Subgroups — #30856195

Order 17152.

616 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14524049	C₂	1	1	yes	maximal, characteristic
2	#22560355	C₂	1	2	yes	maximal, complemented
3	#22560334	C₂	1	1	yes	maximal, characteristic, complemented
4	#22560332	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560312	C₂	1	2	yes	maximal
6	#22560256	C₂	1	1	yes	maximal, characteristic
7	#22560252	C₂	1	1	yes	maximal, characteristic
8	#22560088	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560010	C₂	1	2	yes	maximal
10	#22559964	C₂	1	2	yes	maximal, complemented
11	C₆₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524049	C₂²	1	1	yes	characteristic
13	C₂×#14524049	C₂²	1	1	yes	characteristic
14	C₄×#11761628	C₂²	1	1	yes	characteristic
15	C₂×#14523979	C₂²	1	1	yes	characteristic
16	#16863434	C₂²	1	1	yes	characteristic
17	#16863378	C₂²	1	2	yes	—
18	#16863369	C₂²	1	2	yes	—
19	#16863351	C₂²	1	2	yes	—
20	#16863351	C₂²	1	1	yes	characteristic
21	#16863351	C₂²	1	1	yes	characteristic
22	#16863350	C₄	1	2	yes	complemented
23	#16863350	C₄	1	2	yes	complemented
24	C₄×#11761612	C₂²	1	1	yes	characteristic
25	C₄×#11761611	C₄	1	2	yes	complemented
26	C₄×C₈×D₆₇	C₄	1	2	yes	complemented
27	#16863168	C₂²	1	2	yes	—
28	#16863166	C₂²	1	2	yes	—
29	#16863156	C₂²	1	2	yes	—
30	C₆₇⋊#338	C₂²	1	2	yes	—
31	#16863153	C₂²	1	2	yes	—
32	#16863152	C₂²	1	2	yes	—
33	#16863152	C₂²	1	2	yes	—
34	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
35	#427×C₆₇	C₂²	1	1	yes	characteristic
36	#405×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
38	#339×C₆₇	C₂²	1	2	yes	—
39	C₂×#11761628	C₂³	1	1	yes	characteristic
40	#14524049	—	2	1	no	—
41	#14524049	—	2	1	no	—
42	#14524049	—	2	1	no	—
43	#14524049	—	2	1	no	—
44	#14524049	—	2	1	no	—
45	#14524049	—	2	1	no	—
46	#14524049	—	2	1	no	—
47	#14524049	—	2	1	no	—
48	C₂×#11761612	C₂³	1	2	yes	—
49	C₂×#11761612	C₂³	1	1	yes	characteristic
50	C₂×#11761612	C₂³	1	1	yes	characteristic
51	C₂×#11761611	C₂×C₄	1	2	yes	—
52	C₂×#11761611	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
55	C₄×Dic₁₃₄	—	2	1	no	—
56	C₄×D₂₆₈	—	2	1	no	—
57	C₄×C₂²⋊D₆₇	—	2	2	no	—
58	#14524002	C₂³	1	2	yes	—
59	#14524002	C₂³	1	1	yes	characteristic
60	#14524000	C₂×C₄	1	2	yes	—
61	C₄²×D₆₇	C₂×C₄	1	2	yes	—
62	#14523979	—	2	1	no	—
63	#14523979	—	2	1	no	—
64	#14523977	—	2	1	no	—
65	#14523975	—	2	1	no	—
66	#14523961	—	2	2	no	—
67	#14523959	—	2	2	no	—
68	#14523957	—	2	4	no	—
69	#14523954	C₂×C₄	1	2	yes	—
70	#14523953	—	2	2	no	—
71	#14523953	C₂×C₄	1	2	yes	—
72	#14523953	C₂×C₄	1	2	yes	—
73	C₄×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
74	C₈×Dic₆₇	—	2	2	no	—
75	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
76	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
77	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
78	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
80	#117×C₆₇	C₂³	1	2	yes	—
81	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
82	#108×C₆₇	—	2	1	no	—
83	#108×C₆₇	—	2	1	no	—
84	#107×C₆₇	—	2	1	no	—
85	#106×C₆₇	—	2	1	no	—
86	#97×C₆₇	—	2	2	no	—
87	C₄×C₈×C₆₇	—	2	2	no	—
88	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
92	#11761628	—	2	1	no	—
93	#11761628	—	2	1	no	—
94	#11761628	—	2	1	no	—
95	#11761628	—	2	1	no	—
96	C₂×Dic₁₃₄	#41	1	1	yes	characteristic
97	C₂×D₂₆₈	#41	1	1	yes	characteristic
98	C₂×C₂²⋊D₆₇	#41	1	2	yes	—
99	C₂×C₄×D₆₇	—	2	2	no	—
100	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
101	#11761612	—	2	1	no	—
102	#11761612	—	2	1	no	—
103	#11761612	—	2	1	no	—
104	#11761612	—	2	1	no	—
105	#11761612	—	2	2	no	—
106	#11761612	—	2	2	no	—
107	#11761611	—	2	2	no	—
108	#11761611	—	2	2	no	—
109	#11761611	—	2	2	no	—
110	#11761611	—	2	2	no	—
111	C₂×C₆₇⋊C₈	—	2	2	no	—
112	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
113	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
114	C₈×D₆₇	—	2	2	no	—
115	C₈×D₆₇	—	2	2	no	—
116	C₈×D₆₇	—	2	2	no	—
117	C₈×D₆₇	—	2	2	no	—
118	C₄⋊Dic₆₇	—	2	1	no	—
119	C₄⋊Dic₆₇	—	2	2	no	—
120	Dic₆₇⋊C₄	—	2	2	no	—
121	C₂²⋊Dic₆₇	—	2	1	no	—
122	C₂²⋊Dic₆₇	—	2	2	no	—
123	(C₂×D₆₇)⋊C₄	—	2	2	no	—
124	C₄×Dic₆₇	—	2	2	no	—
125	C₄×Dic₆₇	—	2	2	no	—
126	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₆₇	—	2	1	no	—
128	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
129	M₁₆×C₆₇	—	2	2	no	—
130	M₁₆×C₆₇	—	2	2	no	—
131	C₂×C₈×C₆₇	—	2	2	no	—
132	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
137	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
138	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
139	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
140	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
141	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
142	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
143	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
144	C₄⋊C₄×C₆₇	—	2	2	no	—
145	C₂²⋊C₄×C₆₇	—	2	2	no	—
146	C₄²×C₆₇	—	2	1	no	—
147	C₄²×C₆₇	—	2	2	no	—
148	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
150	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
151	C₂²×D₆₇	#117	1	2	yes	—
152	C₂×C₄×C₆₇	—	2	1	no	—
153	C₂×C₄×C₆₇	—	2	1	no	—
154	C₂×C₄×C₆₇	—	4	2	no	—
155	C₂×C₄×C₆₇	—	4	2	no	—
156	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
162	C₂²⋊D₆₇	—	2	2	no	—
163	C₂²⋊D₆₇	—	2	2	no	—
164	C₂×Dic₆₇	—	2	2	no	—
165	C₂×Dic₆₇	—	4	2	no	—
166	C₂×Dic₆₇	#117	1	2	yes	—
167	D₂₆₈	—	2	1	no	—
168	D₂₆₈	—	2	1	no	—
169	C₄×D₆₇	—	2	2	no	—
170	C₄×D₆₇	—	2	2	no	—
171	C₄×D₆₇	—	4	4	no	—
172	Dic₁₃₄	—	2	1	no	—
173	Dic₁₃₄	—	2	1	no	—
174	C₈×C₆₇	—	4	2	no	—
175	C₈×C₆₇	#117	1	1	yes	characteristic
176	C₈×C₆₇	#117	1	1	yes	characteristic
177	C₈×C₆₇	#117	1	1	yes	characteristic
178	C₈×C₆₇	#117	1	1	yes	characteristic
179	C₈×C₆₇	#117	1	1	yes	characteristic
180	C₈×C₆₇	#117	1	1	yes	characteristic
181	C₈×C₆₇	#117	1	1	yes	characteristic
182	C₈×C₆₇	#117	1	1	yes	characteristic
183	C₆₇⋊C₈	—	2	2	no	—
184	C₆₇⋊C₈	—	2	2	no	—
185	C₆₇⋊C₈	—	4	2	no	—
186	C₂²×C₆₇	—	4	1	no	—
187	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
188	C₂²×C₆₇	#529	1	1	yes	characteristic
189	C₂²×C₆₇	#529	1	1	yes	characteristic
190	C₂×D₆₇	—	2	2	no	—
191	C₂×D₆₇	—	4	2	no	—
192	C₄×C₆₇	—	2	2	no	—
193	C₄×C₆₇	—	4	1	no	—
194	C₄×C₆₇	—	8	2	no	—
195	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
196	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
197	C₄×C₆₇	#529	1	1	yes	characteristic
198	C₄×C₆₇	#529	1	1	yes	characteristic
199	Dic₆₇	—	2	2	no	—
200	Dic₆₇	—	4	2	no	—
201	Dic₆₇	—	8	2	no	—
202	#20787	—	67	1	no	maximal, Sylow
203	C₂×C₆₇	—	2	1	no	—
204	C₂×C₆₇	—	2	1	no	—
205	C₂×C₆₇	—	2	1	no	—
206	C₂×C₆₇	#2283	1	1	yes	characteristic
207	D₆₇	—	4	2	no	—
208	C₄×#131	—	67	1	no	—
209	#1841	—	67	2	no	—
210	#1833	—	67	1	no	—
211	#1833	—	67	1	no	—
212	#1827	—	67	2	no	—
213	#1813	—	67	1	no	—
214	#1812	—	67	1	no	—
215	#1772	—	67	1	no	—
216	#1772	D₆₇	1	1	yes	characteristic, complemented
217	#1757	—	67	2	no	—
218	#1747	—	67	2	no	—
219	C₆₇	#20787	1	1	yes	characteristic, complemented, Sylow
220	C₂×#131	—	67	1	no	—
221	C₂×#131	—	67	1	no	—
222	C₄×#41	—	67	1	no	—
223	C₂×#108	—	67	1	no	—
224	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
225	#427	—	67	1	no	—
226	#427	C₂×D₆₇	1	1	yes	characteristic
227	#413	—	67	2	no	—
228	#410	—	67	2	no	—
229	#405	—	67	1	no	—
230	#405	—	67	1	no	—
231	#405	—	67	2	no	—
232	#405	—	67	2	no	—
233	#405	—	67	2	no	—
234	#405	C₂×D₆₇	1	2	yes	—
235	C₄×M₁₆	—	67	1	no	—
236	C₄×M₁₆	—	67	2	no	—
237	C₂×C₄×C₈	—	67	2	no	—
238	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
239	#344	—	67	2	no	—
240	#344	—	67	2	no	—
241	#339	—	67	2	no	—
242	#339	C₂×D₆₇	1	2	yes	—
243	#338	—	67	2	no	—
244	H(3,ℤ/4)	—	67	2	no	—
245	H(3,ℤ/4)	—	67	2	no	—
246	H(3,ℤ/4)	—	67	2	no	—
247	C₂×#41	—	67	1	no	—
248	#131	—	134	1	no	—
249	#131	—	134	1	no	—
250	#131	—	134	1	no	—
251	#131	—	134	1	no	—
252	#131	—	134	1	no	—
253	#131	—	134	1	no	—
254	#131	—	134	1	no	—
255	#131	—	134	1	no	—
256	C₂×M₁₆	—	67	1	no	—
257	C₂×M₁₆	—	67	1	no	—
258	C₂×M₁₆	—	67	2	no	—
259	C₂×M₁₆	—	67	2	no	—
260	C₂×M₁₆	—	67	2	no	—
261	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
262	C₂²×C₈	—	67	2	no	—
263	C₂²×C₈	—	67	2	no	—
264	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
266	C₄×Q₈	—	134	1	no	—
267	C₄×D₄	—	134	1	no	—
268	C₄×D₄	—	134	2	no	—
269	#117	—	67	1	no	—
270	#117	—	67	2	no	—
271	#117	—	67	2	no	—
272	#117	C₂²×D₆₇	1	2	yes	—
273	C₂×C₄²	—	67	2	no	—
274	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
275	#108	—	2	1	no	—
276	#108	—	2	1	no	—
277	#108	—	134	1	no	—
278	#108	—	134	1	no	—
279	#107	—	2	1	no	—
280	#107	—	134	1	no	—
281	#106	—	2	1	no	—
282	#106	—	134	1	no	—
283	#101	—	134	2	no	—
284	#100	—	134	2	no	—
285	#99	—	134	4	no	—
286	#97	—	2	2	no	—
287	#97	—	67	2	no	—
288	#97	—	67	2	no	—
289	#97	—	67	2	no	—
290	#97	—	134	2	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	67	2	no	—
293	C₄×C₈	—	67	2	no	—
294	C₄×C₈	—	67	2	no	—
295	C₄×C₈	—	134	2	no	—
296	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
297	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
298	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
299	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
300	#41	—	134	1	no	—
301	#41	—	134	1	no	—
302	#41	—	134	1	no	—
303	#41	—	134	1	no	—
304	C₂×Q₈	—	67	1	no	—
305	C₂×D₄	—	67	2	no	—
306	C₂×D₄	—	67	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	67	2	no	—
309	C₂²×C₄	—	134	2	no	—
310	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
311	M₁₆	—	2	2	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	134	2	no	—
314	M₁₆	—	134	2	no	—
315	M₁₆	—	134	1	no	—
316	M₁₆	—	134	1	no	—
317	M₁₆	—	134	1	no	—
318	M₁₆	—	134	1	no	—
319	M₁₆	—	134	2	no	—
320	M₁₆	—	134	2	no	—
321	M₁₆	—	134	2	no	—
322	M₁₆	—	134	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	67	2	no	—
325	C₂×C₈	—	67	2	no	—
326	C₂×C₈	—	134	2	no	—
327	C₂×C₈	—	134	2	no	—
328	C₂×C₈	—	134	2	no	—
329	C₂×C₈	—	134	2	no	—
330	C₂×C₈	—	134	2	no	—
331	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
332	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
335	C₂×C₈	#11761627	1	1	yes	characteristic
336	C₂×C₈	#11761627	1	1	yes	characteristic
337	C₂×C₈	#11761628	1	1	yes	characteristic
338	C₂×C₈	#11761628	1	1	yes	characteristic
339	C₂×C₈	#11761628	1	1	yes	characteristic
340	C₂×C₈	#11761628	1	1	yes	characteristic
341	C₂×C₈	#11761629	1	1	yes	characteristic
342	C₂×C₈	#11761629	1	1	yes	characteristic
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	134	2	no	—
345	C₄⋊C₄	—	134	2	no	—
346	C₄⋊C₄	—	134	1	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	134	2	no	—
349	C₂²⋊C₄	—	134	2	no	—
350	C₂²⋊C₄	—	134	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	67	2	no	—
354	C₄²	—	134	2	no	—
355	C₄²	—	134	2	no	—
356	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
358	C₂³	—	67	2	no	—
359	C₂³	#41×D₆₇	1	1	yes	characteristic
360	Q₈	—	134	1	no	—
361	Q₈	—	134	1	no	—
362	D₄	—	134	2	no	—
363	D₄	—	134	2	no	—
364	D₄	—	134	1	no	—
365	D₄	—	134	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	268	4	no	—
371	C₂×C₄	—	268	2	no	—
372	C₂×C₄	—	67	2	no	—
373	C₂×C₄	—	134	2	no	—
374	C₂×C₄	—	134	2	no	—
375	C₂×C₄	—	134	2	no	—
376	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
377	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
378	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
379	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
380	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
381	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	268	2	no	—
384	C₈	—	134	2	no	—
385	C₈	—	134	2	no	—
386	C₈	#14524000	1	1	yes	characteristic
387	C₈	#14524000	1	1	yes	characteristic
388	C₈	#14524000	1	1	yes	characteristic
389	C₈	#14524000	1	1	yes	characteristic
390	C₈	#14524001	1	1	yes	characteristic
391	C₈	#14524001	1	1	yes	characteristic
392	C₈	#14524001	1	1	yes	characteristic
393	C₈	#14524001	1	1	yes	characteristic
394	C₂²	—	4	1	no	—
395	C₂²	—	268	2	no	—
396	C₂²	—	134	2	no	—
397	C₂²	#117×D₆₇	1	1	yes	characteristic
398	C₂²	#16863928	1	1	yes	characteristic
399	C₂²	#16863933	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	268	2	no	—
404	C₄	—	536	2	no	—
405	C₄	—	134	2	no	—
406	C₄	C₂×#14524000	1	1	yes	characteristic
407	C₄	C₂×#14524001	1	1	yes	characteristic
408	C₄	#16863928	1	1	yes	characteristic
409	C₄	#16863933	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	—	268	2	no	—
414	C₂	#22562605	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#14524001
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1772	C₂
socle	C₂×C₆₇	#2283
prime radical	C₂×#11761628	C₂³
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1772	D₆₇
hypocenter	C₆₇	#20787
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
2. #22560355	C₂	semidirect
3. #22560334	C₂	semidirect
4. #22560332	C₂	semidirect
8. #22560088	C₂	semidirect
10. #22559964	C₂	semidirect
11. C₆₇×#1772	C₂	semidirect
22. #16863350	C₄	semidirect
23. #16863350	C₄	semidirect
25. C₄×#11761611	C₄	semidirect
26. C₄×C₈×D₆₇	C₄	semidirect
216. #1772	D₆₇	semidirect
219. C₆₇	#20787	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14524049	2
#22560355	2
#22560334	2
#22560332	2
#22560312	2
#22560256	2
#22560252	2
#22560088	2
#22560010	2
#22559964	2
C₆₇×#1772	2
#20787	67