
212	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
214	C₄⋊Q₈	—	2	16	no	—
215	C₄⋊Q₈	—	2	4	no	—
216	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
217	#125	—	2	32	no	—
218	#125	—	2	8	no	—
219	#125	C₂³×C₆₇	1	16	yes	—
220	C₄×Q₈	—	2	16	no	—
221	C₄×Q₈	—	2	8	no	—
222	C₄×Q₈	—	2	4	no	—
223	C₄×Q₈	D₄×C₆₇	1	4	yes	—
224	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
225	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
226	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
227	C₂×C₄⋊C₄	—	2	4	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
233	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
234	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
239	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
240	#107	C₂³×C₆₇	1	4	yes	—
241	#107	C₂³×C₆₇	1	8	yes	—
242	#107	C₂³×C₆₇	1	8	yes	—
243	#106	C₂³×C₆₇	1	16	yes	—
244	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
245	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
246	#103	C₂³×C₆₇	1	16	yes	—
247	#103	C₂³×C₆₇	1	8	yes	—
248	C₄×C₈	C₂³×C₆₇	1	8	yes	—
249	C₄×C₈	C₂³×C₆₇	1	4	yes	—
250	C₂×Q₈	—	2	4	no	—
251	C₂×Q₈	—	2	2	no	—
252	C₂×Q₈	—	2	8	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	—	4	8	no	—
255	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
256	C₂×Q₈	C₂×Q₈×C₆₇	1	8	yes	—
257	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
262	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
265	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
266	Q₁₆	C₂×Q₈×C₆₇	1	16	yes	complemented
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	C₂×Q₈×C₆₇	1	4	yes	—
270	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
271	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
272	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
273	C₄⋊C₄	—	2	16	no	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	16	no	—
276	C₄⋊C₄	—	2	8	no	—
277	C₄⋊C₄	—	2	16	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
281	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
282	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
283	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
284	C₄²	—	2	16	no	—
285	C₄²	—	2	8	no	—
286	C₄²	C₂×D₄×C₆₇	1	4	yes	—
287	C₄²	C₂×D₄×C₆₇	1	2	yes	—
288	C₄²	C₂⁴×C₆₇	1	4	yes	—
289	C₄²	C₂⁴×C₆₇	1	2	yes	—
290	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
291	Q₈	—	2	8	no	—
292	Q₈	—	2	8	no	—
293	Q₈	—	2	4	no	—
294	Q₈	—	4	16	no	—
295	Q₈	C₂²×Q₈×C₆₇	1	8	yes	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	4	4	no	—
305	C₂×C₄	#135×C₆₇	1	4	yes	—
306	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
307	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
308	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
310	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
311	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
312	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
313	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
314	C₈	—	2	4	no	—
315	C₈	—	2	2	no	—
316	C₈	C₂²×Q₈×C₆₇	1	4	yes	—
317	C₂²	D₄×Q₈×C₆₇	1	2	yes	—
318	C₂²	C₂×#135×C₆₇	1	2	yes	—
319	C₂²	#578×C₆₇	1	2	yes	—
320	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
321	C₄	—	2	4	no	—
322	C₄	—	2	4	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	8	no	—
325	C₄	—	4	8	no	—
326	C₄	—	4	4	no	—
327	C₄	D₄×Q₈×C₆₇	1	2	yes	—
328	C₄	C₂×#135×C₆₇	1	4	yes	—
329	C₄	C₂³×Q₈×C₆₇	1	1	yes	characteristic
330	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
331	C₂	C₆₇×#3383	1	4	yes	direct product factor
332	C₂	C₂×D₄×Q₈×C₆₇	1	1	yes	characteristic
333	C₂	C₂²×#135×C₆₇	1	1	yes	characteristic
334	C₂	C₂×#578×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄×Q₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3383	C₂	direct (N × H)
41. C₂×Q₁₆×C₆₇	Q₈	semidirect
98. Q₁₆×C₆₇	C₂×Q₈	semidirect
163. C₂×#3383	C₆₇	direct (N × H)
164. C₂×C₆₇	#3383	direct (N × H)
169. #3383	C₂×C₆₇	direct (N × H)
177. C₆₇	C₂×#3383	direct (N × H)
209. C₂×Q₁₆	Q₈×C₆₇	semidirect
266. Q₁₆	C₂×Q₈×C₆₇	semidirect
331. C₂	C₆₇×#3383	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#557×C₆₇	2
C₆₇×#3383	2
C₂×#500×C₆₇	2
C₂×#499×C₆₇	2
C₂×#479×C₆₇	2
C₂×#475×C₆₇	2
C₂×C₈×Q₈×C₆₇	2
C₂×C₄×Q₁₆×C₆₇	2
C₂×#3383	67

Subgroups — C2×C67×#3383 #30740607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3383 #30740607