Subgroups — C₂×C₃×#64149 #13179545

Order 1728.

3932 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#638	C₂	1	4	yes	maximal, complemented
3	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64149	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64149	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₃×#940	—	3	4	no	maximal
8	C₂⁴×C₃³	C₂²	1	2	yes	—
9	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	—
10	C₂×C₃³×D₄	—	2	4	no	—
11	C₂×C₃³×D₄	C₂²	1	4	yes	complemented
12	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×#638	—	2	16	no	—
14	C₂×C₃×#638	C₂²	1	16	yes	complemented
15	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
17	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	4	yes	complemented
18	C₃×C₄×C₃⋊Dic₃	C₂²	1	4	yes	complemented
19	C₂²×C₃²×D₄	—	2	4	no	—
20	C₂²×C₃²×D₄	D₃	1	4	yes	complemented
21	C₂²×C₃²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂²×#638	C₂×C₃	1	4	yes	complemented
23	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×C₃×#67	—	3	16	no	—
25	C₂²×C₃×D₁₂	—	3	4	no	—
26	#64149	C₂×C₃	1	8	yes	direct product factor
27	C₂×C₄×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
28	C₃×#940	—	3	32	no	—
29	C₂×C₃×C₄×Dic₃	—	3	4	no	—
30	C₂³×C₃³	—	2	4	no	—
31	C₂³×C₃³	—	2	8	no	—
32	C₂³×C₃³	C₂³	1	4	yes	—
33	C₂³×C₃³	C₂³	1	1	yes	characteristic
34	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
35	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
36	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	—
37	C₃³×D₄	—	2	8	no	—
38	C₂×C₃³×C₄	D₄	1	4	yes	complemented
39	C₂×C₃³×C₄	C₂³	1	2	yes	—
40	C₃×#638	—	2	32	no	—
41	C₂×C₃×C₃⋊Dic₃	D₄	1	8	yes	complemented
42	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
43	C₃×C₄⋊(C₃⋊D₃)	—	2	8	no	—
44	C₂×C₃×#127	—	9	1	no	—
45	C₂×#940	—	3	4	no	—
46	C₂⁴×C₃²	—	2	8	no	—
47	C₂⁴×C₃²	C₂×D₃	1	8	yes	—
48	C₂⁴×C₃²	C₂²×C₃	1	2	yes	—
49	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	—
50	C₂³×C₃×D₃	—	3	8	no	—
51	C₂×C₃²×D₄	—	2	32	no	—
52	C₂×C₃²×D₄	—	2	16	no	—
53	C₂×C₃²×D₄	—	2	16	no	—
54	C₂×C₃²×D₄	—	2	4	no	—
55	C₂×C₃²×D₄	C₂×D₃	1	16	yes	complemented
56	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	complemented
57	C₂²×C₃²×C₄	—	2	4	no	—
58	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
59	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
60	C₂×#638	—	2	16	no	—
61	C₂×#638	C₂²×C₃	1	16	yes	complemented
62	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
63	C₂×C₄⋊(C₃⋊D₃)	—	2	4	no	—
64	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	4	yes	complemented
65	C₂×C₃×#67	—	3	64	no	—
66	C₂×C₃×#67	—	6	64	no	—
67	C₂²×C₃×Dic₃	—	3	8	no	—
68	C₂×C₃×D₁₂	—	3	16	no	—
69	C₂×C₃×D₁₂	—	6	16	no	—
70	C₄×C₃⋊Dic₃	C₂²×C₃	1	4	yes	complemented
71	C₃×C₄×Dic₃	—	3	16	no	—
72	C₂²×C₃³	—	2	4	no	—
73	C₂²×C₃³	—	2	8	no	—
74	C₂²×C₃³	—	4	8	no	—
75	C₂²×C₃³	C₂×D₄	1	4	yes	—
76	C₂²×C₃³	C₂×D₄	1	2	yes	—
77	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
78	C₂×C₃×C₃⋊D₃	—	2	4	no	—
79	C₂×C₃×C₃⋊D₃	—	2	8	no	—
80	C₂×C₃×C₃⋊D₃	—	4	8	no	—
81	C₃³×C₄	C₂×D₄	1	4	yes	complemented
82	C₃×C₃⋊Dic₃	C₂×D₄	1	8	yes	complemented
83	C₂²×C₃×D₄	—	2	4	no	—
84	C₂²×C₃×D₄	—	9	4	no	—
85	C₂²×C₃×D₄	—	9	1	no	—
86	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
87	C₂²×C₃×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
88	C₂²×#67	—	3	16	no	—
89	C₂²×D₁₂	—	3	4	no	—
90	C₃×#127	—	9	8	no	—
91	C₂×C₃×C₄²	—	9	1	no	—
92	#940	—	3	32	no	—
93	C₂×C₄×Dic₃	—	3	4	no	—
94	C₂³×C₃²	—	2	32	no	—
95	C₂³×C₃²	—	2	16	no	—
96	C₂³×C₃²	—	2	8	no	—
97	C₂³×C₃²	—	2	4	no	—
98	C₂³×C₃²	—	2	4	no	—
99	C₂³×C₃²	—	2	16	no	—
100	C₂³×C₃²	—	2	32	no	—
101	C₂³×C₃²	—	4	32	no	—
102	C₂³×C₃²	C₂²×D₃	1	16	yes	—
103	C₂³×C₃²	C₂²×D₃	1	4	yes	—
104	C₂³×C₃²	C₂³×C₃	1	4	yes	—
105	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
106	C₂²×C₃⋊D₃	—	2	4	no	—
107	C₂²×C₃⋊D₃	—	2	8	no	—
108	C₂²×C₃⋊D₃	C₂³×C₃	1	4	yes	—
109	C₂²×C₃×D₃	—	3	16	no	—
110	C₂²×C₃×D₃	—	6	32	no	—
111	C₂²×C₃×D₃	—	6	16	no	—
112	C₃²×D₄	—	2	64	no	—
113	C₃²×D₄	—	2	32	no	—
114	C₃²×D₄	—	2	8	no	—
115	C₂×C₃²×C₄	—	2	16	no	—
116	C₂×C₃²×C₄	—	2	8	no	—
117	C₂×C₃²×C₄	#67	1	16	yes	complemented
118	C₂×C₃²×C₄	C₃×D₄	1	4	yes	complemented
119	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
120	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
121	#638	—	2	32	no	—
122	C₂×C₃⋊Dic₃	C₃×D₄	1	8	yes	complemented
123	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
124	C₄⋊(C₃⋊D₃)	—	2	8	no	—
125	C₃×#67	—	6	128	no	—
126	C₂×C₃×Dic₃	—	3	32	no	—
127	C₂×C₃×Dic₃	—	3	16	no	—
128	C₃×D₁₂	—	6	32	no	—
129	C₂×#127	—	9	1	no	Sylow
130	C₂×C₃³	—	4	4	no	—
131	C₂×C₃³	#127	1	4	yes	complemented
132	C₂×C₃³	C₂²×D₄	1	2	yes	—
133	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
134	C₃×C₃⋊D₃	—	4	4	no	—
135	C₂⁴×C₃	—	2	8	no	—
136	C₂⁴×C₃	—	9	2	no	—
137	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	—
138	C₂⁴×C₃	C₂×C₃⋊D₃	1	2	yes	—
139	C₂³×D₃	—	3	8	no	—
140	C₂×C₃×D₄	—	2	32	no	—
141	C₂×C₃×D₄	—	2	16	no	—
142	C₂×C₃×D₄	—	2	4	no	—
143	C₂×C₃×D₄	—	2	16	no	—
144	C₂×C₃×D₄	—	9	16	no	—
145	C₂×C₃×D₄	—	9	4	no	—
146	C₂×C₃×D₄	—	18	16	no	—
147	C₂×C₃×D₄	—	18	4	no	—
148	C₂×C₃×D₄	C₂×C₃×D₃	1	16	yes	complemented
149	C₂×C₃×D₄	C₂×C₃⋊D₃	1	4	yes	complemented
150	C₂²×C₃×C₄	—	2	4	no	—
151	C₂²×C₃×C₄	—	9	2	no	—
152	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
153	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
154	C₂×#67	—	3	64	no	—
155	C₂×#67	—	6	64	no	—
156	C₂²×Dic₃	—	3	8	no	—
157	C₂×D₁₂	—	3	16	no	—
158	C₂×D₁₂	—	6	16	no	—
159	C₃×C₄²	—	9	4	no	—
160	C₄×Dic₃	—	3	16	no	—
161	C₂²×C₃²	—	2	32	no	—
162	C₂²×C₃²	—	2	16	no	—
163	C₂²×C₃²	—	2	8	no	—
164	C₂²×C₃²	—	2	4	no	—
165	C₂²×C₃²	—	2	4	no	—
166	C₂²×C₃²	—	2	16	no	—
167	C₂²×C₃²	—	2	8	no	—
168	C₂²×C₃²	—	2	32	no	—
169	C₂²×C₃²	—	4	32	no	—
170	C₂²×C₃²	—	4	64	no	—
171	C₂²×C₃²	—	4	32	no	—
172	C₂²×C₃²	—	4	8	no	—
173	C₂²×C₃²	D₃×D₄	1	16	yes	—
174	C₂²×C₃²	C₂×#67	1	8	yes	—
175	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
176	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
177	C₂²×C₃²	C₂³×D₃	1	4	yes	—
178	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
179	C₂×C₃⋊D₃	—	2	4	no	—
180	C₂×C₃⋊D₃	—	2	8	no	—
181	C₂×C₃⋊D₃	—	4	8	no	—
182	C₂×C₃×D₃	—	6	32	no	—
183	C₂×C₃×D₃	—	6	16	no	—
184	C₂×C₃×D₃	—	12	32	no	—
185	C₃²×C₄	—	2	16	no	—
186	C₃²×C₄	C₂×#67	1	16	yes	complemented
187	C₃²×C₄	C₂×C₃×D₄	1	4	yes	complemented
188	C₃⋊Dic₃	C₂×C₃×D₄	1	8	yes	complemented
189	C₃×Dic₃	—	3	32	no	—
190	C₂²×D₄	—	9	4	no	—
191	C₂²×D₄	—	9	1	no	—
192	C₂²×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
193	#127	—	9	8	no	—
194	C₂×C₄²	—	9	1	no	—
195	C₃³	C₂×#127	1	1	yes	characteristic, complemented, Sylow
196	C₂³×C₃	—	2	32	no	—
197	C₂³×C₃	—	2	32	no	—
198	C₂³×C₃	—	2	16	no	—
199	C₂³×C₃	—	2	8	no	—
200	C₂³×C₃	—	2	4	no	—
201	C₂³×C₃	—	2	4	no	—
202	C₂³×C₃	—	2	16	no	—
203	C₂³×C₃	—	4	32	no	—
204	C₂³×C₃	—	9	4	no	—
205	C₂³×C₃	—	18	8	no	—
206	C₂³×C₃	—	18	4	no	—
207	C₂³×C₃	C₂²×C₃×D₃	1	16	yes	—
208	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
209	C₂³×C₃	C₂²×C₃⋊D₃	1	4	yes	—
210	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
211	C₂²×D₃	—	3	16	no	—
212	C₂²×D₃	—	6	32	no	—
213	C₂²×D₃	—	6	16	no	—
214	C₃×D₄	—	2	64	no	—
215	C₃×D₄	—	2	32	no	—
216	C₃×D₄	—	2	8	no	—
217	C₃×D₄	—	18	32	no	—
218	C₃×D₄	—	18	8	no	—
219	C₂×C₃×C₄	—	2	16	no	—
220	C₂×C₃×C₄	—	2	8	no	—
221	C₂×C₃×C₄	—	9	4	no	—
222	C₂×C₃×C₄	—	9	8	no	—
223	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
224	C₂×C₃×C₄	#638	1	4	yes	complemented
225	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
226	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
227	#67	—	6	128	no	—
228	C₂×Dic₃	—	3	16	no	—
229	C₂×Dic₃	—	3	32	no	—
230	D₁₂	—	6	32	no	—
231	C₂×C₃²	—	2	16	no	—
232	C₂×C₃²	—	2	8	no	—
233	C₂×C₃²	—	2	4	no	—
234	C₂×C₃²	—	4	32	no	—
235	C₂×C₃²	—	4	16	no	—
236	C₂×C₃²	—	4	4	no	—
237	C₂×C₃²	#940	1	16	yes	complemented
238	C₂×C₃²	C₃×#127	1	4	yes	complemented
239	C₂×C₃²	C₂×D₃×D₄	1	8	yes	—
240	C₂×C₃²	C₂²×#67	1	4	yes	—
241	C₂×C₃²	C₂²×C₃×D₄	1	2	yes	—
242	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
243	C₃⋊D₃	—	4	4	no	—
244	C₃×D₃	—	12	16	no	—
245	C₂⁴	—	9	2	no	—
246	C₂⁴	C₂×C₃×C₃⋊D₃	1	2	yes	—
247	C₂×D₄	—	2	4	no	—
248	C₂×D₄	—	9	16	no	—
249	C₂×D₄	—	9	4	no	—
250	C₂×D₄	—	18	16	no	—
251	C₂×D₄	—	18	4	no	—
252	C₂×D₄	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
253	C₂²×C₄	—	9	2	no	—
254	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
255	C₄²	—	9	4	no	—
256	C₂²×C₃	—	2	32	no	—
257	C₂²×C₃	—	2	32	no	—
258	C₂²×C₃	—	2	16	no	—
259	C₂²×C₃	—	2	8	no	—
260	C₂²×C₃	—	2	4	no	—
261	C₂²×C₃	—	2	4	no	—
262	C₂²×C₃	—	2	16	no	—
263	C₂²×C₃	—	2	8	no	—
264	C₂²×C₃	—	4	32	no	—
265	C₂²×C₃	—	4	64	no	—
266	C₂²×C₃	—	4	32	no	—
267	C₂²×C₃	—	4	8	no	—
268	C₂²×C₃	—	18	8	no	—
269	C₂²×C₃	—	18	4	no	—
270	C₂²×C₃	—	36	8	no	—
271	C₂²×C₃	C₃×D₃×D₄	1	16	yes	—
272	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
273	C₂²×C₃	D₄×C₃⋊D₃	1	4	yes	—
274	C₂²×C₃	C₂×#638	1	2	yes	—
275	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
276	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
277	C₂×D₃	—	6	32	no	—
278	C₂×D₃	—	6	16	no	—
279	C₂×D₃	—	12	32	no	—
280	C₃×C₄	—	2	16	no	—
281	C₃×C₄	—	9	8	no	—
282	C₃×C₄	C₂×C₃×#67	1	16	yes	complemented
283	C₃×C₄	C₂×#638	1	4	yes	complemented
284	Dic₃	—	3	32	no	—
285	C₃²	—	2	4	no	—
286	C₃²	C₂×#940	1	4	yes	complemented
287	C₃²	C₂×C₃×#127	1	1	yes	characteristic, complemented
288	C₂³	—	2	8	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	9	4	no	—
291	C₂³	—	18	8	no	—
292	C₂³	—	18	4	no	—
293	C₂³	C₂²×C₃×C₃⋊D₃	1	4	yes	—
294	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
295	D₄	—	2	8	no	—
296	D₄	—	18	32	no	—
297	D₄	—	18	8	no	—
298	C₂×C₄	—	9	4	no	—
299	C₂×C₄	—	9	8	no	—
300	C₂×C₄	C₃×#638	1	4	yes	complemented
301	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
302	C₂×C₃	—	2	8	no	—
303	C₂×C₃	—	2	16	no	—
304	C₂×C₃	—	2	4	no	—
305	C₂×C₃	—	4	32	no	—
306	C₂×C₃	—	4	16	no	—
307	C₂×C₃	—	4	4	no	—
308	C₂×C₃	—	36	4	no	—
309	C₂×C₃	C₃×#940	1	16	yes	complemented
310	C₂×C₃	#64149	1	4	yes	direct product factor
311	C₂×C₃	C₂×C₃×D₃×D₄	1	8	yes	—
312	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
313	C₂×C₃	C₂×D₄×C₃⋊D₃	1	2	yes	—
314	C₂×C₃	C₂²×#638	1	1	yes	characteristic
315	D₃	—	12	16	no	—
316	C₂²	—	2	8	no	—
317	C₂²	—	2	4	no	—
318	C₂²	—	4	8	no	—
319	C₂²	—	18	8	no	—
320	C₂²	—	18	4	no	—
321	C₂²	—	36	8	no	—
322	C₂²	C₃×D₄×C₃⋊D₃	1	4	yes	—
323	C₂²	C₂×C₃×#638	1	2	yes	—
324	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
325	C₄	—	9	8	no	—
326	C₄	C₂×C₃×#638	1	4	yes	complemented
327	C₃	—	2	4	no	—
328	C₃	C₂×C₃×#940	1	4	yes	complemented
329	C₃	C₂×#64149	1	1	yes	characteristic, direct product factor
330	C₂	—	4	4	no	—
331	C₂	—	36	4	no	—
332	C₂	C₃×#64149	1	4	yes	direct product factor
333	C₂	C₂×C₃×D₄×C₃⋊D₃	1	2	yes	—
334	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×D₄	C₂
socle	C₂³×C₃³	C₂³
hypercenter	C₂²×C₃×D₄	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#127
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×D₄	C₂	semidirect
2. C₂²×C₃×#638	C₂	semidirect
3. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
4. C₃×#64149	C₂	direct (N × H)
5. C₂×C₃×C₄×C₃⋊Dic₃	C₂	semidirect
6. C₂×#64149	C₃	direct (N × H)
11. C₂×C₃³×D₄	C₂²	semidirect
14. C₂×C₃×#638	C₂²	semidirect
17. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
18. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
20. C₂²×C₃²×D₄	D₃	semidirect
21. C₂²×C₃²×D₄	C₂×C₃	semidirect
22. C₂²×#638	C₂×C₃	semidirect
23. C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
26. #64149	C₂×C₃	direct (N × H)
27. C₂×C₄×C₃⋊Dic₃	C₂×C₃	semidirect
38. C₂×C₃³×C₄	D₄	semidirect
41. C₂×C₃×C₃⋊Dic₃	D₄	semidirect
55. C₂×C₃²×D₄	C₂×D₃	semidirect
56. C₂×C₃²×D₄	C₂²×C₃	semidirect
61. C₂×#638	C₂²×C₃	semidirect
64. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
70. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
81. C₃³×C₄	C₂×D₄	semidirect
82. C₃×C₃⋊Dic₃	C₂×D₄	semidirect
86. C₂²×C₃×D₄	C₃×D₃	semidirect
87. C₂²×C₃×D₄	C₃⋊D₃	semidirect
117. C₂×C₃²×C₄	#67	semidirect
118. C₂×C₃²×C₄	C₃×D₄	semidirect
122. C₂×C₃⋊Dic₃	C₃×D₄	semidirect
131. C₂×C₃³	#127	semidirect
148. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
149. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
186. C₃²×C₄	C₂×#67	semidirect
187. C₃²×C₄	C₂×C₃×D₄	semidirect
188. C₃⋊Dic₃	C₂×C₃×D₄	semidirect
192. C₂²×D₄	C₃×C₃⋊D₃	semidirect
195. C₃³	C₂×#127	semidirect
223. C₂×C₃×C₄	C₃×#67	semidirect
224. C₂×C₃×C₄	#638	semidirect
237. C₂×C₃²	#940	semidirect
238. C₂×C₃²	C₃×#127	semidirect
252. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
282. C₃×C₄	C₂×C₃×#67	semidirect
283. C₃×C₄	C₂×#638	semidirect
286. C₃²	C₂×#940	semidirect
287. C₃²	C₂×C₃×#127	semidirect
300. C₂×C₄	C₃×#638	semidirect
309. C₂×C₃	C₃×#940	semidirect
310. C₂×C₃	#64149	direct (N × H)
326. C₄	C₂×C₃×#638	semidirect
328. C₃	C₂×C₃×#940	semidirect
329. C₃	C₂×#64149	direct (N × H)
332. C₂	C₃×#64149	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×C₃³×D₄	2
C₂²×C₃×#638	2
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₃×#64149	2
C₂×C₃×C₄×C₃⋊Dic₃	2
C₂×#64149	3
C₂×C₃×#940	3

Subgroups — C2×C3×#64149 #13179545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64149 #13179545