Subgroups — C₆₇×#33189 #30712440

Order 17152.

1030 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#492×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#471×C₆₇	C₂	1	4	yes	maximal, complemented
3	C₆₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3038	C₂	1	1	yes	maximal, characteristic
5	C₄×#131×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1977	C₂	1	4	yes	maximal, complemented
7	C₆₇×#1966	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1848	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₆₇	C₂²	1	2	yes	—
11	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	—
13	C₂×#131×C₆₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
16	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
17	#492×C₆₇	—	2	1	no	—
18	#492×C₆₇	—	2	1	no	—
19	#492×C₆₇	—	2	2	no	—
20	#471×C₆₇	—	2	16	no	—
21	#462×C₆₇	—	2	2	no	—
22	#461×C₆₇	—	2	2	no	—
23	#460×C₆₇	—	2	2	no	—
24	#459×C₆₇	—	2	2	no	—
25	C₂×#108×C₆₇	C₂²	1	4	yes	—
26	#423×C₆₇	C₂²	1	1	yes	characteristic
27	#423×C₆₇	C₂²	1	1	yes	characteristic
28	#419×C₆₇	C₂²	1	2	yes	—
29	#418×C₆₇	C₂²	1	2	yes	—
30	C₂×#101×C₆₇	C₂²	1	4	yes	—
31	C₂×#100×C₆₇	C₂²	1	4	yes	—
32	#405×C₆₇	—	2	2	no	—
33	#405×C₆₇	C₂²	1	2	yes	—
34	C₄×M₁₆×C₆₇	—	2	1	no	—
35	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₆₇	—	2	1	no	—
37	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
39	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
40	C₂²×D₄×C₆₇	—	2	2	no	—
41	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
42	#137×C₆₇	—	2	8	no	—
43	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
44	C₂×Q₁₆×C₆₇	—	2	2	no	—
45	C₂×SD₁₆×C₆₇	—	2	2	no	—
46	C₂×SD₁₆×C₆₇	—	2	2	no	—
47	C₂×SD₁₆×C₆₇	—	2	8	no	—
48	C₂×SD₁₆×C₆₇	—	2	4	no	—
49	C₂×SD₁₆×C₆₇	—	2	4	no	—
50	C₂×SD₁₆×C₆₇	—	2	8	no	—
51	C₂×D₈×C₆₇	—	2	2	no	—
52	#131×C₆₇	—	2	4	no	—
53	#131×C₆₇	D₄	1	8	yes	complemented
54	C₂×M₁₆×C₆₇	—	2	2	no	—
55	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
56	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
57	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₇	—	2	2	no	—
59	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
60	C₄⋊Q₈×C₆₇	—	2	2	no	—
61	C₄⋊Q₈×C₆₇	—	2	1	no	—
62	C₄⋊Q₈×C₆₇	—	2	1	no	—
63	#127×C₆₇	—	2	2	no	—
64	#127×C₆₇	—	2	1	no	—
65	#127×C₆₇	—	2	1	no	—
66	C₄×Q₈×C₆₇	D₄	1	2	yes	—
67	C₄×D₄×C₆₇	—	2	2	no	—
68	C₄×D₄×C₆₇	D₄	1	2	yes	—
69	#117×C₆₇	—	2	1	no	—
70	#117×C₆₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
72	C₂×C₄²×C₆₇	—	2	1	no	—
73	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
74	#108×C₆₇	—	2	8	no	—
75	C₄⋊C₈×C₆₇	—	2	2	no	—
76	C₄⋊C₈×C₆₇	—	2	2	no	—
77	#103×C₆₇	—	2	4	no	—
78	#102×C₆₇	—	2	4	no	—
79	#101×C₆₇	—	2	8	no	—
80	#100×C₆₇	—	2	8	no	—
81	#97×C₆₇	—	2	2	no	—
82	#97×C₆₇	—	2	1	no	—
83	C₄×C₈×C₆₇	—	2	2	no	—
84	C₄×C₈×C₆₇	—	2	1	no	—
85	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
86	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
87	C₄×C₈×C₆₇	D₄	1	2	yes	—
88	C₂⁴×C₆₇	—	2	2	no	—
89	#41×C₆₇	—	2	2	no	—
90	#41×C₆₇	C₂×D₄	1	4	yes	—
91	C₂×Q₈×C₆₇	—	2	4	no	—
92	C₂×Q₈×C₆₇	—	2	2	no	—
93	C₂×Q₈×C₆₇	—	2	2	no	—
94	C₂×Q₈×C₆₇	—	2	4	no	—
95	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
96	C₂×D₄×C₆₇	—	2	1	no	—
97	C₂×D₄×C₆₇	—	2	4	no	—
98	C₂×D₄×C₆₇	—	2	2	no	—
99	C₂×D₄×C₆₇	—	2	2	no	—
100	C₂×D₄×C₆₇	—	2	4	no	—
101	C₂×D₄×C₆₇	—	4	2	no	—
102	C₂×D₄×C₆₇	—	4	2	no	—
103	C₂×D₄×C₆₇	—	8	4	no	—
104	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₆₇	—	2	1	no	—
106	C₂²×C₄×C₆₇	—	2	2	no	—
107	C₂²×C₄×C₆₇	—	2	2	no	—
108	C₂²×C₄×C₆₇	#41	1	2	yes	—
109	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₆₇	—	4	4	no	—
111	SD₁₆×C₆₇	—	4	4	no	—
112	SD₁₆×C₆₇	—	4	4	no	—
113	SD₁₆×C₆₇	—	4	8	no	—
114	SD₁₆×C₆₇	—	4	8	no	—
115	D₈×C₆₇	—	4	4	no	—
116	M₁₆×C₆₇	—	2	2	no	—
117	M₁₆×C₆₇	—	2	8	no	—
118	M₁₆×C₆₇	—	2	4	no	—
119	M₁₆×C₆₇	—	2	4	no	—
120	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
121	C₂×C₈×C₆₇	—	2	2	no	—
122	C₂×C₈×C₆₇	—	2	8	no	—
123	C₂×C₈×C₆₇	—	2	2	no	—
124	C₂×C₈×C₆₇	—	2	2	no	—
125	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
126	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₆₇	#41	1	4	yes	—
129	C₄⋊C₄×C₆₇	—	2	2	no	—
130	C₄⋊C₄×C₆₇	—	4	2	no	—
131	C₄⋊C₄×C₆₇	—	4	2	no	—
132	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
133	C₂²⋊C₄×C₆₇	—	2	1	no	—
134	C₂²⋊C₄×C₆₇	—	2	2	no	—
135	C₄²×C₆₇	—	2	2	no	—
136	C₄²×C₆₇	—	2	1	no	—
137	C₄²×C₆₇	C₂×D₄	1	2	yes	—
138	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂³×C₆₇	—	2	1	no	—
141	C₂³×C₆₇	—	4	2	no	—
142	C₂³×C₆₇	—	4	4	no	—
143	C₂³×C₆₇	—	8	4	no	—
144	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
145	Q₈×C₆₇	—	2	1	no	—
146	Q₈×C₆₇	—	4	4	no	—
147	Q₈×C₆₇	—	4	2	no	—
148	Q₈×C₆₇	—	4	2	no	—
149	Q₈×C₆₇	#127	1	2	yes	—
150	D₄×C₆₇	—	2	4	no	—
151	D₄×C₆₇	—	2	1	no	—
152	D₄×C₆₇	—	4	4	no	—
153	D₄×C₆₇	—	4	2	no	—
154	D₄×C₆₇	—	4	2	no	—
155	D₄×C₆₇	—	8	4	no	—
156	D₄×C₆₇	—	8	4	no	—
157	D₄×C₆₇	#127	1	2	yes	—
158	C₂×C₄×C₆₇	—	2	1	no	—
159	C₂×C₄×C₆₇	—	2	4	no	—
160	C₂×C₄×C₆₇	—	2	4	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	4	4	no	—
163	C₂×C₄×C₆₇	—	4	2	no	—
164	C₂×C₄×C₆₇	—	4	4	no	—
165	C₂×C₄×C₆₇	#121	1	2	yes	—
166	C₂×C₄×C₆₇	#121	1	2	yes	—
167	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
171	C₈×C₆₇	—	2	4	no	—
172	C₈×C₆₇	—	4	2	no	—
173	C₈×C₆₇	—	4	2	no	—
174	C₈×C₆₇	#121	1	4	yes	—
175	C₈×C₆₇	#121	1	4	yes	—
176	C₂²×C₆₇	—	2	2	no	—
177	C₂²×C₆₇	—	2	2	no	—
178	C₂²×C₆₇	—	4	2	no	—
179	C₂²×C₆₇	—	8	2	no	—
180	C₂²×C₆₇	—	8	4	no	—
181	C₂²×C₆₇	—	16	4	no	—
182	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
183	C₂²×C₆₇	#532	1	2	yes	—
184	C₄×C₆₇	—	2	2	no	—
185	C₄×C₆₇	—	2	2	no	—
186	C₄×C₆₇	—	4	2	no	—
187	C₄×C₆₇	—	8	2	no	—
188	C₄×C₆₇	#471	1	4	yes	complemented
189	C₄×C₆₇	C₂×#121	1	2	yes	—
190	C₄×C₆₇	C₂×#127	1	1	yes	characteristic
191	C₄×C₆₇	#532	1	1	yes	characteristic
192	#33189	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂×C₆₇	—	2	2	no	—
194	C₂×C₆₇	—	4	2	no	—
195	C₂×C₆₇	—	16	2	no	—
196	C₂×C₆₇	#2856	1	1	yes	characteristic
197	C₂×C₆₇	C₂×#471	1	2	yes	—
198	C₂×#492	C₂×C₆₇	1	1	yes	characteristic, complemented
199	C₂×#471	C₂×C₆₇	1	4	yes	complemented
200	#3039	C₂×C₆₇	1	1	yes	characteristic, complemented
201	#3038	C₂×C₆₇	1	1	yes	characteristic
202	C₄×#131	C₂×C₆₇	1	1	yes	characteristic, complemented
203	#1977	C₂×C₆₇	1	4	yes	complemented
204	#1966	C₂×C₆₇	1	1	yes	characteristic, complemented
205	#1965	C₂×C₆₇	1	1	yes	characteristic, complemented
206	#1848	C₂×C₆₇	1	1	yes	characteristic, complemented
207	C₆₇	#33189	1	1	yes	characteristic, direct product factor, Sylow
208	C₂×#137	C₂²×C₆₇	1	2	yes	—
209	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
210	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	—
211	C₂×#131	C₂²×C₆₇	1	2	yes	—
212	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
213	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
214	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
215	#492	—	2	1	no	—
216	#492	—	2	1	no	—
217	#492	—	2	2	no	—
218	#471	—	2	16	no	—
219	#462	—	2	2	no	—
220	#461	—	2	2	no	—
221	#460	—	2	2	no	—
222	#459	—	2	2	no	—
223	C₂×#108	C₂²×C₆₇	1	4	yes	—
224	#423	C₂²×C₆₇	1	1	yes	characteristic
225	#423	C₂²×C₆₇	1	1	yes	characteristic
226	#419	C₂²×C₆₇	1	2	yes	—
227	#418	C₂²×C₆₇	1	2	yes	—
228	C₂×#101	C₂²×C₆₇	1	4	yes	—
229	C₂×#100	C₂²×C₆₇	1	4	yes	—
230	#405	—	2	2	no	—
231	#405	C₂²×C₆₇	1	2	yes	—
232	C₄×M₁₆	—	2	1	no	—
233	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
234	C₂×C₄×C₈	—	2	1	no	—
235	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
236	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
237	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
238	C₂²×D₄	—	2	2	no	—
239	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
240	#137	—	2	8	no	—
241	AGL(1,ℤ/8)	—	2	8	no	—
242	C₂×Q₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×SD₁₆	—	2	2	no	—
245	C₂×SD₁₆	—	2	8	no	—
246	C₂×SD₁₆	—	2	4	no	—
247	C₂×SD₁₆	—	2	4	no	—
248	C₂×SD₁₆	—	2	8	no	—
249	C₂×D₈	—	2	2	no	—
250	#131	—	2	4	no	—
251	#131	D₄×C₆₇	1	8	yes	complemented
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
254	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
255	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	#127	—	2	2	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	C₄×Q₈	D₄×C₆₇	1	2	yes	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	D₄×C₆₇	1	2	yes	—
267	#117	—	2	1	no	—
268	#117	C₂³×C₆₇	1	1	yes	characteristic
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
272	#108	—	2	8	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	2	no	—
275	#103	—	2	4	no	—
276	#102	—	2	4	no	—
277	#101	—	2	8	no	—
278	#100	—	2	8	no	—
279	#97	—	2	2	no	—
280	#97	—	2	1	no	—
281	C₄×C₈	—	2	2	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
284	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
285	C₄×C₈	D₄×C₆₇	1	2	yes	—
286	C₂⁴	—	2	2	no	—
287	#41	—	2	2	no	—
288	#41	C₂×D₄×C₆₇	1	4	yes	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	8	4	no	—
302	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	#41×C₆₇	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
308	Q₁₆	—	4	4	no	—
309	SD₁₆	—	4	4	no	—
310	SD₁₆	—	4	4	no	—
311	SD₁₆	—	4	8	no	—
312	SD₁₆	—	4	8	no	—
313	D₈	—	4	4	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	8	no	—
316	M₁₆	—	2	4	no	—
317	M₁₆	—	2	4	no	—
318	M₁₆	C₂×D₄×C₆₇	1	4	yes	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	8	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
324	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
326	C₂×C₈	#41×C₆₇	1	4	yes	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
336	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
337	C₄²	C₂×D₄×C₆₇	1	2	yes	—
338	C₂³	—	2	1	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	8	4	no	—
342	C₂³	C₂×#41×C₆₇	1	1	yes	characteristic
343	Q₈	—	2	1	no	—
344	Q₈	—	4	4	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	2	no	—
347	Q₈	#127×C₆₇	1	2	yes	—
348	D₄	—	2	4	no	—
349	D₄	—	2	1	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	8	4	no	—
354	D₄	—	8	4	no	—
355	D₄	#127×C₆₇	1	2	yes	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	#121×C₆₇	1	2	yes	—
364	C₂×C₄	#121×C₆₇	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
369	C₈	—	2	4	no	—
370	C₈	—	4	2	no	—
371	C₈	—	4	2	no	—
372	C₈	#121×C₆₇	1	4	yes	—
373	C₈	#121×C₆₇	1	4	yes	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	8	4	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	4	no	—
380	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
381	C₂²	#532×C₆₇	1	2	yes	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	#471×C₆₇	1	4	yes	complemented
387	C₄	C₂×#121×C₆₇	1	2	yes	—
388	C₄	C₂×#127×C₆₇	1	1	yes	characteristic
389	C₄	#532×C₆₇	1	1	yes	characteristic
390	C₂	—	2	2	no	—
391	C₂	—	4	2	no	—
392	C₂	—	16	2	no	—
393	C₂	C₆₇×#2856	1	1	yes	characteristic
394	C₂	C₂×#471×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₆₇×#3038	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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. C₂×#492×C₆₇	C₂	semidirect
2. C₂×#471×C₆₇	C₂	semidirect
3. C₆₇×#3039	C₂	semidirect
5. C₄×#131×C₆₇	C₂	semidirect
6. C₆₇×#1977	C₂	semidirect
7. C₆₇×#1966	C₂	semidirect
8. C₆₇×#1965	C₂	semidirect
9. C₆₇×#1848	C₂	semidirect
53. #131×C₆₇	D₄	semidirect
188. C₄×C₆₇	#471	semidirect
192. #33189	C₆₇	direct (N × H)
198. C₂×#492	C₂×C₆₇	semidirect
199. C₂×#471	C₂×C₆₇	semidirect
200. #3039	C₂×C₆₇	semidirect
202. C₄×#131	C₂×C₆₇	semidirect
203. #1977	C₂×C₆₇	semidirect
204. #1966	C₂×C₆₇	semidirect
205. #1965	C₂×C₆₇	semidirect
206. #1848	C₂×C₆₇	semidirect
207. C₆₇	#33189	direct (N × H)
251. #131	D₄×C₆₇	semidirect
386. C₄	#471×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#492×C₆₇	2
C₂×#471×C₆₇	2
C₆₇×#3039	2
C₆₇×#3038	2
C₄×#131×C₆₇	2
C₆₇×#1977	2
C₆₇×#1966	2
C₆₇×#1965	2
C₆₇×#1848	2
#33189	67

Subgroups — C67×#33189 #30712440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33189 #30712440