Subgroups — C₂×C₃×#3176 #10679287

Order 768.

2098 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#540	C₂	1	2	yes	maximal, complemented
2	C₃×#3176	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#490	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#466	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#442	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×C₄×D₈	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#3176	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₃×D₈	C₂²	1	2	yes	—
13	C₂²×C₃×D₈	C₂²	1	2	yes	—
14	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
16	C₃×#540	—	2	8	no	—
17	C₃×#540	C₂²	1	16	yes	complemented
18	C₂×C₃×#127	C₂²	1	2	yes	—
19	C₂×C₃×#125	C₂²	1	2	yes	—
20	C₂×C₃×#123	—	2	4	no	—
21	C₂×C₃×#121	—	2	4	no	—
22	C₂×C₃×#121	C₂²	1	4	yes	—
23	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
24	C₂×C₃×#117	C₂²	1	1	yes	characteristic
25	C₃×#499	C₂²	1	8	yes	complemented
26	C₃×#493	C₂²	1	8	yes	complemented
27	C₃×#490	C₂²	1	16	yes	complemented
28	C₃×#469	C₂²	1	16	yes	complemented
29	C₃×#466	C₂²	1	16	yes	complemented
30	C₃×#442	C₂²	1	16	yes	complemented
31	C₃×C₄×D₈	C₂²	1	16	yes	complemented
32	C₂×C₃×#107	C₂²	1	2	yes	—
33	C₂×C₃×#106	C₂²	1	2	yes	—
34	C₂×C₃×#102	C₂²	1	4	yes	—
35	C₂×C₃×#102	C₂²	1	4	yes	—
36	C₃×#405	C₂²	1	8	yes	complemented
37	C₂×C₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₃×#97	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
41	C₂×#540	C₂×C₃	1	2	yes	complemented
42	#3176	C₂×C₃	1	16	yes	direct product factor
43	C₂×#499	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#493	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#490	C₂×C₃	1	2	yes	complemented
46	C₂×#469	C₂×C₃	1	2	yes	complemented
47	C₂×#466	C₂×C₃	1	2	yes	complemented
48	C₂×#442	C₂×C₃	1	2	yes	complemented
49	C₂×C₄×D₈	C₂×C₃	1	2	yes	complemented
50	C₂×#405	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂²×C₃×D₄	—	2	4	no	—
52	C₂²×C₃×D₄	—	2	4	no	—
53	C₂²×C₃×D₄	C₂³	1	4	yes	—
54	C₂³×C₃×C₄	—	2	4	no	—
55	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
56	C₂×C₃×D₈	—	2	8	no	—
57	C₂×C₃×D₈	—	2	8	no	—
58	C₂×C₃×D₈	C₂³	1	8	yes	—
59	C₂×C₃×D₈	C₂³	1	8	yes	—
60	C₂×C₃×M₁₆	—	2	4	no	—
61	C₂×C₃×M₁₆	C₂³	1	4	yes	—
62	C₂²×C₃×C₈	—	2	4	no	—
63	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₈	C₂³	1	4	yes	—
65	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
68	C₃×#127	—	2	4	no	—
69	C₃×#127	C₂³	1	8	yes	—
70	C₃×#125	—	2	4	no	—
71	C₃×#125	C₂³	1	8	yes	—
72	C₃×#123	—	2	32	no	—
73	C₃×#121	—	2	8	no	—
74	C₃×#121	—	2	32	no	—
75	C₃×#121	C₂³	1	16	yes	—
76	C₃×C₄×D₄	—	2	8	no	—
77	C₃×C₄×D₄	C₂³	1	16	yes	—
78	C₃×#117	D₄	1	4	yes	—
79	C₃×#117	C₂³	1	4	yes	—
80	C₂×C₃×C₄⋊C₄	—	2	4	no	—
81	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
82	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
83	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
84	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
85	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
86	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
88	C₃×#107	C₂³	1	8	yes	—
89	C₃×#106	C₂³	1	8	yes	—
90	C₃×#102	C₂³	1	16	yes	—
91	C₃×#102	C₂³	1	16	yes	—
92	C₃×#97	C₂³	1	4	yes	—
93	C₃×#97	C₂³	1	4	yes	—
94	C₃×C₄×C₈	C₂³	1	4	yes	—
95	C₃×C₄×C₈	C₂³	1	4	yes	—
96	C₂²×D₈	C₂²×C₃	1	2	yes	—
97	C₂²×D₈	C₂²×C₃	1	2	yes	—
98	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
99	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
100	#540	—	2	8	no	—
101	#540	C₂²×C₃	1	16	yes	complemented
102	C₂×#127	C₂²×C₃	1	2	yes	—
103	C₂×#125	C₂²×C₃	1	2	yes	—
104	C₂×#123	—	2	4	no	—
105	C₂×#121	—	2	4	no	—
106	C₂×#121	C₂²×C₃	1	4	yes	—
107	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
108	C₂×#117	C₂²×C₃	1	1	yes	characteristic
109	#499	C₂²×C₃	1	8	yes	complemented
110	#493	C₂²×C₃	1	8	yes	complemented
111	#490	C₂²×C₃	1	16	yes	complemented
112	#469	C₂²×C₃	1	16	yes	complemented
113	#466	C₂²×C₃	1	16	yes	complemented
114	#442	C₂²×C₃	1	16	yes	complemented
115	C₄×D₈	C₂²×C₃	1	16	yes	complemented
116	C₂×#107	C₂²×C₃	1	2	yes	—
117	C₂×#106	C₂²×C₃	1	2	yes	—
118	C₂×#102	C₂²×C₃	1	4	yes	—
119	C₂×#102	C₂²×C₃	1	4	yes	—
120	#405	C₂²×C₃	1	8	yes	complemented
121	C₂×#97	C₂²×C₃	1	1	yes	characteristic
122	C₂×#97	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
125	C₂⁴×C₃	—	2	4	no	—
126	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×D₄	—	2	16	no	—
128	C₂×C₃×D₄	—	2	4	no	—
129	C₂×C₃×D₄	—	2	16	no	—
130	C₂×C₃×D₄	—	2	8	no	—
131	C₂×C₃×D₄	—	2	8	no	—
132	C₂×C₃×D₄	—	8	8	no	—
133	C₂×C₃×D₄	—	8	8	no	—
134	C₂×C₃×D₄	C₂⁴	1	8	yes	—
135	C₂²×C₃×C₄	—	2	2	no	—
136	C₂²×C₃×C₄	—	2	2	no	—
137	C₂²×C₃×C₄	—	2	4	no	—
138	C₂²×C₃×C₄	—	2	16	no	—
139	C₂²×C₃×C₄	—	8	8	no	—
140	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
141	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
142	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
143	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
145	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
146	C₃×D₈	—	2	16	no	—
147	C₃×D₈	—	2	16	no	—
148	C₃×M₁₆	—	2	8	no	—
149	C₂×C₃×C₈	—	2	2	no	—
150	C₂×C₃×C₈	—	2	2	no	—
151	C₂×C₃×C₈	—	2	8	no	—
152	C₂×C₃×C₈	#41	1	4	yes	—
153	C₂×C₃×C₈	#41	1	4	yes	—
154	C₂×C₃×C₈	C₂⁴	1	2	yes	—
155	C₂×C₃×C₈	C₂⁴	1	2	yes	—
156	C₂×C₃×C₈	C₂⁴	1	2	yes	—
157	C₂×C₃×C₈	C₂⁴	1	2	yes	—
158	C₃×C₄⋊C₄	—	2	16	no	—
159	C₃×C₄⋊C₄	—	2	4	no	—
160	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
161	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
162	C₃×C₂²⋊C₄	—	2	16	no	—
163	C₃×C₂²⋊C₄	—	2	16	no	—
164	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
165	C₃×C₄²	C₂×D₄	1	2	yes	—
166	C₃×C₄²	C₂×D₄	1	2	yes	—
167	C₃×C₄²	C₂⁴	1	2	yes	—
168	C₃×C₄²	C₂⁴	1	2	yes	—
169	C₂²×D₄	—	2	4	no	—
170	C₂²×D₄	—	2	4	no	—
171	C₂²×D₄	C₂³×C₃	1	4	yes	—
172	C₂³×C₄	—	2	4	no	—
173	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
174	C₂×D₈	—	2	8	no	—
175	C₂×D₈	—	2	8	no	—
176	C₂×D₈	C₂³×C₃	1	8	yes	—
177	C₂×D₈	C₂³×C₃	1	8	yes	—
178	C₂×M₁₆	—	2	4	no	—
179	C₂×M₁₆	C₂³×C₃	1	4	yes	—
180	C₂²×C₈	—	2	4	no	—
181	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₈	C₂³×C₃	1	4	yes	—
183	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
186	#127	—	2	4	no	—
187	#127	C₂³×C₃	1	8	yes	—
188	#125	—	2	4	no	—
189	#125	C₂³×C₃	1	8	yes	—
190	#123	—	2	32	no	—
191	#121	—	2	8	no	—
192	#121	—	2	32	no	—
193	#121	C₂³×C₃	1	16	yes	—
194	C₄×D₄	—	2	8	no	—
195	C₄×D₄	C₂³×C₃	1	16	yes	—
196	#117	C₃×D₄	1	4	yes	—
197	#117	C₂³×C₃	1	4	yes	—
198	C₂×C₄⋊C₄	—	2	4	no	—
199	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
200	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
201	C₂×C₂²⋊C₄	—	2	4	no	—
202	C₂×C₂²⋊C₄	—	2	4	no	—
203	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
204	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
206	#107	C₂³×C₃	1	8	yes	—
207	#106	C₂³×C₃	1	8	yes	—
208	#102	C₂³×C₃	1	16	yes	—
209	#102	C₂³×C₃	1	16	yes	—
210	#97	C₂³×C₃	1	4	yes	—
211	#97	C₂³×C₃	1	4	yes	—
212	C₄×C₈	C₂³×C₃	1	4	yes	—
213	C₄×C₈	C₂³×C₃	1	4	yes	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	2	4	no	—
216	C₂³×C₃	—	2	8	no	—
217	C₂³×C₃	—	4	8	no	—
218	C₂³×C₃	—	4	8	no	—
219	C₂³×C₃	—	4	8	no	—
220	C₂³×C₃	C₂²×D₄	1	2	yes	—
221	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
222	C₃×D₄	—	2	8	no	—
223	C₃×D₄	—	2	8	no	—
224	C₃×D₄	—	4	8	no	—
225	C₃×D₄	—	8	16	no	—
226	C₃×D₄	—	8	16	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	8	no	—
234	C₂×C₃×C₄	—	4	8	no	—
235	C₂×C₃×C₄	—	8	16	no	—
236	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
237	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
238	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
239	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂×#41	1	2	yes	—
241	C₂×C₃×C₄	C₂×#41	1	2	yes	—
242	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
243	C₃×C₈	—	2	2	no	—
244	C₃×C₈	—	2	2	no	—
245	C₃×C₈	C₂×#41	1	4	yes	—
246	C₃×C₈	C₂×#41	1	4	yes	—
247	C₂⁴	—	2	4	no	—
248	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂×D₄	—	2	16	no	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	—	2	16	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	8	no	—
254	C₂×D₄	—	8	8	no	—
255	C₂×D₄	—	8	8	no	—
256	C₂×D₄	C₂⁴×C₃	1	8	yes	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	16	no	—
261	C₂²×C₄	—	8	8	no	—
262	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
263	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
264	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
266	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
267	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
268	D₈	—	2	16	no	—
269	D₈	—	2	16	no	—
270	M₁₆	—	2	8	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	8	no	—
274	C₂×C₈	C₃×#41	1	4	yes	—
275	C₂×C₈	C₃×#41	1	4	yes	—
276	C₂×C₈	C₂⁴×C₃	1	2	yes	—
277	C₂×C₈	C₂⁴×C₃	1	2	yes	—
278	C₂×C₈	C₂⁴×C₃	1	2	yes	—
279	C₂×C₈	C₂⁴×C₃	1	2	yes	—
280	C₄⋊C₄	—	2	16	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
283	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
284	C₂²⋊C₄	—	2	16	no	—
285	C₂²⋊C₄	—	2	16	no	—
286	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
287	C₄²	C₂×C₃×D₄	1	2	yes	—
288	C₄²	C₂×C₃×D₄	1	2	yes	—
289	C₄²	C₂⁴×C₃	1	2	yes	—
290	C₄²	C₂⁴×C₃	1	2	yes	—
291	C₂²×C₃	—	2	2	no	—
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	4	4	no	—
294	C₂²×C₃	—	4	8	no	—
295	C₂²×C₃	—	4	8	no	—
296	C₂²×C₃	—	4	8	no	—
297	C₂²×C₃	—	8	16	no	—
298	C₂²×C₃	#532	1	2	yes	—
299	C₂²×C₃	#576	1	4	yes	—
300	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	2	4	no	—
303	C₃×C₄	—	2	4	no	—
304	C₃×C₄	—	4	8	no	—
305	C₃×C₄	#532	1	2	yes	—
306	C₃×C₄	C₂²×#41	1	1	yes	characteristic
307	C₃×C₄	C₂²×#41	1	1	yes	characteristic
308	C₂³	—	2	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	8	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	4	8	no	—
314	C₂³	C₂²×C₃×D₄	1	2	yes	—
315	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
316	D₄	—	2	8	no	—
317	D₄	—	2	8	no	—
318	D₄	—	4	8	no	—
319	D₄	—	8	16	no	—
320	D₄	—	8	16	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	4	8	no	—
329	C₂×C₄	—	8	16	no	—
330	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
331	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
332	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
333	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
334	C₂×C₄	C₂×C₃×#41	1	2	yes	—
335	C₂×C₄	C₂×C₃×#41	1	2	yes	—
336	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
337	C₈	—	2	2	no	—
338	C₈	—	2	2	no	—
339	C₈	C₂×C₃×#41	1	4	yes	—
340	C₈	C₂×C₃×#41	1	4	yes	—
341	C₂×C₃	—	4	2	no	—
342	C₂×C₃	—	8	8	no	—
343	C₂×C₃	#3176	1	4	yes	direct product factor
344	C₂×C₃	C₂×#532	1	1	yes	characteristic
345	C₂×C₃	C₂×#576	1	2	yes	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	8	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	8	16	no	—
353	C₂²	C₃×#532	1	2	yes	—
354	C₂²	C₃×#576	1	4	yes	—
355	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	4	no	—
358	C₄	—	2	4	no	—
359	C₄	—	4	8	no	—
360	C₄	C₃×#532	1	2	yes	—
361	C₄	C₂²×C₃×#41	1	1	yes	characteristic
362	C₄	C₂²×C₃×#41	1	1	yes	characteristic
363	C₃	C₂×#3176	1	1	yes	characteristic, direct product factor, Sylow
364	C₂	—	4	2	no	—
365	C₂	—	8	8	no	—
366	C₂	C₃×#3176	1	4	yes	direct product factor
367	C₂	C₂×C₃×#532	1	1	yes	characteristic
368	C₂	C₂×C₃×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#540	C₂	semidirect
2. C₃×#3176	C₂	direct (N × H)
3. C₂×C₃×#499	C₂	semidirect
4. C₂×C₃×#493	C₂	semidirect
5. C₂×C₃×#490	C₂	semidirect
6. C₂×C₃×#469	C₂	semidirect
7. C₂×C₃×#466	C₂	semidirect
8. C₂×C₃×#442	C₂	semidirect
9. C₂×C₃×C₄×D₈	C₂	semidirect
10. C₂×C₃×#405	C₂	semidirect
11. C₂×#3176	C₃	direct (N × H)
17. C₃×#540	C₂²	semidirect
25. C₃×#499	C₂²	semidirect
26. C₃×#493	C₂²	semidirect
27. C₃×#490	C₂²	semidirect
28. C₃×#469	C₂²	semidirect
29. C₃×#466	C₂²	semidirect
30. C₃×#442	C₂²	semidirect
31. C₃×C₄×D₈	C₂²	semidirect
36. C₃×#405	C₂²	semidirect
41. C₂×#540	C₂×C₃	semidirect
42. #3176	C₂×C₃	direct (N × H)
43. C₂×#499	C₂×C₃	semidirect
44. C₂×#493	C₂×C₃	semidirect
45. C₂×#490	C₂×C₃	semidirect
46. C₂×#469	C₂×C₃	semidirect
47. C₂×#466	C₂×C₃	semidirect
48. C₂×#442	C₂×C₃	semidirect
49. C₂×C₄×D₈	C₂×C₃	semidirect
50. C₂×#405	C₂×C₃	semidirect
101. #540	C₂²×C₃	semidirect
109. #499	C₂²×C₃	semidirect
110. #493	C₂²×C₃	semidirect
111. #490	C₂²×C₃	semidirect
112. #469	C₂²×C₃	semidirect
113. #466	C₂²×C₃	semidirect
114. #442	C₂²×C₃	semidirect
115. C₄×D₈	C₂²×C₃	semidirect
120. #405	C₂²×C₃	semidirect
343. C₂×C₃	#3176	direct (N × H)
363. C₃	C₂×#3176	direct (N × H)
366. C₂	C₃×#3176	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×#540	2
C₃×#3176	2
C₂×C₃×#499	2
C₂×C₃×#493	2
C₂×C₃×#490	2
C₂×C₃×#469	2
C₂×C₃×#466	2
C₂×C₃×#442	2
C₂×C₃×C₄×D₈	2
C₂×C₃×#405	2
C₂×#3176	3

Subgroups — C2×C3×#3176 #10679287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3176 #10679287