Subgroups — C₂×C₃×#3142 #10679224

Order 768.

2182 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3142	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#491	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#490	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#488	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#417	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#3142	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₃×#41	C₂²	1	2	yes	—
11	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
12	C₃×#532	—	2	4	no	—
13	C₃×#532	C₂²	1	8	yes	—
14	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#127	C₂²	1	1	yes	characteristic
16	C₂×C₃×#125	—	2	2	no	—
17	C₂×C₃×#125	—	2	4	no	—
18	C₂×C₃×#125	C₂²	1	2	yes	—
19	C₂×C₃×#125	C₂²	1	2	yes	—
20	C₂×C₃×#125	C₂²	1	8	yes	complemented
21	C₂×C₃×#124	C₂²	1	2	yes	—
22	C₂×C₃×#121	—	2	2	no	—
23	C₂×C₃×C₄×D₄	—	2	2	no	—
24	C₂²×C₃×C₄⋊C₄	—	2	2	no	—
25	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
27	C₃×#491	C₂²	1	16	yes	complemented
28	C₃×#490	C₂²	1	16	yes	complemented
29	C₃×#488	C₂²	1	32	yes	complemented
30	C₃×#417	C₂²	1	32	yes	complemented
31	C₂×C₃×#103	C₂²	1	8	yes	—
32	C₂×C₃×#102	C₂²	1	8	yes	—
33	C₃×C₄×M₁₆	C₂²	1	8	yes	complemented
34	C₂×C₃×#97	C₂²	1	2	yes	—
35	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
36	C₂×#532	C₂×C₃	1	1	yes	characteristic
37	C₂²×#125	C₂×C₃	1	1	yes	characteristic, complemented
38	#3142	C₂×C₃	1	16	yes	direct product factor
39	C₂×#491	C₂×C₃	1	2	yes	complemented
40	C₂×#490	C₂×C₃	1	2	yes	complemented
41	C₂×#488	C₂×C₃	1	4	yes	complemented
42	C₂×#417	C₂×C₃	1	4	yes	complemented
43	C₂×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×C₃×#41	—	2	4	no	—
45	C₂×C₃×#41	—	2	16	no	—
46	C₂×C₃×#41	C₂³	1	8	yes	—
47	C₂²×C₃×Q₈	C₂³	1	2	yes	—
48	C₂²×C₃×D₄	—	2	2	no	—
49	C₂²×C₃×D₄	—	2	2	no	—
50	C₂²×C₃×D₄	C₂³	1	2	yes	—
51	C₂³×C₃×C₄	—	2	2	no	—
52	C₂³×C₃×C₄	—	2	2	no	—
53	C₂³×C₃×C₄	D₄	1	2	yes	—
54	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
55	C₂×C₃×M₁₆	—	2	8	no	—
56	C₂×C₃×M₁₆	C₂³	1	8	yes	—
57	C₂²×C₃×C₈	C₂³	1	4	yes	—
58	C₃×C₄⋊Q₈	—	2	2	no	—
59	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₃×#127	—	2	2	no	—
61	C₃×#127	C₂³	1	4	yes	—
62	C₃×#125	—	2	4	no	—
63	C₃×#125	—	2	4	no	—
64	C₃×#125	—	2	16	no	—
65	C₃×#125	C₂³	1	8	yes	—
66	C₃×#125	C₂³	1	8	yes	—
67	C₃×#124	—	2	4	no	—
68	C₃×#124	C₂³	1	8	yes	—
69	C₃×#121	—	2	16	no	—
70	C₃×C₄×D₄	—	2	16	no	—
71	C₂×C₃×C₄⋊C₄	—	2	4	no	—
72	C₂×C₃×C₄⋊C₄	—	2	4	no	—
73	C₂×C₃×C₄⋊C₄	—	2	16	no	—
74	C₂×C₃×C₄⋊C₄	—	2	4	no	—
75	C₂×C₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
80	C₂×C₃×C₄²	D₄	1	2	yes	—
81	C₂×C₃×C₄²	D₄	1	4	yes	—
82	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₄²	C₂³	1	4	yes	—
85	C₃×#103	C₂³	1	32	yes	—
86	C₃×#102	C₂³	1	32	yes	—
87	C₃×#97	C₂³	1	8	yes	—
88	C₃×C₄×C₈	C₂³	1	8	yes	—
89	C₂²×#41	C₂²×C₃	1	2	yes	—
90	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
91	#532	—	2	4	no	—
92	#532	C₂²×C₃	1	8	yes	—
93	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
94	C₂×#127	C₂²×C₃	1	1	yes	characteristic
95	C₂×#125	—	2	2	no	—
96	C₂×#125	—	2	4	no	—
97	C₂×#125	C₂²×C₃	1	2	yes	—
98	C₂×#125	C₂²×C₃	1	2	yes	—
99	C₂×#125	C₂²×C₃	1	8	yes	complemented
100	C₂×#124	C₂²×C₃	1	2	yes	—
101	C₂×#121	—	2	2	no	—
102	C₂×C₄×D₄	—	2	2	no	—
103	C₂²×C₄⋊C₄	—	2	2	no	—
104	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
105	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
106	#491	C₂²×C₃	1	16	yes	complemented
107	#490	C₂²×C₃	1	16	yes	complemented
108	#488	C₂²×C₃	1	32	yes	complemented
109	#417	C₂²×C₃	1	32	yes	complemented
110	C₂×#103	C₂²×C₃	1	8	yes	—
111	C₂×#102	C₂²×C₃	1	8	yes	—
112	C₄×M₁₆	C₂²×C₃	1	8	yes	complemented
113	C₂×#97	C₂²×C₃	1	2	yes	—
114	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
115	C₂⁴×C₃	—	2	2	no	—
116	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
117	C₃×#41	—	2	32	no	—
118	C₃×#41	—	4	16	no	—
119	C₂×C₃×Q₈	—	2	2	no	—
120	C₂×C₃×Q₈	—	2	8	no	—
121	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
122	C₂×C₃×D₄	—	2	8	no	—
123	C₂×C₃×D₄	—	2	8	no	—
124	C₂×C₃×D₄	—	2	2	no	—
125	C₂×C₃×D₄	—	2	8	no	—
126	C₂×C₃×D₄	—	4	8	no	—
127	C₂×C₃×D₄	—	4	8	no	—
128	C₂×C₃×D₄	C₂⁴	1	4	yes	—
129	C₂²×C₃×C₄	—	2	8	no	—
130	C₂²×C₃×C₄	—	2	2	no	—
131	C₂²×C₃×C₄	—	2	4	no	—
132	C₂²×C₃×C₄	—	2	8	no	—
133	C₂²×C₃×C₄	—	4	4	no	—
134	C₂²×C₃×C₄	—	4	8	no	—
135	C₂²×C₃×C₄	—	4	8	no	—
136	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
137	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
138	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
139	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
140	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₃×C₄	#41	1	8	yes	—
142	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
143	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
144	C₃×M₁₆	—	2	16	no	—
145	C₂×C₃×C₈	—	2	8	no	—
146	C₂×C₃×C₈	C₂⁴	1	8	yes	—
147	C₃×C₄⋊C₄	—	2	16	no	—
148	C₃×C₄⋊C₄	—	2	16	no	—
149	C₃×C₄⋊C₄	—	2	8	no	—
150	C₃×C₄⋊C₄	—	2	4	no	—
151	C₃×C₄⋊C₄	—	2	8	no	—
152	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
153	C₃×C₂²⋊C₄	—	2	16	no	—
154	C₃×C₄²	C₂×D₄	1	8	yes	—
155	C₃×C₄²	C₂×D₄	1	2	yes	—
156	C₃×C₄²	C₂×D₄	1	2	yes	—
157	C₃×C₄²	C₂⁴	1	2	yes	—
158	C₃×C₄²	C₂⁴	1	2	yes	—
159	C₂×#41	—	2	4	no	—
160	C₂×#41	—	2	16	no	—
161	C₂×#41	C₂³×C₃	1	8	yes	—
162	C₂²×Q₈	C₂³×C₃	1	2	yes	—
163	C₂²×D₄	—	2	2	no	—
164	C₂²×D₄	—	2	2	no	—
165	C₂²×D₄	C₂³×C₃	1	2	yes	—
166	C₂³×C₄	—	2	2	no	—
167	C₂³×C₄	—	2	2	no	—
168	C₂³×C₄	C₃×D₄	1	2	yes	—
169	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
170	C₂×M₁₆	—	2	8	no	—
171	C₂×M₁₆	C₂³×C₃	1	8	yes	—
172	C₂²×C₈	C₂³×C₃	1	4	yes	—
173	C₄⋊Q₈	—	2	2	no	—
174	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
175	#127	—	2	2	no	—
176	#127	C₂³×C₃	1	4	yes	—
177	#125	—	2	4	no	—
178	#125	—	2	4	no	—
179	#125	—	2	16	no	—
180	#125	C₂³×C₃	1	8	yes	—
181	#125	C₂³×C₃	1	8	yes	—
182	#124	—	2	4	no	—
183	#124	C₂³×C₃	1	8	yes	—
184	#121	—	2	16	no	—
185	C₄×D₄	—	2	16	no	—
186	C₂×C₄⋊C₄	—	2	4	no	—
187	C₂×C₄⋊C₄	—	2	4	no	—
188	C₂×C₄⋊C₄	—	2	16	no	—
189	C₂×C₄⋊C₄	—	2	2	no	—
190	C₂×C₄⋊C₄	—	2	4	no	—
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
193	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
194	C₂×C₂²⋊C₄	—	2	4	no	—
195	C₂×C₄²	C₃×D₄	1	2	yes	—
196	C₂×C₄²	C₃×D₄	1	4	yes	—
197	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₄²	C₂³×C₃	1	4	yes	—
200	#103	C₂³×C₃	1	32	yes	—
201	#102	C₂³×C₃	1	32	yes	—
202	#97	C₂³×C₃	1	8	yes	—
203	C₄×C₈	C₂³×C₃	1	8	yes	—
204	C₂³×C₃	—	2	4	no	—
205	C₂³×C₃	—	2	4	no	—
206	C₂³×C₃	—	4	4	no	—
207	C₂³×C₃	—	4	8	no	—
208	C₂³×C₃	#124	1	4	yes	—
209	C₂³×C₃	C₂²×D₄	1	2	yes	—
210	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
211	C₃×Q₈	—	2	8	no	—
212	C₃×Q₈	—	4	4	no	—
213	C₃×D₄	—	2	8	no	—
214	C₃×D₄	—	4	16	no	—
215	C₃×D₄	—	4	16	no	—
216	C₃×D₄	—	4	4	no	—
217	C₂×C₃×C₄	—	2	4	no	—
218	C₂×C₃×C₄	—	2	4	no	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	2	8	no	—
221	C₂×C₃×C₄	—	4	8	no	—
222	C₂×C₃×C₄	—	4	16	no	—
223	C₂×C₃×C₄	—	4	4	no	—
224	C₂×C₃×C₄	—	4	8	no	—
225	C₂×C₃×C₄	—	4	16	no	—
226	C₂×C₃×C₄	#124	1	4	yes	—
227	C₂×C₃×C₄	#124	1	8	yes	—
228	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
229	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
230	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
231	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×#41	1	4	yes	—
233	C₂×C₃×C₄	C₂×#41	1	8	yes	—
234	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
235	C₃×C₈	—	2	8	no	—
236	C₂⁴	—	2	2	no	—
237	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
238	#41	—	2	32	no	—
239	#41	—	4	16	no	—
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	—	2	8	no	—
242	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
243	C₂×D₄	—	2	8	no	—
244	C₂×D₄	—	2	8	no	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	—	2	8	no	—
247	C₂×D₄	—	4	8	no	—
248	C₂×D₄	—	4	8	no	—
249	C₂×D₄	C₂⁴×C₃	1	4	yes	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	—	4	8	no	—
256	C₂²×C₄	—	4	8	no	—
257	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
258	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
259	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
260	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
262	C₂²×C₄	C₃×#41	1	8	yes	—
263	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
264	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
265	M₁₆	—	2	16	no	—
266	C₂×C₈	—	2	8	no	—
267	C₂×C₈	C₂⁴×C₃	1	8	yes	—
268	C₄⋊C₄	—	2	16	no	—
269	C₄⋊C₄	—	2	16	no	—
270	C₄⋊C₄	—	2	8	no	—
271	C₄⋊C₄	—	2	4	no	—
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
274	C₂²⋊C₄	—	2	16	no	—
275	C₄²	C₂×C₃×D₄	1	8	yes	—
276	C₄²	C₂×C₃×D₄	1	2	yes	—
277	C₄²	C₂×C₃×D₄	1	2	yes	—
278	C₄²	C₂⁴×C₃	1	2	yes	—
279	C₄²	C₂⁴×C₃	1	2	yes	—
280	C₂²×C₃	—	2	8	no	—
281	C₂²×C₃	—	2	4	no	—
282	C₂²×C₃	—	4	4	no	—
283	C₂²×C₃	—	4	8	no	—
284	C₂²×C₃	—	8	8	no	—
285	C₂²×C₃	C₂×#124	1	4	yes	—
286	C₂²×C₃	C₂×#124	1	2	yes	—
287	C₂²×C₃	#575	1	4	yes	—
288	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	2	4	no	—
291	C₃×C₄	—	4	4	no	—
292	C₃×C₄	—	4	8	no	—
293	C₃×C₄	C₂×#124	1	4	yes	—
294	C₃×C₄	C₂×#124	1	2	yes	—
295	C₃×C₄	C₂²×#41	1	2	yes	—
296	C₂³	—	2	4	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	4	8	no	—
299	C₂³	—	4	4	no	—
300	C₂³	C₃×#124	1	4	yes	—
301	C₂³	C₂²×C₃×D₄	1	2	yes	—
302	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
303	Q₈	—	2	8	no	—
304	Q₈	—	4	4	no	—
305	D₄	—	2	8	no	—
306	D₄	—	4	16	no	—
307	D₄	—	4	16	no	—
308	D₄	—	4	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	4	8	no	—
314	C₂×C₄	—	4	16	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	16	no	—
318	C₂×C₄	C₃×#124	1	4	yes	—
319	C₂×C₄	C₃×#124	1	8	yes	—
320	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
321	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
322	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
323	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
324	C₂×C₄	C₂×C₃×#41	1	4	yes	—
325	C₂×C₄	C₂×C₃×#41	1	8	yes	—
326	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
327	C₈	—	2	8	no	—
328	C₂×C₃	—	2	4	no	—
329	C₂×C₃	—	8	4	no	—
330	C₂×C₃	#3142	1	4	yes	direct product factor
331	C₂×C₃	C₂²×#124	1	1	yes	characteristic
332	C₂×C₃	C₂×#575	1	2	yes	—
333	C₂²	—	2	8	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	8	no	—
337	C₂²	—	8	8	no	—
338	C₂²	C₂×C₃×#124	1	4	yes	—
339	C₂²	C₂×C₃×#124	1	2	yes	—
340	C₂²	C₃×#575	1	4	yes	—
341	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
342	C₄	—	2	4	no	—
343	C₄	—	2	4	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	8	no	—
346	C₄	C₂×C₃×#124	1	4	yes	—
347	C₄	C₂×C₃×#124	1	2	yes	—
348	C₄	C₂²×C₃×#41	1	2	yes	—
349	C₃	C₂×#3142	1	1	yes	characteristic, direct product factor, Sylow
350	C₂	—	2	4	no	—
351	C₂	—	8	4	no	—
352	C₂	C₃×#3142	1	4	yes	direct product factor
353	C₂	C₂²×C₃×#124	1	1	yes	characteristic
354	C₂	C₂×C₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂×C₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×#125	C₂	semidirect
3. C₃×#3142	C₂	direct (N × H)
4. C₂×C₃×#491	C₂	semidirect
5. C₂×C₃×#490	C₂	semidirect
6. C₂×C₃×#488	C₂	semidirect
7. C₂×C₃×#417	C₂	semidirect
8. C₂×C₃×C₄×M₁₆	C₂	semidirect
9. C₂×#3142	C₃	direct (N × H)
20. C₂×C₃×#125	C₂²	semidirect
27. C₃×#491	C₂²	semidirect
28. C₃×#490	C₂²	semidirect
29. C₃×#488	C₂²	semidirect
30. C₃×#417	C₂²	semidirect
33. C₃×C₄×M₁₆	C₂²	semidirect
37. C₂²×#125	C₂×C₃	semidirect
38. #3142	C₂×C₃	direct (N × H)
39. C₂×#491	C₂×C₃	semidirect
40. C₂×#490	C₂×C₃	semidirect
41. C₂×#488	C₂×C₃	semidirect
42. C₂×#417	C₂×C₃	semidirect
43. C₂×C₄×M₁₆	C₂×C₃	semidirect
99. C₂×#125	C₂²×C₃	semidirect
106. #491	C₂²×C₃	semidirect
107. #490	C₂²×C₃	semidirect
108. #488	C₂²×C₃	semidirect
109. #417	C₂²×C₃	semidirect
112. C₄×M₁₆	C₂²×C₃	semidirect
330. C₂×C₃	#3142	direct (N × H)
349. C₃	C₂×#3142	direct (N × H)
352. C₂	C₃×#3142	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#532	2
C₂²×C₃×#125	2
C₃×#3142	2
C₂×C₃×#491	2
C₂×C₃×#490	2
C₂×C₃×#488	2
C₂×C₃×#417	2
C₂×C₃×C₄×M₁₆	2
C₂×#3142	3

Subgroups — C2×C3×#3142 #10679224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3142 #10679224