Subgroups — C₂×C₃×#4696 #11874240

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#204	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#875	C₂	1	2	yes	maximal, complemented
5	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4696	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#495	—	3	1	no	maximal
8	C₂×#4696	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
10	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
15	C₂×C₃×Dic₁₂	—	2	4	no	—
16	C₂×C₃×Dic₁₂	C₂²	1	4	yes	complemented
17	C₂×C₃×D₂₄	—	2	4	no	—
18	C₂×C₃×D₂₄	C₂²	1	4	yes	—
19	C₂×C₃×#204	—	2	8	no	—
20	C₂×C₃×#204	C₂²	1	8	yes	complemented
21	C₃×#875	—	2	4	no	—
22	C₃×#875	C₂²	1	8	yes	complemented
23	C₃²×C₄×C₈	C₂²	1	4	yes	complemented
24	C₂²×C₃×Q₁₆	—	3	1	no	—
25	C₂²×C₃×SD₁₆	—	3	2	no	—
26	C₂²×C₃×D₈	—	3	1	no	—
27	C₂×C₃×#124	—	3	2	no	—
28	C₂²×Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic
30	C₂²×#204	C₂×C₃	1	2	yes	complemented
31	C₂×#875	C₂×C₃	1	2	yes	complemented
32	C₃×#495	—	3	8	no	—
33	C₂×C₃×C₄×C₈	—	2	1	no	—
34	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
36	#4696	C₂×C₃	1	8	yes	direct product factor
37	C₂³×C₃×D₃	—	2	2	no	—
38	C₂²×C₃²×C₄	D₄	1	2	yes	—
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂²×C₃×Dic₃	—	2	2	no	—
41	C₂×C₃×D₁₂	—	2	4	no	—
42	C₂×C₃×D₁₂	—	2	4	no	—
43	C₂×C₃×D₁₂	—	2	2	no	—
44	C₂×C₃×D₁₂	C₂³	1	4	yes	—
45	C₂×C₃×Dic₆	—	2	4	no	—
46	C₂×C₃×Dic₆	—	2	4	no	—
47	C₂×C₃×Dic₆	—	2	2	no	—
48	C₂×C₃×Dic₆	C₂³	1	4	yes	—
49	C₂×C₃²×C₈	D₄	1	4	yes	—
50	C₂×C₃²×C₈	D₄	1	4	yes	—
51	C₂×C₃²×C₈	C₂³	1	2	yes	—
52	C₂×C₃²×C₈	C₂³	1	2	yes	—
53	C₃²×C₄²	D₄	1	2	yes	—
54	C₃²×C₄²	C₂³	1	2	yes	—
55	C₃×(C₂×D₃)⋊C₄	—	2	16	no	—
56	C₃×Dic₁₂	—	2	8	no	—
57	C₃×D₂₄	—	2	8	no	—
58	C₃×#204	—	2	16	no	—
59	C₂×#495	—	3	1	no	Sylow
60	C₂²×C₃×Q₈	—	3	2	no	—
61	C₂²×C₃×D₄	—	3	2	no	—
62	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
63	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
64	C₂×C₃×Q₁₆	—	3	4	no	—
65	C₂×C₃×Q₁₆	—	6	4	no	—
66	C₂×C₃×SD₁₆	—	3	8	no	—
67	C₂×C₃×SD₁₆	—	6	8	no	—
68	C₂×C₃×D₈	—	3	4	no	—
69	C₂×C₃×D₈	—	6	4	no	—
70	C₂²×C₃×C₈	—	2	1	no	—
71	C₂²×C₃×C₈	—	2	1	no	—
72	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₃×#124	—	3	8	no	—
77	C₃×#124	—	6	4	no	—
78	C₂×C₃×C₂²⋊C₄	—	6	4	no	—
79	C₂×C₃×C₄²	—	2	1	no	—
80	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
81	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
82	C₂×(C₂×D₃)⋊C₄	—	2	4	no	—
83	C₂×Dic₁₂	—	2	4	no	—
84	C₂×Dic₁₂	C₂²×C₃	1	4	yes	complemented
85	C₂×D₂₄	—	2	4	no	—
86	C₂×D₂₄	C₂²×C₃	1	4	yes	—
87	C₂×#204	—	2	8	no	—
88	C₂×#204	C₂²×C₃	1	8	yes	complemented
89	#875	—	2	4	no	—
90	#875	C₂²×C₃	1	8	yes	complemented
91	C₃×C₄×C₈	—	2	4	no	—
92	C₃×C₄×C₈	C₂×D₃	1	4	yes	complemented
93	C₃×C₄×C₈	C₂²×C₃	1	4	yes	complemented
94	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₃×D₃	—	2	4	no	—
96	C₂²×C₃×D₃	—	4	4	no	—
97	C₂²×C₃×D₃	—	4	8	no	—
98	C₂×C₃²×C₄	—	2	4	no	—
99	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
100	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
102	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
103	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
104	C₂×C₃×Dic₃	—	2	4	no	—
105	C₂×C₃×Dic₃	—	4	4	no	—
106	C₃×D₁₂	—	2	4	no	—
107	C₃×D₁₂	—	2	4	no	—
108	C₃×D₁₂	—	4	4	no	—
109	C₃×Dic₆	—	2	4	no	—
110	C₃×Dic₆	—	2	4	no	—
111	C₃×Dic₆	—	4	4	no	—
112	C₃²×C₈	C₂×D₄	1	4	yes	—
113	C₃²×C₈	C₂×D₄	1	4	yes	—
114	C₂²×Q₁₆	—	3	1	no	—
115	C₂²×SD₁₆	—	3	2	no	—
116	C₂²×D₈	—	3	1	no	—
117	C₂×#124	—	3	2	no	—
118	#495	—	3	8	no	—
119	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic, complemented
120	C₂⁴×C₃	—	6	2	no	—
121	C₂³×D₃	—	2	2	no	—
122	C₂×C₃×Q₈	—	3	4	no	—
123	C₂×C₃×Q₈	—	6	2	no	—
124	C₂×C₃×Q₈	—	6	4	no	—
125	C₂×C₃×Q₈	—	6	4	no	—
126	C₂×C₃×D₄	—	3	4	no	—
127	C₂×C₃×D₄	—	6	4	no	—
128	C₂×C₃×D₄	—	6	4	no	—
129	C₂×C₃×D₄	—	6	2	no	—
130	C₂²×C₃×C₄	—	2	2	no	—
131	C₂²×C₃×C₄	—	2	1	no	—
132	C₂²×C₃×C₄	—	6	2	no	—
133	C₂²×C₃×C₄	D₁₂	1	2	yes	—
134	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
135	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
137	C₂²×Dic₃	—	2	2	no	—
138	C₂×D₁₂	—	2	4	no	—
139	C₂×D₁₂	—	2	4	no	—
140	C₂×D₁₂	—	2	2	no	—
141	C₂×D₁₂	C₂³×C₃	1	4	yes	—
142	C₂×Dic₆	—	2	4	no	—
143	C₂×Dic₆	—	2	4	no	—
144	C₂×Dic₆	—	2	2	no	—
145	C₂×Dic₆	C₂³×C₃	1	4	yes	—
146	C₃×Q₁₆	—	6	8	no	—
147	C₃×SD₁₆	—	6	16	no	—
148	C₃×D₈	—	6	8	no	—
149	C₂×C₃×C₈	—	2	4	no	—
150	C₂×C₃×C₈	—	2	4	no	—
151	C₂×C₃×C₈	—	2	2	no	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	D₁₂	1	4	yes	—
154	C₂×C₃×C₈	D₁₂	1	4	yes	—
155	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
156	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
157	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
158	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
159	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
160	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
161	C₃×C₂²⋊C₄	—	6	16	no	—
162	C₃×C₄²	—	2	2	no	—
163	C₃×C₄²	—	2	2	no	—
164	C₃×C₄²	D₁₂	1	2	yes	—
165	C₃×C₄²	C₃×D₄	1	2	yes	—
166	C₃×C₄²	C₂²×D₃	1	2	yes	—
167	C₃×C₄²	C₂³×C₃	1	2	yes	—
168	(C₂×D₃)⋊C₄	—	2	16	no	—
169	Dic₁₂	—	2	8	no	—
170	D₂₄	—	2	8	no	—
171	#204	—	2	16	no	—
172	C₂²×C₃²	#127	1	2	yes	—
173	C₂²×C₃²	#135	1	4	yes	—
174	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₃×D₃	—	4	4	no	—
176	C₂×C₃×D₃	—	4	8	no	—
177	C₂×C₃×D₃	—	8	8	no	—
178	C₃²×C₄	—	2	4	no	—
179	C₃²×C₄	#127	1	2	yes	—
180	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
181	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
182	C₃×Dic₃	—	4	4	no	—
183	C₂²×Q₈	—	3	2	no	—
184	C₂²×D₄	—	3	2	no	—
185	C₂×Q₁₆	—	3	4	no	—
186	C₂×Q₁₆	—	6	4	no	—
187	C₂×SD₁₆	—	3	8	no	—
188	C₂×SD₁₆	—	6	8	no	—
189	C₂×D₈	—	3	4	no	—
190	C₂×D₈	—	6	4	no	—
191	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
192	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
193	#124	—	3	8	no	—
194	#124	—	6	4	no	—
195	C₂×C₂²⋊C₄	—	6	4	no	—
196	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
197	C₄×C₈	C₂×C₃×D₃	1	4	yes	complemented
198	C₂³×C₃	—	2	1	no	—
199	C₂³×C₃	—	6	4	no	—
200	C₂³×C₃	—	12	4	no	—
201	C₂³×C₃	—	12	8	no	—
202	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
203	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
204	C₂²×D₃	—	2	4	no	—
205	C₂²×D₃	—	4	4	no	—
206	C₂²×D₃	—	4	8	no	—
207	C₃×Q₈	—	6	4	no	—
208	C₃×Q₈	—	6	4	no	—
209	C₃×Q₈	—	12	4	no	—
210	C₃×D₄	—	6	4	no	—
211	C₃×D₄	—	6	4	no	—
212	C₃×D₄	—	12	4	no	—
213	C₂×C₃×C₄	—	2	8	no	—
214	C₂×C₃×C₄	—	2	4	no	—
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	4	no	—
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	6	4	no	—
222	C₂×C₃×C₄	—	12	4	no	—
223	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
224	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
226	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
227	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
228	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
230	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
231	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
233	C₂×Dic₃	—	2	4	no	—
234	C₂×Dic₃	—	4	4	no	—
235	D₁₂	—	2	4	no	—
236	D₁₂	—	2	4	no	—
237	D₁₂	—	4	4	no	—
238	Dic₆	—	2	4	no	—
239	Dic₆	—	2	4	no	—
240	Dic₆	—	4	4	no	—
241	C₃×C₈	—	2	4	no	—
242	C₃×C₈	—	2	4	no	—
243	C₃×C₈	C₂×D₁₂	1	4	yes	—
244	C₃×C₈	C₂×D₁₂	1	4	yes	—
245	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
246	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
247	C₂×C₃²	#495	1	4	yes	complemented
248	C₂×C₃²	C₂×#127	1	1	yes	characteristic
249	C₂×C₃²	C₂×#135	1	2	yes	—
250	C₃×D₃	—	8	4	no	—
251	C₂⁴	—	6	2	no	—
252	C₂×Q₈	—	3	4	no	—
253	C₂×Q₈	—	6	2	no	—
254	C₂×Q₈	—	6	4	no	—
255	C₂×Q₈	—	6	4	no	—
256	C₂×D₄	—	3	4	no	—
257	C₂×D₄	—	6	4	no	—
258	C₂×D₄	—	6	4	no	—
259	C₂×D₄	—	6	2	no	—
260	C₂²×C₄	—	6	2	no	—
261	C₂²×C₄	C₃×D₁₂	1	2	yes	—
262	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
263	Q₁₆	—	6	8	no	—
264	SD₁₆	—	6	16	no	—
265	D₈	—	6	8	no	—
266	C₂×C₈	C₃×D₁₂	1	4	yes	—
267	C₂×C₈	C₃×D₁₂	1	4	yes	—
268	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
269	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
270	C₂²⋊C₄	—	6	16	no	—
271	C₄²	C₃×D₁₂	1	2	yes	—
272	C₄²	C₂²×C₃×D₃	1	2	yes	—
273	C₂²×C₃	—	2	4	no	—
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	—	12	4	no	—
277	C₂²×C₃	—	12	8	no	—
278	C₂²×C₃	—	24	8	no	—
279	C₂²×C₃	#874	1	2	yes	—
280	C₂²×C₃	#904	1	4	yes	—
281	C₂²×C₃	C₃×#127	1	2	yes	—
282	C₂²×C₃	C₃×#135	1	4	yes	—
283	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
284	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
285	C₂×D₃	—	4	8	no	—
286	C₂×D₃	—	4	4	no	—
287	C₂×D₃	—	8	8	no	—
288	C₃×C₄	—	2	8	no	—
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	2	4	no	—
291	C₃×C₄	—	2	1	no	—
292	C₃×C₄	—	2	1	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	12	4	no	—
295	C₃×C₄	#874	1	2	yes	—
296	C₃×C₄	C₃×#127	1	2	yes	—
297	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
298	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
299	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
300	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
301	Dic₃	—	4	4	no	—
302	C₃²	C₂×#495	1	1	yes	characteristic, complemented, Sylow
303	C₂³	—	6	4	no	—
304	C₂³	—	12	8	no	—
305	C₂³	—	12	4	no	—
306	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
307	Q₈	—	6	4	no	—
308	Q₈	—	6	4	no	—
309	Q₈	—	12	4	no	—
310	D₄	—	6	4	no	—
311	D₄	—	6	4	no	—
312	D₄	—	12	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	6	4	no	—
315	C₂×C₄	—	12	4	no	—
316	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
317	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
318	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
319	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
320	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
321	C₈	C₂×C₃×D₁₂	1	4	yes	—
322	C₈	C₂×C₃×D₁₂	1	4	yes	—
323	C₂×C₃	—	2	4	no	—
324	C₂×C₃	—	2	1	no	—
325	C₂×C₃	—	2	2	no	—
326	C₂×C₃	—	24	4	no	—
327	C₂×C₃	#4696	1	4	yes	direct product factor
328	C₂×C₃	C₃×#495	1	4	yes	complemented
329	C₂×C₃	C₂×#874	1	1	yes	characteristic
330	C₂×C₃	C₂×#904	1	2	yes	—
331	C₂×C₃	C₂×C₃×#127	1	1	yes	characteristic
332	C₂×C₃	C₂×C₃×#135	1	2	yes	—
333	D₃	—	8	4	no	—
334	C₂²	—	12	4	no	—
335	C₂²	—	12	8	no	—
336	C₂²	—	24	8	no	—
337	C₂²	C₃×#874	1	2	yes	—
338	C₂²	C₃×#904	1	4	yes	—
339	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
340	C₄	—	2	4	no	—
341	C₄	—	12	4	no	—
342	C₄	C₃×#874	1	2	yes	—
343	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
344	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
345	C₃	—	2	1	no	—
346	C₃	C₂×#4696	1	1	yes	characteristic, direct product factor
347	C₃	C₂×C₃×#495	1	1	yes	characteristic, complemented
348	C₂	—	24	4	no	—
349	C₂	C₃×#4696	1	4	yes	direct product factor
350	C₂	C₂×C₃×#874	1	1	yes	characteristic
351	C₂	C₂×C₃×#904	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₂₄	C₂
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₂×C₃×#495
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Dic₁₂	C₂	semidirect
3. C₂²×C₃×#204	C₂	semidirect
4. C₂×C₃×#875	C₂	semidirect
5. C₂×C₃²×C₄×C₈	C₂	semidirect
6. C₃×#4696	C₂	direct (N × H)
8. C₂×#4696	C₃	direct (N × H)
16. C₂×C₃×Dic₁₂	C₂²	semidirect
20. C₂×C₃×#204	C₂²	semidirect
22. C₃×#875	C₂²	semidirect
23. C₃²×C₄×C₈	C₂²	semidirect
28. C₂²×Dic₁₂	C₂×C₃	semidirect
30. C₂²×#204	C₂×C₃	semidirect
31. C₂×#875	C₂×C₃	semidirect
34. C₂×C₃×C₄×C₈	D₃	semidirect
35. C₂×C₃×C₄×C₈	C₂×C₃	semidirect
36. #4696	C₂×C₃	direct (N × H)
84. C₂×Dic₁₂	C₂²×C₃	semidirect
88. C₂×#204	C₂²×C₃	semidirect
90. #875	C₂²×C₃	semidirect
92. C₃×C₄×C₈	C₂×D₃	semidirect
93. C₃×C₄×C₈	C₂²×C₃	semidirect
119. C₂×C₄×C₈	C₃×D₃	semidirect
197. C₄×C₈	C₂×C₃×D₃	semidirect
247. C₂×C₃²	#495	semidirect
302. C₃²	C₂×#495	semidirect
327. C₂×C₃	#4696	direct (N × H)
328. C₂×C₃	C₃×#495	semidirect
346. C₃	C₂×#4696	direct (N × H)
347. C₃	C₂×C₃×#495	semidirect
349. C₂	C₃×#4696	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×Dic₁₂	2
C₂²×C₃×D₂₄	2
C₂²×C₃×#204	2
C₂×C₃×#875	2
C₂×C₃²×C₄×C₈	2
C₃×#4696	2
C₂×C₃×#495	3
C₂×#4696	3

Subgroups — C2×C3×#4696 #11874240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4696 #11874240