Subgroups — C₂×C₃×#2388 #10653142

Order 768.

6238 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	C₂³×C₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×D₄	C₂	1	3	yes	maximal, complemented
3	C₃×#2388	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#395	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#394	C₂	1	3	yes	maximal, complemented
6	C₂×C₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#392	C₂	1	3	yes	maximal, complemented
8	C₂×C₃×C₄×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
9	C₂×#2388	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₃×#41	—	2	24	no	—
11	C₂²×C₃×#41	C₂²	1	8	yes	complemented
12	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
13	C₂³×C₃×D₄	C₂²	1	3	yes	—
14	C₂³×C₃×D₄	C₂²	1	3	yes	—
15	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
16	C₂⁴×C₃×C₄	C₂²	1	3	yes	—
17	C₂×C₃×C₄×D₄	—	2	24	no	—
18	C₂×C₃×C₄×D₄	C₂²	1	24	yes	complemented
19	C₂²×C₃×C₄⋊C₄	C₂²	1	3	yes	—
20	C₂²×C₃×C₂²⋊C₄	C₂²	1	3	yes	—
21	C₂²×C₃×C₂²⋊C₄	C₂²	1	3	yes	—
22	C₂²×C₃×C₂²⋊C₄	C₂²	1	6	yes	—
23	C₂²×C₃×C₄²	C₂²	1	3	yes	—
24	C₃×#395	C₂²	1	8	yes	complemented
25	C₃×#394	C₂²	1	24	yes	complemented
26	C₃×#393	C₂²	1	8	yes	complemented
27	C₃×#392	C₂²	1	24	yes	complemented
28	C₃×C₄×C₂²⋊C₄	C₂²	1	24	yes	complemented
29	C₂×C₃×#95	C₂²	1	3	yes	—
30	C₂×C₃×#95	C₂²	1	3	yes	—
31	C₂³×#41	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₄	C₂×C₃	1	3	yes	complemented
33	#2388	C₂×C₃	1	16	yes	direct product factor
34	C₂×#395	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#394	C₂×C₃	1	3	yes	complemented
36	C₂×#393	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#392	C₂×C₃	1	3	yes	complemented
38	C₂×C₄×C₂²⋊C₄	C₂×C₃	1	3	yes	complemented
39	C₂⁵×C₃	C₂³	1	3	yes	—
40	C₂⁵×C₃	C₂³	1	1	yes	characteristic
41	C₂×C₃×#41	—	2	128	no	—
42	C₂×C₃×#41	—	2	96	no	—
43	C₂²×C₃×Q₈	—	2	12	no	—
44	C₂²×C₃×Q₈	C₂³	1	4	yes	—
45	C₂²×C₃×D₄	—	2	24	no	—
46	C₂²×C₃×D₄	—	2	12	no	—
47	C₂²×C₃×D₄	—	2	12	no	—
48	C₂²×C₃×D₄	—	2	12	no	—
49	C₂²×C₃×D₄	—	2	12	no	—
50	C₂²×C₃×D₄	C₂³	1	12	yes	—
51	C₂²×C₃×D₄	C₂³	1	12	yes	—
52	C₂³×C₃×C₄	—	2	24	no	—
53	C₂³×C₃×C₄	—	2	12	no	—
54	C₂³×C₃×C₄	D₄	1	24	yes	complemented
55	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
56	C₂³×C₃×C₄	C₂³	1	4	yes	—
57	C₂³×C₃×C₄	C₂³	1	3	yes	—
58	C₂³×C₃×C₄	C₂³	1	3	yes	—
59	C₂³×C₃×C₄	C₂³	1	12	yes	—
60	C₂³×C₃×C₄	C₂³	1	3	yes	—
61	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
62	C₃×C₄×D₄	—	2	96	no	—
63	C₂×C₃×C₄⋊C₄	—	2	12	no	—
64	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
65	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
66	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
67	C₂×C₃×C₂²⋊C₄	—	2	24	no	—
68	C₂×C₃×C₂²⋊C₄	C₂³	1	24	yes	—
69	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
70	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
71	C₂×C₃×C₄²	—	2	12	no	—
72	C₂×C₃×C₄²	C₂³	1	12	yes	—
73	C₃×#95	C₂³	1	12	yes	—
74	C₃×#95	C₂³	1	12	yes	—
75	C₂²×#41	—	2	24	no	—
76	C₂²×#41	C₂²×C₃	1	8	yes	complemented
77	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
78	C₂³×D₄	C₂²×C₃	1	3	yes	—
79	C₂³×D₄	C₂²×C₃	1	3	yes	—
80	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂⁴×C₄	C₂²×C₃	1	3	yes	—
82	C₂×C₄×D₄	—	2	24	no	—
83	C₂×C₄×D₄	C₂²×C₃	1	24	yes	complemented
84	C₂²×C₄⋊C₄	C₂²×C₃	1	3	yes	—
85	C₂²×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
86	C₂²×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
87	C₂²×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
88	C₂²×C₄²	C₂²×C₃	1	3	yes	—
89	#395	C₂²×C₃	1	8	yes	complemented
90	#394	C₂²×C₃	1	24	yes	complemented
91	#393	C₂²×C₃	1	8	yes	complemented
92	#392	C₂²×C₃	1	24	yes	complemented
93	C₄×C₂²⋊C₄	C₂²×C₃	1	24	yes	complemented
94	C₂×#95	C₂²×C₃	1	3	yes	—
95	C₂×#95	C₂²×C₃	1	3	yes	—
96	C₂⁴×C₃	—	2	6	no	—
97	C₂⁴×C₃	—	2	12	no	—
98	C₂⁴×C₃	—	2	12	no	—
99	C₂⁴×C₃	—	2	6	no	—
100	C₂⁴×C₃	—	2	6	no	—
101	C₂⁴×C₃	—	2	6	no	—
102	C₂⁴×C₃	C₂×D₄	1	12	yes	—
103	C₂⁴×C₃	#41	1	4	yes	complemented
104	C₂⁴×C₃	C₂⁴	1	6	yes	—
105	C₂⁴×C₃	C₂⁴	1	2	yes	—
106	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
107	C₃×#41	—	2	256	no	—
108	C₂×C₃×Q₈	—	2	32	no	—
109	C₂×C₃×Q₈	—	2	24	no	—
110	C₂×C₃×D₄	—	2	96	no	—
111	C₂×C₃×D₄	—	2	96	no	—
112	C₂×C₃×D₄	—	2	24	no	—
113	C₂×C₃×D₄	—	2	48	no	—
114	C₂×C₃×D₄	—	2	24	no	—
115	C₂×C₃×D₄	—	2	24	no	—
116	C₂×C₃×D₄	—	2	24	no	—
117	C₂²×C₃×C₄	—	2	6	no	—
118	C₂²×C₃×C₄	—	2	12	no	—
119	C₂²×C₃×C₄	—	2	6	no	—
120	C₂²×C₃×C₄	—	2	96	no	—
121	C₂²×C₃×C₄	—	2	48	no	—
122	C₂²×C₃×C₄	—	2	6	no	—
123	C₂²×C₃×C₄	—	2	6	no	—
124	C₂²×C₃×C₄	—	2	12	no	—
125	C₂²×C₃×C₄	—	2	24	no	—
126	C₂²×C₃×C₄	—	4	16	no	—
127	C₂²×C₃×C₄	C₂×D₄	1	12	yes	—
128	C₂²×C₃×C₄	C₂×D₄	1	12	yes	—
129	C₂²×C₃×C₄	C₂×D₄	1	48	yes	complemented
130	C₂²×C₃×C₄	#41	1	12	yes	complemented
131	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
132	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
133	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
134	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
135	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
136	C₃×C₄⋊C₄	—	2	24	no	—
137	C₃×C₂²⋊C₄	—	2	24	no	—
138	C₃×C₂²⋊C₄	—	2	24	no	—
139	C₃×C₂²⋊C₄	—	2	48	no	—
140	C₃×C₄²	—	2	24	no	—
141	C₂⁵	C₂³×C₃	1	3	yes	—
142	C₂⁵	C₂³×C₃	1	1	yes	characteristic
143	C₂×#41	—	2	128	no	—
144	C₂×#41	—	2	96	no	—
145	C₂²×Q₈	—	2	12	no	—
146	C₂²×Q₈	C₂³×C₃	1	4	yes	—
147	C₂²×D₄	—	2	12	no	—
148	C₂²×D₄	—	2	24	no	—
149	C₂²×D₄	—	2	12	no	—
150	C₂²×D₄	—	2	12	no	—
151	C₂²×D₄	—	2	12	no	—
152	C₂²×D₄	C₂³×C₃	1	12	yes	—
153	C₂²×D₄	C₂³×C₃	1	12	yes	—
154	C₂³×C₄	—	2	24	no	—
155	C₂³×C₄	—	2	12	no	—
156	C₂³×C₄	C₃×D₄	1	24	yes	complemented
157	C₂³×C₄	C₂³×C₃	1	3	yes	—
158	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
159	C₂³×C₄	C₂³×C₃	1	4	yes	—
160	C₂³×C₄	C₂³×C₃	1	3	yes	—
161	C₂³×C₄	C₂³×C₃	1	12	yes	—
162	C₂³×C₄	C₂³×C₃	1	3	yes	—
163	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
164	C₄×D₄	—	2	96	no	—
165	C₂×C₄⋊C₄	—	2	12	no	—
166	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
167	C₂×C₂²⋊C₄	—	2	12	no	—
168	C₂×C₂²⋊C₄	—	2	12	no	—
169	C₂×C₂²⋊C₄	—	2	24	no	—
170	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
171	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
172	C₂×C₂²⋊C₄	C₂³×C₃	1	24	yes	—
173	C₂×C₄²	—	2	12	no	—
174	C₂×C₄²	C₂³×C₃	1	12	yes	—
175	#95	C₂³×C₃	1	12	yes	—
176	#95	C₂³×C₃	1	12	yes	—
177	C₂³×C₃	—	2	24	no	—
178	C₂³×C₃	—	2	24	no	—
179	C₂³×C₃	—	2	24	no	—
180	C₂³×C₃	—	2	24	no	—
181	C₂³×C₃	—	2	6	no	—
182	C₂³×C₃	—	2	12	no	—
183	C₂³×C₃	—	2	12	no	—
184	C₂³×C₃	—	2	6	no	—
185	C₂³×C₃	—	2	6	no	—
186	C₂³×C₃	—	2	6	no	—
187	C₂³×C₃	—	4	4	no	—
188	C₂³×C₃	—	4	24	no	—
189	C₂³×C₃	—	4	12	no	—
190	C₂³×C₃	—	4	24	no	—
191	C₂³×C₃	C₂²×D₄	1	12	yes	—
192	C₂³×C₃	C₂²×D₄	1	6	yes	—
193	C₂³×C₃	C₂×#41	1	2	yes	—
194	C₂³×C₃	C₂×#41	1	6	yes	—
195	C₂³×C₃	C₂×#41	1	4	yes	complemented
196	C₂³×C₃	C₂⁵	1	1	yes	characteristic
197	C₃×Q₈	—	2	32	no	—
198	C₃×D₄	—	2	96	no	—
199	C₃×D₄	—	2	96	no	—
200	C₂×C₃×C₄	—	2	24	no	—
201	C₂×C₃×C₄	—	2	24	no	—
202	C₂×C₃×C₄	—	2	6	no	—
203	C₂×C₃×C₄	—	2	12	no	—
204	C₂×C₃×C₄	—	2	6	no	—
205	C₂×C₃×C₄	—	2	96	no	—
206	C₂×C₃×C₄	—	2	6	no	—
207	C₂×C₃×C₄	—	2	6	no	—
208	C₂×C₃×C₄	—	2	12	no	—
209	C₂×C₃×C₄	—	4	4	no	—
210	C₂×C₃×C₄	—	4	12	no	—
211	C₂×C₃×C₄	—	4	16	no	—
212	C₂×C₃×C₄	#120	1	16	yes	—
213	C₂×C₃×C₄	C₂²×D₄	1	12	yes	—
214	C₂×C₃×C₄	C₂²×D₄	1	12	yes	—
215	C₂×C₃×C₄	C₂×#41	1	12	yes	complemented
216	C₂⁴	—	2	6	no	—
217	C₂⁴	—	2	12	no	—
218	C₂⁴	—	2	12	no	—
219	C₂⁴	—	2	6	no	—
220	C₂⁴	—	2	6	no	—
221	C₂⁴	—	2	6	no	—
222	C₂⁴	C₂×C₃×D₄	1	12	yes	—
223	C₂⁴	C₃×#41	1	4	yes	complemented
224	C₂⁴	C₂⁴×C₃	1	6	yes	—
225	C₂⁴	C₂⁴×C₃	1	2	yes	—
226	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
227	#41	—	2	256	no	—
228	C₂×Q₈	—	2	32	no	—
229	C₂×Q₈	—	2	24	no	—
230	C₂×D₄	—	2	96	no	—
231	C₂×D₄	—	2	96	no	—
232	C₂×D₄	—	2	24	no	—
233	C₂×D₄	—	2	48	no	—
234	C₂×D₄	—	2	24	no	—
235	C₂×D₄	—	2	24	no	—
236	C₂×D₄	—	2	24	no	—
237	C₂²×C₄	—	2	6	no	—
238	C₂²×C₄	—	2	12	no	—
239	C₂²×C₄	—	2	6	no	—
240	C₂²×C₄	—	2	96	no	—
241	C₂²×C₄	—	2	48	no	—
242	C₂²×C₄	—	2	6	no	—
243	C₂²×C₄	—	2	6	no	—
244	C₂²×C₄	—	2	12	no	—
245	C₂²×C₄	—	2	24	no	—
246	C₂²×C₄	—	4	16	no	—
247	C₂²×C₄	C₂×C₃×D₄	1	12	yes	—
248	C₂²×C₄	C₂×C₃×D₄	1	12	yes	—
249	C₂²×C₄	C₂×C₃×D₄	1	48	yes	complemented
250	C₂²×C₄	C₃×#41	1	12	yes	complemented
251	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
252	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
253	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
254	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
255	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
256	C₄⋊C₄	—	2	24	no	—
257	C₂²⋊C₄	—	2	24	no	—
258	C₂²⋊C₄	—	2	24	no	—
259	C₂²⋊C₄	—	2	48	no	—
260	C₄²	—	2	24	no	—
261	C₂²×C₃	—	2	12	no	—
262	C₂²×C₃	—	2	12	no	—
263	C₂²×C₃	—	2	12	no	—
264	C₂²×C₃	—	2	12	no	—
265	C₂²×C₃	—	4	48	no	—
266	C₂²×C₃	—	4	16	no	—
267	C₂²×C₃	—	4	2	no	—
268	C₂²×C₃	—	4	12	no	—
269	C₂²×C₃	—	4	6	no	—
270	C₂²×C₃	—	4	12	no	—
271	C₂²×C₃	C₂×#120	1	4	yes	—
272	C₂²×C₃	#525	1	12	yes	—
273	C₂²×C₃	#532	1	12	yes	—
274	C₂²×C₃	C₂³×D₄	1	3	yes	—
275	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
276	C₂²×C₃	C₂²×#41	1	3	yes	—
277	C₃×C₄	—	2	12	no	—
278	C₃×C₄	—	2	12	no	—
279	C₃×C₄	—	4	2	no	—
280	C₃×C₄	—	4	6	no	—
281	C₃×C₄	C₂×#120	1	8	yes	—
282	C₂³	—	2	6	no	—
283	C₂³	—	2	12	no	—
284	C₂³	—	2	12	no	—
285	C₂³	—	2	6	no	—
286	C₂³	—	2	6	no	—
287	C₂³	—	2	6	no	—
288	C₂³	—	2	24	no	—
289	C₂³	—	2	24	no	—
290	C₂³	—	2	24	no	—
291	C₂³	—	2	24	no	—
292	C₂³	—	4	4	no	—
293	C₂³	—	4	24	no	—
294	C₂³	—	4	12	no	—
295	C₂³	—	4	24	no	—
296	C₂³	C₂²×C₃×D₄	1	12	yes	—
297	C₂³	C₂²×C₃×D₄	1	6	yes	—
298	C₂³	C₂×C₃×#41	1	2	yes	—
299	C₂³	C₂×C₃×#41	1	6	yes	—
300	C₂³	C₂×C₃×#41	1	4	yes	complemented
301	C₂³	C₂⁵×C₃	1	1	yes	characteristic
302	Q₈	—	2	32	no	—
303	D₄	—	2	96	no	—
304	D₄	—	2	96	no	—
305	C₂×C₄	—	2	6	no	—
306	C₂×C₄	—	2	12	no	—
307	C₂×C₄	—	2	6	no	—
308	C₂×C₄	—	2	24	no	—
309	C₂×C₄	—	2	24	no	—
310	C₂×C₄	—	2	96	no	—
311	C₂×C₄	—	2	6	no	—
312	C₂×C₄	—	2	6	no	—
313	C₂×C₄	—	2	12	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	12	no	—
316	C₂×C₄	—	4	16	no	—
317	C₂×C₄	C₃×#120	1	16	yes	—
318	C₂×C₄	C₂²×C₃×D₄	1	12	yes	—
319	C₂×C₄	C₂²×C₃×D₄	1	12	yes	—
320	C₂×C₄	C₂×C₃×#41	1	12	yes	complemented
321	C₂×C₃	—	4	12	no	—
322	C₂×C₃	—	4	4	no	—
323	C₂×C₃	#2388	1	8	yes	direct product factor
324	C₂×C₃	C₂²×#120	1	1	yes	characteristic
325	C₂×C₃	C₂×#525	1	3	yes	—
326	C₂×C₃	C₂×#532	1	3	yes	—
327	C₂²	—	2	12	no	—
328	C₂²	—	2	12	no	—
329	C₂²	—	2	12	no	—
330	C₂²	—	2	12	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	12	no	—
333	C₂²	—	4	48	no	—
334	C₂²	—	4	16	no	—
335	C₂²	—	4	6	no	—
336	C₂²	—	4	12	no	—
337	C₂²	C₂×C₃×#120	1	4	yes	—
338	C₂²	C₃×#525	1	12	yes	—
339	C₂²	C₃×#532	1	12	yes	—
340	C₂²	C₂³×C₃×D₄	1	3	yes	—
341	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
342	C₂²	C₂²×C₃×#41	1	3	yes	—
343	C₄	—	2	12	no	—
344	C₄	—	2	12	no	—
345	C₄	—	4	2	no	—
346	C₄	—	4	6	no	—
347	C₄	C₂×C₃×#120	1	8	yes	—
348	C₃	C₂×#2388	1	1	yes	characteristic, direct product factor, Sylow
349	C₂	—	4	12	no	—
350	C₂	—	4	4	no	—
351	C₂	C₃×#2388	1	8	yes	direct product factor
352	C₂	C₂²×C₃×#120	1	1	yes	characteristic
353	C₂	C₂×C₃×#525	1	3	yes	—
354	C₂	C₂×C₃×#532	1	3	yes	—

	subgroup	G/H
center	C₂³×C₃×C₄	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
socle	C₂⁴×C₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×#41	C₂	semidirect
2. C₂²×C₃×C₄×D₄	C₂	semidirect
3. C₃×#2388	C₂	direct (N × H)
4. C₂×C₃×#395	C₂	semidirect
5. C₂×C₃×#394	C₂	semidirect
6. C₂×C₃×#393	C₂	semidirect
7. C₂×C₃×#392	C₂	semidirect
8. C₂×C₃×C₄×C₂²⋊C₄	C₂	semidirect
9. C₂×#2388	C₃	direct (N × H)
11. C₂²×C₃×#41	C₂²	semidirect
18. C₂×C₃×C₄×D₄	C₂²	semidirect
24. C₃×#395	C₂²	semidirect
25. C₃×#394	C₂²	semidirect
26. C₃×#393	C₂²	semidirect
27. C₃×#392	C₂²	semidirect
28. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
31. C₂³×#41	C₂×C₃	semidirect
32. C₂²×C₄×D₄	C₂×C₃	semidirect
33. #2388	C₂×C₃	direct (N × H)
34. C₂×#395	C₂×C₃	semidirect
35. C₂×#394	C₂×C₃	semidirect
36. C₂×#393	C₂×C₃	semidirect
37. C₂×#392	C₂×C₃	semidirect
38. C₂×C₄×C₂²⋊C₄	C₂×C₃	semidirect
54. C₂³×C₃×C₄	D₄	semidirect
76. C₂²×#41	C₂²×C₃	semidirect
83. C₂×C₄×D₄	C₂²×C₃	semidirect
89. #395	C₂²×C₃	semidirect
90. #394	C₂²×C₃	semidirect
91. #393	C₂²×C₃	semidirect
92. #392	C₂²×C₃	semidirect
93. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
103. C₂⁴×C₃	#41	semidirect
129. C₂²×C₃×C₄	C₂×D₄	semidirect
130. C₂²×C₃×C₄	#41	semidirect
156. C₂³×C₄	C₃×D₄	semidirect
195. C₂³×C₃	C₂×#41	semidirect
215. C₂×C₃×C₄	C₂×#41	semidirect
223. C₂⁴	C₃×#41	semidirect
249. C₂²×C₄	C₂×C₃×D₄	semidirect
250. C₂²×C₄	C₃×#41	semidirect
300. C₂³	C₂×C₃×#41	semidirect
320. C₂×C₄	C₂×C₃×#41	semidirect
323. C₂×C₃	#2388	direct (N × H)
348. C₃	C₂×#2388	direct (N × H)
351. C₂	C₃×#2388	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×#41	2
C₂²×C₃×C₄×D₄	2
C₃×#2388	2
C₂×C₃×#395	2
C₂×C₃×#394	2
C₂×C₃×#393	2
C₂×C₃×#392	2
C₂×C₃×C₄×C₂²⋊C₄	2
C₂×#2388	3

Subgroups — C2×C3×#2388 #10653142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#2388 #10653142