Subgroups — C₆₇×#25987 #30705238

Order 17152.

850 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3083	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2898	C₂	1	2	yes	maximal
3	C₆₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2064	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2028	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1866	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1859	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1816	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1793	C₂	1	1	yes	maximal, characteristic
10	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×#131×C₆₇	C₂²	1	2	yes	—
12	#544×C₆₇	C₂²	1	1	yes	characteristic
13	#520×C₆₇	C₂²	1	2	yes	—
14	#479×C₆₇	—	2	2	no	—
15	#478×C₆₇	—	2	2	no	—
16	#477×C₆₇	—	2	2	no	—
17	#474×C₆₇	—	2	2	no	—
18	C₂×#108×C₆₇	C₂²	1	2	yes	—
19	#428×C₆₇	C₂²	1	2	yes	—
20	C₂×#107×C₆₇	C₂²	1	2	yes	—
21	#424×C₆₇	C₂²	1	2	yes	—
22	C₂×#104×C₆₇	C₂²	1	2	yes	—
23	#419×C₆₇	—	2	2	no	—
24	#419×C₆₇	C₂²	1	2	yes	—
25	#417×C₆₇	—	2	2	no	—
26	#417×C₆₇	C₂²	1	2	yes	—
27	#417×C₆₇	C₂²	1	2	yes	—
28	#416×C₆₇	—	2	2	no	—
29	#416×C₆₇	C₂²	1	2	yes	—
30	C₂×#103×C₆₇	—	2	2	no	—
31	C₂×#103×C₆₇	C₂²	1	2	yes	—
32	C₂×#101×C₆₇	C₂²	1	1	yes	characteristic
33	#391×C₆₇	C₂²	1	1	yes	characteristic
34	#384×C₆₇	C₂²	1	1	yes	characteristic
35	#343×C₆₇	C₂²	1	1	yes	characteristic
36	#343×C₆₇	C₂²	1	2	yes	—
37	#339×C₆₇	C₂²	1	2	yes	—
38	#336×C₆₇	C₂²	1	1	yes	characteristic
39	2₋¹⁺⁴×C₆₇	—	2	4	no	—
40	2₋¹⁺⁴×C₆₇	—	4	1	no	—
41	2₋¹⁺⁴×C₆₇	Q₈	1	4	yes	complemented
42	C₂×#41×C₆₇	—	2	2	no	—
43	C₂×#41×C₆₇	—	4	1	no	—
44	C₂×#41×C₆₇	C₂³	1	2	yes	—
45	C₂²×Q₈×C₆₇	—	2	2	no	—
46	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
47	#131×C₆₇	—	2	4	no	—
48	#131×C₆₇	—	4	2	no	—
49	C₂×M₁₆×C₆₇	—	2	2	no	—
50	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
51	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₆₇	—	2	2	no	—
53	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₆₇	—	2	2	no	—
55	#125×C₆₇	—	2	2	no	—
56	C₂²⋊Q₈×C₆₇	—	4	1	no	—
57	C₄×Q₈×C₆₇	—	2	2	no	—
58	C₄×D₄×C₆₇	—	2	2	no	—
59	C₄×D₄×C₆₇	—	4	2	no	—
60	#117×C₆₇	—	2	2	no	—
61	#117×C₆₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₇	—	4	1	no	—
64	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
67	#108×C₆₇	—	4	2	no	—
68	#107×C₆₇	—	2	2	no	—
69	#107×C₆₇	—	2	2	no	—
70	#107×C₆₇	—	2	2	no	—
71	#106×C₆₇	—	2	2	no	—
72	C₄⋊C₈×C₆₇	—	2	2	no	—
73	C₄⋊C₈×C₆₇	—	2	2	no	—
74	#104×C₆₇	—	2	4	no	—
75	#103×C₆₇	—	2	2	no	—
76	#103×C₆₇	—	2	2	no	—
77	#103×C₆₇	—	2	2	no	—
78	#103×C₆₇	—	2	2	no	—
79	#103×C₆₇	—	2	2	no	—
80	#103×C₆₇	—	2	2	no	—
81	#103×C₆₇	D₄	1	2	yes	—
82	#103×C₆₇	D₄	1	2	yes	—
83	#102×C₆₇	—	2	2	no	—
84	#102×C₆₇	—	2	2	no	—
85	#102×C₆₇	D₄	1	2	yes	—
86	#102×C₆₇	D₄	1	2	yes	—
87	#101×C₆₇	—	4	1	no	—
88	#95×C₆₇	—	4	1	no	—
89	#41×C₆₇	—	2	2	no	—
90	#41×C₆₇	—	2	2	no	—
91	#41×C₆₇	—	2	8	no	—
92	#41×C₆₇	—	4	4	no	—
93	#41×C₆₇	—	4	4	no	—
94	#41×C₆₇	—	4	4	no	—
95	#41×C₆₇	C₂×Q₈	1	4	yes	—
96	#41×C₆₇	#41	1	4	yes	—
97	C₂×Q₈×C₆₇	—	2	1	no	—
98	C₂×Q₈×C₆₇	—	2	8	no	—
99	C₂×Q₈×C₆₇	—	2	2	no	—
100	C₂×Q₈×C₆₇	—	2	2	no	—
101	C₂×Q₈×C₆₇	—	4	1	no	—
102	C₂×Q₈×C₆₇	—	4	1	no	—
103	C₂×Q₈×C₆₇	—	4	4	no	—
104	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₆₇	C₂×Q₈	1	2	yes	—
106	C₂×D₄×C₆₇	—	2	2	no	—
107	C₂×D₄×C₆₇	—	4	1	no	—
108	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₆₇	—	2	2	no	—
110	C₂²×C₄×C₆₇	—	2	1	no	—
111	C₂²×C₄×C₆₇	—	2	1	no	—
112	C₂²×C₄×C₆₇	—	2	2	no	—
113	C₂²×C₄×C₆₇	—	2	1	no	—
114	C₂²×C₄×C₆₇	—	4	2	no	—
115	C₂²×C₄×C₆₇	—	4	2	no	—
116	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
117	M₁₆×C₆₇	—	2	2	no	—
118	M₁₆×C₆₇	—	2	2	no	—
119	M₁₆×C₆₇	—	2	2	no	—
120	M₁₆×C₆₇	—	2	2	no	—
121	M₁₆×C₆₇	—	4	4	no	—
122	C₂×C₈×C₆₇	—	2	2	no	—
123	C₂×C₈×C₆₇	—	2	2	no	—
124	C₂×C₈×C₆₇	—	2	2	no	—
125	C₂×C₈×C₆₇	—	2	2	no	—
126	C₂×C₈×C₆₇	—	4	4	no	—
127	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₆₇	—	2	2	no	—
130	C₄⋊C₄×C₆₇	—	2	2	no	—
131	C₄⋊C₄×C₆₇	—	2	2	no	—
132	C₄⋊C₄×C₆₇	—	4	2	no	—
133	C₄⋊C₄×C₆₇	—	4	1	no	—
134	C₄⋊C₄×C₆₇	—	4	2	no	—
135	C₄⋊C₄×C₆₇	—	8	2	no	—
136	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
138	C₂²⋊C₄×C₆₇	—	2	2	no	—
139	C₂²⋊C₄×C₆₇	—	4	2	no	—
140	C₄²×C₆₇	—	2	2	no	—
141	C₄²×C₆₇	—	2	2	no	—
142	C₄²×C₆₇	—	4	2	no	—
143	C₂³×C₆₇	—	2	2	no	—
144	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
145	Q₈×C₆₇	—	2	2	no	—
146	Q₈×C₆₇	—	2	4	no	—
147	Q₈×C₆₇	—	4	4	no	—
148	Q₈×C₆₇	—	4	2	no	—
149	Q₈×C₆₇	—	16	1	no	—
150	Q₈×C₆₇	C₂²⋊Q₈	1	4	yes	—
151	D₄×C₆₇	—	2	4	no	—
152	D₄×C₆₇	—	2	4	no	—
153	D₄×C₆₇	—	2	2	no	—
154	D₄×C₆₇	—	4	4	no	—
155	D₄×C₆₇	C₂²⋊Q₈	1	4	yes	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	2	4	no	—
158	C₂×C₄×C₆₇	—	2	4	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	4	8	no	—
164	C₂×C₄×C₆₇	—	4	1	no	—
165	C₂×C₄×C₆₇	—	4	1	no	—
166	C₂×C₄×C₆₇	—	4	1	no	—
167	C₂×C₄×C₆₇	—	4	1	no	—
168	C₂×C₄×C₆₇	—	4	2	no	—
169	C₂×C₄×C₆₇	—	4	1	no	—
170	C₂×C₄×C₆₇	—	8	2	no	—
171	C₂×C₄×C₆₇	—	8	1	no	—
172	C₂×C₄×C₆₇	—	16	2	no	—
173	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
174	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
176	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
177	C₈×C₆₇	—	2	2	no	—
178	C₈×C₆₇	—	2	2	no	—
179	C₈×C₆₇	—	4	2	no	—
180	C₈×C₆₇	—	4	2	no	—
181	C₂²×C₆₇	—	2	1	no	—
182	C₂²×C₆₇	—	2	1	no	—
183	C₂²×C₆₇	—	2	4	no	—
184	C₂²×C₆₇	—	4	2	no	—
185	C₂²×C₆₇	—	4	2	no	—
186	C₂²×C₆₇	#543	1	1	yes	characteristic
187	C₂²×C₆₇	D₄²	1	1	yes	characteristic
188	C₂²×C₆₇	#551	1	1	yes	characteristic
189	C₄×C₆₇	—	2	4	no	—
190	C₄×C₆₇	—	4	2	no	—
191	C₄×C₆₇	—	4	2	no	—
192	C₄×C₆₇	—	4	2	no	—
193	C₄×C₆₇	—	4	2	no	—
194	C₄×C₆₇	—	8	2	no	—
195	C₄×C₆₇	—	8	1	no	—
196	C₄×C₆₇	C₂×C₂²⋊Q₈	1	2	yes	—
197	C₄×C₆₇	#546	1	2	yes	—
198	#25987	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂×C₆₇	—	2	1	no	—
200	C₂×C₆₇	—	2	1	no	—
201	C₂×C₆₇	—	4	4	no	—
202	C₂×C₆₇	#2437	1	1	yes	characteristic
203	C₂×C₆₇	#3288	1	1	yes	characteristic
204	C₂×C₆₇	#3293	1	1	yes	characteristic
205	#3083	C₂×C₆₇	1	2	yes	complemented
206	#2898	C₂×C₆₇	1	2	yes	—
207	#2095	C₂×C₆₇	1	1	yes	characteristic, complemented
208	#2064	C₂×C₆₇	1	2	yes	complemented
209	#2028	C₂×C₆₇	1	1	yes	characteristic, complemented
210	#1866	C₂×C₆₇	1	2	yes	complemented
211	#1859	C₂×C₆₇	1	2	yes	complemented
212	#1816	C₂×C₆₇	1	2	yes	complemented
213	#1793	C₂×C₆₇	1	1	yes	characteristic
214	C₆₇	#25987	1	1	yes	characteristic, direct product factor, Sylow
215	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
216	C₂×#131	C₂²×C₆₇	1	2	yes	—
217	#544	C₂²×C₆₇	1	1	yes	characteristic
218	#520	C₂²×C₆₇	1	2	yes	—
219	#479	—	2	2	no	—
220	#478	—	2	2	no	—
221	#477	—	2	2	no	—
222	#474	—	2	2	no	—
223	C₂×#108	C₂²×C₆₇	1	2	yes	—
224	#428	C₂²×C₆₇	1	2	yes	—
225	C₂×#107	C₂²×C₆₇	1	2	yes	—
226	#424	C₂²×C₆₇	1	2	yes	—
227	C₂×#104	C₂²×C₆₇	1	2	yes	—
228	#419	—	2	2	no	—
229	#419	C₂²×C₆₇	1	2	yes	—
230	#417	—	2	2	no	—
231	#417	C₂²×C₆₇	1	2	yes	—
232	#417	C₂²×C₆₇	1	2	yes	—
233	#416	—	2	2	no	—
234	#416	C₂²×C₆₇	1	2	yes	—
235	C₂×#103	—	2	2	no	—
236	C₂×#103	C₂²×C₆₇	1	2	yes	—
237	C₂×#101	C₂²×C₆₇	1	1	yes	characteristic
238	#391	C₂²×C₆₇	1	1	yes	characteristic
239	#384	C₂²×C₆₇	1	1	yes	characteristic
240	#343	C₂²×C₆₇	1	2	yes	—
241	#343	C₂²×C₆₇	1	1	yes	characteristic
242	#339	C₂²×C₆₇	1	2	yes	—
243	#336	C₂²×C₆₇	1	1	yes	characteristic
244	2₋¹⁺⁴	—	2	4	no	—
245	2₋¹⁺⁴	—	4	1	no	—
246	2₋¹⁺⁴	Q₈×C₆₇	1	4	yes	complemented
247	C₂×#41	—	2	2	no	—
248	C₂×#41	—	4	1	no	—
249	C₂×#41	C₂³×C₆₇	1	2	yes	—
250	C₂²×Q₈	—	2	2	no	—
251	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
252	#131	—	2	4	no	—
253	#131	—	4	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
256	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
259	C₄⋊Q₈	—	2	2	no	—
260	#125	—	2	2	no	—
261	C₂²⋊Q₈	—	4	1	no	—
262	C₄×Q₈	—	2	2	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	4	2	no	—
265	#117	—	2	2	no	—
266	#117	C₂³×C₆₇	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	4	1	no	—
269	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
272	#108	—	4	2	no	—
273	#107	—	2	2	no	—
274	#107	—	2	2	no	—
275	#107	—	2	2	no	—
276	#106	—	2	2	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	#104	—	2	4	no	—
280	#103	—	2	2	no	—
281	#103	—	2	2	no	—
282	#103	—	2	2	no	—
283	#103	—	2	2	no	—
284	#103	—	2	2	no	—
285	#103	—	2	2	no	—
286	#103	D₄×C₆₇	1	2	yes	—
287	#103	D₄×C₆₇	1	2	yes	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#102	D₄×C₆₇	1	2	yes	—
291	#102	D₄×C₆₇	1	2	yes	—
292	#101	—	4	1	no	—
293	#95	—	4	1	no	—
294	#41	—	2	2	no	—
295	#41	—	2	2	no	—
296	#41	—	2	8	no	—
297	#41	—	4	4	no	—
298	#41	—	4	4	no	—
299	#41	—	4	4	no	—
300	#41	C₂×Q₈×C₆₇	1	4	yes	—
301	#41	#41×C₆₇	1	4	yes	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	8	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×Q₈	—	4	4	no	—
309	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
310	C₂×Q₈	C₂×Q₈×C₆₇	1	2	yes	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	4	4	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	4	4	no	—
332	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
333	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	8	2	no	—
341	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
342	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
350	Q₈	—	2	2	no	—
351	Q₈	—	2	4	no	—
352	Q₈	—	4	4	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	16	1	no	—
355	Q₈	C₂²⋊Q₈×C₆₇	1	4	yes	—
356	D₄	—	2	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	4	no	—
360	D₄	C₂²⋊Q₈×C₆₇	1	4	yes	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	—	16	2	no	—
378	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
379	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
381	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	#543×C₆₇	1	1	yes	characteristic
392	C₂²	D₄²×C₆₇	1	1	yes	characteristic
393	C₂²	#551×C₆₇	1	1	yes	characteristic
394	C₄	—	2	4	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	1	no	—
401	C₄	C₂×C₂²⋊Q₈×C₆₇	1	2	yes	—
402	C₄	#546×C₆₇	1	2	yes	—
403	C₂	—	2	1	no	—
404	C₂	—	2	1	no	—
405	C₂	—	4	4	no	—
406	C₂	C₆₇×#2437	1	1	yes	characteristic
407	C₂	C₆₇×#3288	1	1	yes	characteristic
408	C₂	C₆₇×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×2₋¹⁺⁴×C₆₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3083	C₂	semidirect
3. C₆₇×#2095	C₂	semidirect
4. C₆₇×#2064	C₂	semidirect
5. C₆₇×#2028	C₂	semidirect
6. C₆₇×#1866	C₂	semidirect
7. C₆₇×#1859	C₂	semidirect
8. C₆₇×#1816	C₂	semidirect
41. 2₋¹⁺⁴×C₆₇	Q₈	semidirect
198. #25987	C₆₇	direct (N × H)
205. #3083	C₂×C₆₇	semidirect
207. #2095	C₂×C₆₇	semidirect
208. #2064	C₂×C₆₇	semidirect
209. #2028	C₂×C₆₇	semidirect
210. #1866	C₂×C₆₇	semidirect
211. #1859	C₂×C₆₇	semidirect
212. #1816	C₂×C₆₇	semidirect
214. C₆₇	#25987	direct (N × H)
246. 2₋¹⁺⁴	Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3083	2
C₆₇×#2898	2
C₆₇×#2095	2
C₆₇×#2064	2
C₆₇×#2028	2
C₆₇×#1866	2
C₆₇×#1859	2
C₆₇×#1816	2
C₆₇×#1793	2
#25987	67

Subgroups — C67×#25987 #30705238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#25987 #30705238