Subgroups — #30869751

Order 17152.

772 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570703	C₂	1	1	yes	maximal, characteristic
2	#22569127	C₂	1	1	yes	maximal, characteristic
3	#22569078	C₂	1	1	yes	maximal, characteristic, complemented
4	#22561124	C₂	1	1	yes	maximal, characteristic, complemented
5	#22561107	C₂	1	1	yes	maximal, characteristic
6	#22560745	C₂	1	2	yes	maximal, complemented
7	#22560730	C₂	1	2	yes	maximal, complemented
8	#22560704	C₂	1	2	yes	maximal, complemented
9	#22560683	C₂	1	2	yes	maximal, complemented
10	#22560333	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1747	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524076	C₂²	1	2	yes	—
13	C₂×#14524065	C₂²	1	1	yes	characteristic
14	C₂²×Dic₂₆₈	C₂²	1	1	yes	characteristic
15	#16864162	C₂²	1	2	yes	—
16	#16863972	C₂²	1	2	yes	—
17	#16863873	C₂²	1	2	yes	—
18	#16863790	C₄	1	4	yes	complemented
19	#16863780	C₄	1	2	yes	complemented
20	#16863776	C₄	1	2	yes	complemented
21	#16863519	—	2	2	no	—
22	#16863514	—	2	2	no	—
23	#16863504	—	2	2	no	—
24	C₄×Dic₂₆₈	—	2	2	no	—
25	C₂×#14523979	C₂²	1	1	yes	characteristic
26	#16863434	C₂²	1	1	yes	characteristic
27	#16863414	C₂²	1	2	yes	—
28	#16863412	C₂²	1	2	yes	—
29	#16863406	C₂²	1	2	yes	—
30	#16863404	C₂²	1	2	yes	—
31	C₂×#14523961	C₂²	1	2	yes	—
32	#16863369	C₂²	1	2	yes	—
33	#16863167	C₂²	1	2	yes	—
34	#16863152	C₂²	1	2	yes	—
35	#405×C₆₇	C₂²	1	1	yes	characteristic
36	#405×C₆₇	C₂²	1	1	yes	characteristic
37	#405×C₆₇	C₂²	1	1	yes	characteristic
38	#338×C₆₇	C₂²	1	1	yes	characteristic
39	H(3,ℤ/4)×C₆₇	C₂²	1	1	yes	characteristic
40	H(3,ℤ/4)×C₆₇	C₂²	1	1	yes	characteristic
41	H(3,ℤ/4)×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#11761628	C₂³	1	2	yes	—
43	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
44	#14524076	—	4	2	no	—
45	#14524076	—	4	2	no	—
46	#14524065	—	2	1	no	—
47	#14524065	—	2	1	no	—
48	#14524065	—	2	1	no	—
49	#14524065	—	2	1	no	—
50	C₂×Dic₂₆₈	—	2	1	no	—
51	C₂×Dic₂₆₈	—	2	1	no	—
52	C₂×Dic₂₆₈	—	2	1	no	—
53	C₂×Dic₂₆₈	—	2	1	no	—
54	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic
55	C₂×Dic₂₆₈	C₂×C₄	1	2	yes	—
56	C₂×Dic₂₆₈	C₂×C₄	1	2	yes	—
57	C₂×Dic₂₆₈	C₂×C₄	1	4	yes	—
58	C₂×#11761617	C₂×C₄	1	2	yes	—
59	C₂×#11761617	C₂×C₄	1	4	yes	—
60	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
61	#14524051	—	4	2	no	—
62	#14524049	—	2	4	no	—
63	C₂×#11761612	C₂³	1	2	yes	—
64	M₁₆×D₆₇	—	4	2	no	—
65	#14524043	C₂×C₄	1	4	yes	—
66	#14524031	C₂×C₄	1	4	yes	—
67	#14524027	—	4	2	no	—
68	#14524023	—	4	2	no	—
69	C₄×Dic₁₃₄	—	2	4	no	—
70	#14524008	—	4	2	no	—
71	#14524002	C₂³	1	2	yes	—
72	#14523999	—	4	2	no	—
73	#14523979	—	2	1	no	—
74	#14523979	—	2	1	no	—
75	#14523977	—	2	1	no	—
76	#14523975	—	2	1	no	—
77	#14523971	—	2	4	no	—
78	#14523969	—	4	2	no	—
79	#14523968	—	2	4	no	—
80	#14523966	—	4	2	no	—
81	#14523961	—	4	2	no	—
82	#14523957	—	4	2	no	—
83	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
87	#117×C₆₇	C₂³	1	1	yes	characteristic
88	#117×C₆₇	C₂³	1	1	yes	characteristic
89	#117×C₆₇	C₂³	1	1	yes	characteristic
90	#97×C₆₇	—	2	1	no	—
91	#97×C₆₇	C₂×C₄	1	2	yes	—
92	#97×C₆₇	D₄	1	2	yes	—
93	C₄×C₈×C₆₇	—	2	1	no	—
94	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₆₇	D₄	1	2	yes	—
96	#11761628	—	2	2	no	—
97	#11761628	—	2	2	no	—
98	#11761628	—	2	2	no	—
99	#11761628	—	2	2	no	—
100	C₂×Dic₁₃₄	—	2	2	no	—
101	C₂×Dic₁₃₄	—	2	2	no	—
102	C₂×Dic₁₃₄	—	2	2	no	—
103	C₂×Dic₁₃₄	—	2	2	no	—
104	C₂×Dic₁₃₄	—	2	2	no	—
105	C₂×Dic₁₃₄	C₂²×C₄	1	4	yes	—
106	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
107	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
108	C₂×C₂²⋊D₆₇	—	2	2	no	—
109	C₂²×Dic₆₇	—	2	2	no	—
110	C₂×C₄×D₆₇	—	2	2	no	—
111	Dic₂₆₈	—	2	2	no	—
112	Dic₂₆₈	—	2	2	no	—
113	Dic₂₆₈	—	2	2	no	—
114	Dic₂₆₈	—	2	2	no	—
115	Dic₂₆₈	—	2	1	no	—
116	Dic₂₆₈	—	2	1	no	—
117	Dic₂₆₈	—	4	4	no	—
118	#11761617	—	2	2	no	—
119	#11761617	—	2	2	no	—
120	#11761617	—	4	4	no	—
121	D₅₃₆	—	2	1	no	—
122	D₅₃₆	—	2	1	no	—
123	#11761612	—	2	2	no	—
124	#11761612	—	2	2	no	—
125	#11761611	—	4	4	no	—
126	C₂×C₆₇⋊C₈	—	2	2	no	—
127	C₈×D₆₇	—	4	4	no	—
128	C₄⋊Dic₆₇	—	2	2	no	—
129	C₄⋊Dic₆₇	—	4	4	no	—
130	Dic₆₇⋊C₄	—	4	4	no	—
131	C₂²⋊Dic₆₇	—	2	2	no	—
132	(C₂×D₆₇)⋊C₄	—	4	4	no	—
133	C₄×Dic₆₇	—	2	2	no	—
134	C₄×Dic₆₇	—	4	4	no	—
135	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
136	M₁₆×C₆₇	—	2	1	no	—
137	M₁₆×C₆₇	—	2	1	no	—
138	M₁₆×C₆₇	—	2	1	no	—
139	M₁₆×C₆₇	—	2	1	no	—
140	M₁₆×C₆₇	—	2	1	no	—
141	M₁₆×C₆₇	—	2	1	no	—
142	C₂×C₈×C₆₇	—	2	1	no	—
143	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
150	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
151	C₄⋊C₄×C₆₇	—	2	1	no	—
152	C₄⋊C₄×C₆₇	—	2	1	no	—
153	C₄⋊C₄×C₆₇	—	2	1	no	—
154	C₂²⋊C₄×C₆₇	—	2	1	no	—
155	C₂²⋊C₄×C₆₇	—	2	1	no	—
156	C₂²⋊C₄×C₆₇	—	2	1	no	—
157	C₄²×C₆₇	—	2	1	no	—
158	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
159	C₄²×C₆₇	C₂×D₄	1	2	yes	—
160	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	—	4	1	no	—
165	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²⋊D₆₇	—	4	2	no	—
172	C₂²⋊D₆₇	—	4	2	no	—
173	C₂×Dic₆₇	—	2	4	no	—
174	C₂×Dic₆₇	—	2	2	no	—
175	C₂×Dic₆₇	—	4	2	no	—
176	C₂×Dic₆₇	—	4	2	no	—
177	C₂×Dic₆₇	—	4	2	no	—
178	D₂₆₈	—	2	2	no	—
179	D₂₆₈	—	2	2	no	—
180	C₄×D₆₇	—	4	2	no	—
181	C₄×D₆₇	—	4	2	no	—
182	Dic₁₃₄	—	2	2	no	—
183	Dic₁₃₄	—	2	4	no	—
184	Dic₁₃₄	—	2	4	no	—
185	Dic₁₃₄	—	2	2	no	—
186	Dic₁₃₄	—	4	2	no	—
187	Dic₁₃₄	—	4	2	no	—
188	C₈×C₆₇	—	2	2	no	—
189	C₈×C₆₇	—	2	2	no	—
190	C₈×C₆₇	—	4	1	no	—
191	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
192	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
193	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
194	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
195	C₆₇⋊C₈	—	4	2	no	—
196	C₂²×C₆₇	—	4	1	no	—
197	C₂²×C₆₇	#518	1	1	yes	characteristic
198	C₂²×C₆₇	#535	1	1	yes	characteristic
199	C₂²×C₆₇	#540	1	1	yes	characteristic
200	C₂×D₆₇	—	4	2	no	—
201	C₂×D₆₇	—	8	2	no	—
202	C₄×C₆₇	—	4	2	no	—
203	C₄×C₆₇	—	4	2	no	—
204	C₄×C₆₇	—	8	1	no	—
205	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₆₇	#518	1	1	yes	characteristic
207	C₄×C₆₇	#535	1	1	yes	characteristic
208	C₄×C₆₇	#540	1	1	yes	characteristic
209	Dic₆₇	—	4	4	no	—
210	Dic₆₇	—	4	2	no	—
211	Dic₆₇	—	8	2	no	—
212	#22285	—	67	1	no	maximal, Sylow
213	C₂×C₆₇	—	2	1	no	—
214	C₂×C₆₇	—	2	1	no	—
215	C₂×C₆₇	—	2	1	no	—
216	C₂×C₆₇	#2328	1	1	yes	characteristic
217	D₆₇	—	8	2	no	—
218	#3156	—	67	1	no	—
219	#2957	—	67	1	no	—
220	#2950	—	67	1	no	—
221	#1979	—	67	1	no	—
222	#1976	—	67	1	no	—
223	#1912	—	67	2	no	—
224	#1909	—	67	2	no	—
225	#1905	—	67	2	no	—
226	#1902	—	67	2	no	—
227	#1833	—	67	1	no	—
228	#1747	D₆₇	1	1	yes	characteristic, complemented
229	C₆₇	#22285	1	1	yes	characteristic, complemented, Sylow
230	C₂×#137	—	67	2	no	—
231	C₂×#135	—	67	1	no	—
232	C₂²×Q₁₆	—	67	1	no	—
233	#568	—	67	2	no	—
234	#536	—	67	2	no	—
235	#519	—	67	2	no	—
236	#497	—	67	4	no	—
237	#495	—	67	2	no	—
238	#494	—	67	2	no	—
239	#444	—	134	2	no	—
240	#443	—	134	2	no	—
241	#441	—	134	2	no	—
242	C₄×Q₁₆	—	134	2	no	—
243	C₂×#108	—	67	1	no	—
244	#427	—	67	1	no	—
245	#421	—	67	2	no	—
246	#421	—	67	2	no	—
247	#419	—	67	2	no	—
248	#419	—	67	2	no	—
249	C₂×#101	—	67	2	no	—
250	#410	—	67	2	no	—
251	#405	C₂×D₆₇	1	1	yes	characteristic
252	#405	C₂×D₆₇	1	1	yes	characteristic
253	#405	C₂×D₆₇	1	1	yes	characteristic
254	#344	—	67	2	no	—
255	#338	C₂×D₆₇	1	1	yes	characteristic
256	H(3,ℤ/4)	—	67	2	no	—
257	H(3,ℤ/4)	C₂×D₆₇	1	1	yes	characteristic
258	H(3,ℤ/4)	C₂×D₆₇	1	1	yes	characteristic
259	H(3,ℤ/4)	C₂×D₆₇	1	1	yes	characteristic
260	C₂×#41	—	67	2	no	—
261	C₂²×Q₈	—	67	2	no	—
262	#137	—	268	2	no	—
263	#137	—	268	2	no	—
264	#135	—	134	1	no	—
265	#135	—	134	1	no	—
266	#135	—	134	1	no	—
267	#135	—	134	1	no	—
268	C₂×Q₁₆	—	67	4	no	—
269	C₂×Q₁₆	—	67	2	no	—
270	C₂×Q₁₆	—	67	2	no	—
271	C₂×Q₁₆	—	67	1	no	—
272	C₂×Q₁₆	—	134	1	no	—
273	C₂×Q₁₆	—	134	1	no	—
274	C₂×Q₁₆	—	134	1	no	—
275	C₂×Q₁₆	—	134	1	no	—
276	C₂×SD₁₆	—	67	4	no	—
277	C₂×SD₁₆	—	67	2	no	—
278	C₂×D₈	—	67	1	no	—
279	#131	—	268	2	no	—
280	#131	—	134	4	no	—
281	C₂×M₁₆	—	268	2	no	—
282	C₂×M₁₆	—	67	2	no	—
283	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
284	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
285	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
287	C₄⋊Q₈	—	67	4	no	—
288	#124	—	67	4	no	—
289	#123	—	268	2	no	—
290	C₂²⋊Q₈	—	268	2	no	—
291	C₄×Q₈	—	268	2	no	—
292	C₄×Q₈	—	134	4	no	—
293	#117	—	268	2	no	—
294	#117	—	67	2	no	—
295	#117	C₂²×D₆₇	1	1	yes	characteristic
296	#117	C₂²×D₆₇	1	1	yes	characteristic
297	#117	C₂²×D₆₇	1	1	yes	characteristic
298	#108	—	134	1	no	—
299	#108	—	134	1	no	—
300	#107	—	134	1	no	—
301	#106	—	134	1	no	—
302	#104	—	268	2	no	—
303	#104	—	134	4	no	—
304	#103	—	268	2	no	—
305	#103	—	134	4	no	—
306	#101	—	268	2	no	—
307	#99	—	268	2	no	—
308	#97	—	2	1	no	—
309	#97	C₄×D₆₇	1	2	yes	—
310	#97	D₂₆₈	1	2	yes	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	C₄×D₆₇	1	2	yes	—
313	C₄×C₈	D₂₆₈	1	2	yes	—
314	#41	—	134	2	no	—
315	#41	—	134	2	no	—
316	#41	—	134	2	no	—
317	#41	—	134	2	no	—
318	C₂×Q₈	—	67	4	no	—
319	C₂×Q₈	—	67	2	no	—
320	C₂×Q₈	—	134	2	no	—
321	C₂×Q₈	—	134	2	no	—
322	C₂×Q₈	—	134	2	no	—
323	C₂×Q₈	—	134	2	no	—
324	C₂×Q₈	—	134	2	no	—
325	C₂×D₄	—	67	2	no	—
326	C₂×D₄	—	134	2	no	—
327	C₂²×C₄	—	134	2	no	—
328	C₂²×C₄	—	134	2	no	—
329	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
330	Q₁₆	—	268	4	no	—
331	Q₁₆	—	134	2	no	—
332	Q₁₆	—	134	2	no	—
333	Q₁₆	—	134	2	no	—
334	Q₁₆	—	134	2	no	—
335	Q₁₆	—	134	1	no	—
336	Q₁₆	—	134	1	no	—
337	SD₁₆	—	268	4	no	—
338	SD₁₆	—	134	2	no	—
339	SD₁₆	—	134	2	no	—
340	D₈	—	134	1	no	—
341	D₈	—	134	1	no	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	2	1	no	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	268	4	no	—
349	M₁₆	—	134	2	no	—
350	M₁₆	—	134	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	268	4	no	—
353	C₂×C₈	—	134	2	no	—
354	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
355	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
356	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
357	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
358	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
359	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
360	C₂×C₈	#11761628	1	1	yes	characteristic
361	C₂×C₈	#11761628	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	268	4	no	—
366	C₄⋊C₄	—	268	4	no	—
367	C₄⋊C₄	—	134	2	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	268	4	no	—
372	C₂²⋊C₄	—	134	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	268	4	no	—
375	C₄²	—	134	2	no	—
376	C₄²	C₂×C₄×D₆₇	1	2	yes	—
377	C₄²	C₂×D₂₆₈	1	2	yes	—
378	C₂³	—	134	2	no	—
379	C₂³	#14524089	1	1	yes	characteristic
380	Q₈	—	268	2	no	—
381	Q₈	—	268	2	no	—
382	Q₈	—	134	2	no	—
383	Q₈	—	134	4	no	—
384	Q₈	—	134	4	no	—
385	Q₈	—	134	2	no	—
386	D₄	—	268	2	no	—
387	D₄	—	268	2	no	—
388	D₄	—	134	2	no	—
389	D₄	—	134	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	268	2	no	—
394	C₂×C₄	—	268	2	no	—
395	C₂×C₄	—	268	2	no	—
396	C₂×C₄	—	268	2	no	—
397	C₂×C₄	—	268	2	no	—
398	C₂×C₄	—	134	4	no	—
399	C₂×C₄	—	134	2	no	—
400	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
402	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
403	C₂×C₄	#14524089	1	1	yes	characteristic
404	C₂×C₄	#14524089	1	1	yes	characteristic
405	C₂×C₄	#14524089	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	268	2	no	—
410	C₈	C₄×D₂₆₈	1	1	yes	characteristic
411	C₈	C₄×D₂₆₈	1	1	yes	characteristic
412	C₈	C₄×D₂₆₈	1	1	yes	characteristic
413	C₈	C₄×D₂₆₈	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	268	2	no	—
416	C₂²	—	536	2	no	—
417	C₂²	#16863870	1	1	yes	characteristic
418	C₂²	#16863965	1	1	yes	characteristic
419	C₂²	#16864001	1	1	yes	characteristic
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	268	2	no	—
424	C₄	—	268	4	no	—
425	C₄	—	536	2	no	—
426	C₄	C₂×C₄×D₂₆₈	1	1	yes	characteristic
427	C₄	#16863870	1	1	yes	characteristic
428	C₄	#16863965	1	1	yes	characteristic
429	C₄	#16864001	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	536	2	no	—
434	C₂	#22562934	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22562934
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1747	C₂
socle	C₂×C₆₇	#2328
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1747	D₆₇
hypocenter	C₆₇	#22285
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1747

Complements

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

N	H ≅ G/N	type
3. #22569078	C₂	semidirect
4. #22561124	C₂	semidirect
6. #22560745	C₂	semidirect
7. #22560730	C₂	semidirect
8. #22560704	C₂	semidirect
9. #22560683	C₂	semidirect
10. #22560333	C₂	semidirect
11. C₆₇×#1747	C₂	semidirect
18. #16863790	C₄	semidirect
19. #16863780	C₄	semidirect
20. #16863776	C₄	semidirect
228. #1747	D₆₇	semidirect
229. C₆₇	#22285	semidirect

Maximal subgroups

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

subgroup	index
#22570703	2
#22569127	2
#22569078	2
#22561124	2
#22561107	2
#22560745	2
#22560730	2
#22560704	2
#22560683	2
#22560333	2
C₆₇×#1747	2
#22285	67