Subgroups — #31008926

Order 17152.

582 conjugacy classes of subgroups.

The subgroup lattice has 386 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	#22562015	C₂	1	2	yes	maximal, complemented
3	#22562013	C₂	1	2	yes	maximal, complemented
4	#22562012	C₂	1	1	yes	maximal, characteristic, complemented
5	#22562010	C₂	1	1	yes	maximal, characteristic, complemented
6	#22562010	C₂	1	1	yes	maximal, characteristic, complemented
7	#22561966	C₂	1	2	yes	maximal, complemented
8	#22561821	C₂	1	2	yes	maximal
9	#22561802	C₂	1	1	yes	maximal, characteristic, complemented
10	#346×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524049	C₄	1	1	yes	characteristic
13	C₂×#14524049	C₂²	1	1	yes	characteristic
14	C₄×#11761628	C₄	1	1	yes	characteristic
15	C₂×#14523982	C₂²	1	2	yes	—
16	C₂×C₁₆×D₆₇	C₂²	1	2	yes	—
17	#16863351	C₄	1	1	yes	characteristic
18	#16863351	C₂²	1	1	yes	characteristic
19	#16863350	C₄	1	1	yes	characteristic
20	#16863350	C₄	1	1	yes	characteristic
21	#16863350	C₂²	1	1	yes	characteristic
22	#16863350	C₂²	1	1	yes	characteristic
23	C₄×#11761612	C₄	1	1	yes	characteristic
24	C₄×#11761611	C₄	1	1	yes	characteristic
25	C₄×#11761611	C₄	1	1	yes	characteristic
26	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
28	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	2	yes	—
29	Dic₆₇⋊C₁₆	C₂²	1	2	yes	—
30	Dic₆₇⋊C₁₆	C₂²	1	2	yes	—
31	C₂²⋊(C₆₇⋊C₁₆)	C₂²	1	2	yes	—
32	(C₂×D₆₇)⋊C₁₆	C₂²	1	2	yes	—
33	(C₂×D₆₇)⋊C₁₆	C₂²	1	2	yes	—
34	#16863172	C₂²	1	1	yes	characteristic
35	#16863172	C₂²	1	1	yes	characteristic
36	#16863171	C₂²	1	2	yes	—
37	C₁₆×Dic₆₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₄⋊C₁₆×C₆₇	C₂²	1	2	yes	—
40	C₂²⋊C₁₆×C₆₇	C₂²	1	2	yes	—
41	#346×C₆₇	C₂²	1	1	yes	characteristic
42	#346×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#11761628	C₂×C₄	1	1	yes	characteristic
44	#14524049	—	2	4	no	—
45	#14524049	—	2	4	no	—
46	C₂×#11761612	C₂×C₄	1	1	yes	characteristic
47	C₂×#11761612	C₂×C₄	1	1	yes	characteristic
48	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
49	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
50	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
51	C₂×#11761611	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
56	C₄×Dic₁₃₄	C₈	1	2	yes	—
57	C₄×D₂₆₈	C₈	1	2	yes	—
58	C₄×C₂²⋊D₆₇	C₈	1	2	yes	—
59	C₄×C₂²⋊D₆₇	C₈	1	2	yes	—
60	#14524002	C₂×C₄	1	1	yes	characteristic
61	#14524000	C₂×C₄	1	1	yes	characteristic
62	#14524000	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
65	#14523982	—	2	4	no	—
66	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
67	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
68	C₁₆×D₆₇	—	2	4	no	—
69	#14523954	C₂×C₄	1	1	yes	characteristic
70	#14523954	C₂×C₄	1	1	yes	characteristic
71	#14523953	C₂×C₄	1	1	yes	characteristic
72	#14523953	C₂×C₄	1	1	yes	characteristic
73	#14523953	C₂×C₄	1	1	yes	characteristic
74	#14523953	C₂×C₄	1	1	yes	characteristic
75	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
78	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
80	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
85	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
86	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
87	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
90	#11761628	—	2	2	no	—
91	#11761628	—	2	2	no	—
92	C₂×Dic₁₃₄	C₂×C₈	1	1	yes	characteristic
93	C₂×D₂₆₈	C₂×C₈	1	1	yes	characteristic
94	C₂×C₂²⋊D₆₇	C₂×C₈	1	1	yes	characteristic
95	C₂×C₂²⋊D₆₇	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₆₇	C₂×C₈	1	2	yes	—
97	C₂×C₄×D₆₇	C₂×C₈	1	2	yes	—
98	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
100	#11761612	—	2	2	no	—
101	#11761612	—	2	2	no	—
102	#11761611	—	2	2	no	—
103	#11761611	—	2	2	no	—
104	#11761611	—	2	2	no	—
105	#11761611	—	2	2	no	—
106	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
110	C₈×D₆₇	—	2	2	no	—
111	C₈×D₆₇	—	2	2	no	—
112	C₈×D₆₇	M₁₆	1	4	yes	—
113	C₈×D₆₇	#41	1	4	yes	—
114	C₄⋊Dic₆₇	C₂×C₈	1	2	yes	—
115	Dic₆₇⋊C₄	C₂×C₈	1	2	yes	—
116	Dic₆₇⋊C₄	C₂×C₈	1	2	yes	—
117	C₂²⋊Dic₆₇	C₂×C₈	1	2	yes	—
118	(C₂×D₆₇)⋊C₄	C₂×C₈	1	2	yes	—
119	(C₂×D₆₇)⋊C₄	C₂×C₈	1	2	yes	—
120	C₄×Dic₆₇	C₂×C₈	1	2	yes	—
121	C₄×Dic₆₇	C₂×C₈	1	2	yes	—
122	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
123	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₆₇⋊C₁₆	—	2	2	no	—
125	C₆₇⋊C₁₆	—	2	2	no	—
126	C₂²×C₄×C₆₇	C₂×C₈	1	2	yes	—
127	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₆₇	—	2	2	no	—
129	C₂×C₈×C₆₇	—	2	2	no	—
130	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
134	C₄²×C₆₇	C₂×C₈	1	2	yes	—
135	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
137	C₁₆×C₆₇	—	2	2	no	—
138	C₁₆×C₆₇	—	2	2	no	—
139	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
140	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
141	C₂²×D₆₇	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₆₇	—	2	1	no	—
143	C₂×C₄×C₆₇	—	2	1	no	—
144	C₂×C₄×C₆₇	—	4	2	no	—
145	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂²×C₈	1	2	yes	—
147	C₂×C₄×C₆₇	C₂²×C₈	1	2	yes	—
148	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
149	C₂²⋊D₆₇	—	2	2	no	—
150	C₂²⋊D₆₇	—	2	2	no	—
151	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
152	C₂×Dic₆₇	C₂²×C₈	1	2	yes	—
153	C₂×Dic₆₇	C₂²×C₈	1	2	yes	—
154	C₂×Dic₆₇	C₂²×C₈	1	1	yes	characteristic
155	D₂₆₈	—	2	2	no	—
156	C₄×D₆₇	—	2	1	no	—
157	C₄×D₆₇	—	2	1	no	—
158	C₄×D₆₇	—	4	2	no	—
159	C₄×D₆₇	—	4	2	no	—
160	C₄×D₆₇	#117	1	2	yes	—
161	C₄×D₆₇	C₂×M₁₆	1	2	yes	—
162	Dic₁₃₄	—	2	2	no	—
163	C₈×C₆₇	—	2	1	no	—
164	C₈×C₆₇	—	2	1	no	—
165	C₈×C₆₇	C₂×M₁₆	1	2	yes	—
166	C₈×C₆₇	C₂×#41	1	2	yes	—
167	C₆₇⋊C₈	—	2	1	no	—
168	C₆₇⋊C₈	—	2	1	no	—
169	C₆₇⋊C₈	#117	1	2	yes	—
170	C₆₇⋊C₈	C₂×M₁₆	1	2	yes	—
171	C₂²×C₆₇	—	2	2	no	—
172	C₂²×C₆₇	—	2	1	no	—
173	C₂²×C₆₇	C₂³×C₈	1	1	yes	characteristic
174	C₂×D₆₇	—	2	2	no	—
175	C₂×D₆₇	—	2	2	no	—
176	C₂×D₆₇	—	2	1	no	—
177	C₂×D₆₇	#431	1	2	yes	—
178	C₄×C₆₇	—	2	2	no	—
179	C₄×C₆₇	—	2	2	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
182	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
183	Dic₆₇	—	2	2	no	—
184	Dic₆₇	—	2	2	no	—
185	Dic₆₇	—	2	1	no	—
186	Dic₆₇	#431	1	2	yes	—
187	#33421	—	67	1	no	maximal, Sylow
188	C₂×C₆₇	—	4	1	no	—
189	C₂×C₆₇	C₂×#431	1	1	yes	characteristic
190	C₂×C₆₇	#3407	1	2	yes	—
191	D₆₇	—	2	2	no	—
192	D₆₇	—	4	1	no	—
193	C₄×#131	—	67	1	no	—
194	#2164	—	67	2	no	—
195	#2164	—	67	2	no	—
196	#2163	—	67	1	no	—
197	#2163	—	67	1	no	—
198	#2163	—	67	1	no	—
199	#2163	D₆₇	1	1	yes	characteristic, complemented
200	#2151	—	67	2	no	—
201	#2113	—	67	2	no	—
202	C₄×M₃₂	—	67	1	no	—
203	C₂×#346	—	67	1	no	—
204	C₆₇	#33421	1	1	yes	characteristic, complemented, Sylow
205	C₂×#131	—	67	1	no	—
206	C₂×#131	—	67	1	no	—
207	C₄×#41	—	67	1	no	—
208	C₂×M₃₂	—	67	2	no	—
209	C₂²×C₁₆	—	67	2	no	—
210	#405	—	67	1	no	—
211	#405	—	67	1	no	—
212	#405	—	67	1	no	—
213	#405	—	67	1	no	—
214	#405	—	67	1	no	—
215	#405	—	67	1	no	—
216	C₄×M₁₆	—	67	1	no	—
217	C₄×M₁₆	—	67	1	no	—
218	C₄×M₁₆	—	67	1	no	—
219	C₂×C₄×C₈	—	67	1	no	—
220	C₂×C₄×C₈	—	67	1	no	—
221	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
222	C₄⋊C₁₆	—	67	2	no	—
223	C₄⋊C₁₆	—	67	2	no	—
224	C₄⋊C₁₆	—	67	2	no	—
225	C₄⋊C₁₆	C₂×D₆₇	1	2	yes	—
226	C₂²⋊C₁₆	—	67	2	no	—
227	C₂²⋊C₁₆	—	67	2	no	—
228	C₂²⋊C₁₆	—	67	2	no	—
229	C₂²⋊C₁₆	C₂×D₆₇	1	2	yes	—
230	#346	—	67	2	no	—
231	#346	—	67	1	no	—
232	#346	—	67	1	no	—
233	#346	C₂×D₆₇	1	1	yes	characteristic
234	#346	C₂×D₆₇	1	1	yes	characteristic
235	C₄×C₁₆	—	67	2	no	—
236	C₂×#41	—	67	1	no	—
237	#131	—	134	4	no	—
238	#131	—	134	4	no	—
239	C₂×M₁₆	—	67	1	no	—
240	C₂×M₁₆	—	67	1	no	—
241	C₂×M₁₆	—	67	1	no	—
242	C₂×M₁₆	—	67	1	no	—
243	C₂×M₁₆	—	67	1	no	—
244	C₂×M₁₆	—	67	1	no	—
245	C₂²×C₈	—	67	1	no	—
246	C₂²×C₈	—	67	1	no	—
247	C₂²×C₈	—	67	1	no	—
248	C₂²×C₈	—	67	1	no	—
249	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
250	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
251	C₄×Q₈	—	67	2	no	—
252	C₄×D₄	—	67	2	no	—
253	C₄×D₄	—	67	2	no	—
254	C₄×D₄	—	67	2	no	—
255	#117	—	67	1	no	—
256	#117	—	67	1	no	—
257	#117	—	67	1	no	—
258	C₂×C₄²	—	67	1	no	—
259	C₂×C₄²	—	67	1	no	—
260	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
261	M₃₂	—	134	4	no	—
262	C₂×C₁₆	—	67	2	no	—
263	C₂×C₁₆	—	67	2	no	—
264	C₂×C₁₆	—	134	4	no	—
265	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
266	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
267	#97	—	67	1	no	—
268	#97	—	67	1	no	—
269	#97	—	67	1	no	—
270	#97	—	67	1	no	—
271	#97	—	67	1	no	—
272	#97	—	67	1	no	—
273	C₄×C₈	—	67	1	no	—
274	C₄×C₈	—	67	1	no	—
275	C₄×C₈	—	67	1	no	—
276	C₄×C₈	—	67	1	no	—
277	C₄×C₈	—	67	1	no	—
278	C₄×C₈	—	67	1	no	—
279	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
280	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
281	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
282	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
283	#41	—	134	2	no	—
284	#41	—	134	2	no	—
285	C₂×Q₈	—	67	1	no	—
286	C₂×D₄	—	67	1	no	—
287	C₂×D₄	—	67	1	no	—
288	C₂×D₄	—	67	1	no	—
289	C₂²×C₄	—	67	2	no	—
290	C₂²×C₄	—	67	2	no	—
291	C₂²×C₄	—	67	1	no	—
292	C₂²×C₄	—	67	1	no	—
293	C₂²×C₄	C₈×D₆₇	1	2	yes	—
294	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
295	M₁₆	—	134	2	no	—
296	M₁₆	—	134	2	no	—
297	M₁₆	—	134	2	no	—
298	M₁₆	—	134	2	no	—
299	M₁₆	—	134	2	no	—
300	M₁₆	—	134	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	67	1	no	—
304	C₂×C₈	—	67	1	no	—
305	C₂×C₈	—	67	4	no	—
306	C₂×C₈	—	67	4	no	—
307	C₂×C₈	—	67	1	no	—
308	C₂×C₈	—	67	1	no	—
309	C₂×C₈	—	134	2	no	—
310	C₂×C₈	—	134	2	no	—
311	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
312	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
313	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
314	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
315	C₄⋊C₄	—	67	2	no	—
316	C₄⋊C₄	—	67	2	no	—
317	C₄⋊C₄	—	67	2	no	—
318	C₂²⋊C₄	—	67	2	no	—
319	C₂²⋊C₄	—	67	2	no	—
320	C₂²⋊C₄	—	67	2	no	—
321	C₄²	—	67	2	no	—
322	C₄²	—	67	2	no	—
323	C₄²	—	67	1	no	—
324	C₄²	—	67	1	no	—
325	C₄²	C₈×D₆₇	1	2	yes	—
326	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
327	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
328	C₁₆	—	2	2	no	—
329	C₁₆	—	2	2	no	—
330	C₁₆	—	134	2	no	—
331	C₁₆	—	134	2	no	—
332	C₂³	—	67	1	no	—
333	C₂³	—	67	1	no	—
334	C₂³	C₂×C₈×D₆₇	1	1	yes	characteristic
335	Q₈	—	134	2	no	—
336	D₄	—	134	2	no	—
337	D₄	—	134	2	no	—
338	D₄	—	134	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	268	2	no	—
343	C₂×C₄	—	268	2	no	—
344	C₂×C₄	—	67	1	no	—
345	C₂×C₄	—	67	2	no	—
346	C₂×C₄	—	67	2	no	—
347	C₂×C₄	—	67	2	no	—
348	C₂×C₄	—	67	2	no	—
349	C₂×C₄	—	67	1	no	—
350	C₂×C₄	—	134	1	no	—
351	C₂×C₄	—	134	1	no	—
352	C₂×C₄	C₂×C₈×D₆₇	1	2	yes	—
353	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
354	C₂×C₄	C₂×C₈×D₆₇	1	2	yes	—
355	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	67	2	no	—
359	C₈	—	67	2	no	—
360	C₈	—	134	1	no	—
361	C₈	—	134	1	no	—
362	C₈	M₁₆×D₆₇	1	2	yes	—
363	C₈	#41×D₆₇	1	2	yes	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	67	2	no	—
367	C₂²	—	134	1	no	—
368	C₂²	—	134	2	no	—
369	C₂²	—	134	2	no	—
370	C₂²	C₂²×C₈×D₆₇	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	67	2	no	—
375	C₄	—	134	1	no	—
376	C₄	—	134	2	no	—
377	C₄	—	134	2	no	—
378	C₄	#117×D₆₇	1	1	yes	characteristic
379	C₄	C₂×M₁₆×D₆₇	1	1	yes	characteristic
380	C₂	—	4	1	no	—
381	C₂	—	268	1	no	—
382	C₂	—	134	2	no	—
383	C₂	#431×D₆₇	1	1	yes	characteristic
384	C₂	#22573311	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₆₇
commutator, socle	C₂²×C₆₇	C₂³×C₈
Fitting	C₆₇×#2163	C₂
prime radical	C₂×#11761628	C₂×C₄
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	#2163	D₆₇
hypocenter	C₆₇	#33421
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. #22562015	C₂	semidirect
3. #22562013	C₂	semidirect
4. #22562012	C₂	semidirect
5. #22562010	C₂	semidirect
6. #22562010	C₂	semidirect
7. #22561966	C₂	semidirect
9. #22561802	C₂	semidirect
10. #346×D₆₇	C₂	semidirect
11. C₆₇×#2163	C₂	semidirect
199. #2163	D₆₇	semidirect
204. C₆₇	#33421	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
#22562015	2
#22562013	2
#22562012	2
#22562010	2
#22561966	2
#22561821	2
#22561802	2
#346×D₆₇	2
C₆₇×#2163	2
#33421	67