Subgroups — C₂×C₃×#64138 #13179540

Order 1728.

2996 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³×C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#638	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3757	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64138	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3752	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3750	C₂	1	2	yes	maximal, complemented
7	C₂×#64138	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#929	—	3	4	no	maximal
9	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃³×C₄	—	2	4	no	—
12	C₂²×C₃³×C₄	C₂²	1	2	yes	—
13	C₂²×C₃³×C₄	C₂²	1	4	yes	complemented
14	C₂×C₃×#638	—	2	4	no	—
15	C₂×C₃×#638	C₂²	1	4	yes	—
16	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
18	C₃×#3757	C₂²	1	4	yes	complemented
19	C₃×#3752	C₂²	1	8	yes	complemented
20	C₃×#3750	C₂²	1	8	yes	complemented
21	C₂³×C₃²×C₄	—	2	4	no	—
22	C₂³×C₃²×C₄	D₃	1	4	yes	complemented
23	C₂³×C₃²×C₄	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×#638	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₃×#67	—	3	4	no	—
26	C₂×#3757	C₂×C₃	1	1	yes	characteristic, complemented
27	#64138	C₂×C₃	1	8	yes	direct product factor
28	C₂×#3752	C₂×C₃	1	2	yes	complemented
29	C₂×#3750	C₂×C₃	1	2	yes	complemented
30	C₂×C₃×#217	—	3	4	no	—
31	C₃×#929	—	3	32	no	—
32	C₂×C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
33	C₂×C₃×Dic₃⋊C₄	—	3	8	no	—
34	C₂³×C₃³	—	2	4	no	—
35	C₂³×C₃³	D₄	1	4	yes	—
36	C₂³×C₃³	C₂³	1	2	yes	—
37	C₂³×C₃³	C₂³	1	1	yes	characteristic
38	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
39	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
40	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
41	C₂×C₃³×C₄	—	2	4	no	—
42	C₂×C₃³×C₄	—	2	8	no	—
43	C₂×C₃³×C₄	C₂³	1	4	yes	—
44	C₃×#638	—	2	8	no	—
45	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
46	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
47	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
48	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
49	C₂×C₃×#123	—	9	1	no	—
50	C₂×#929	—	3	4	no	—
51	C₂⁴×C₃²	—	2	4	no	—
52	C₂⁴×C₃²	C₂×D₃	1	4	yes	—
53	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
54	C₂³×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
55	C₂³×C₃×D₃	—	3	4	no	—
56	C₂²×C₃²×C₄	—	2	32	no	—
57	C₂²×C₃²×C₄	—	2	8	no	—
58	C₂²×C₃²×C₄	—	2	16	no	—
59	C₂²×C₃²×C₄	—	2	16	no	—
60	C₂²×C₃²×C₄	—	2	4	no	—
61	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
62	C₂²×C₃²×C₄	C₂×D₃	1	16	yes	complemented
63	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
64	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	complemented
65	C₂×#638	—	2	4	no	—
66	C₂×#638	C₂²×C₃	1	4	yes	—
67	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
69	C₂×C₃×#67	—	3	16	no	—
70	C₂×C₃×#67	—	6	16	no	—
71	C₂²×C₃×Dic₃	—	3	4	no	—
72	C₂²×C₃×Dic₃	—	3	8	no	—
73	#3757	C₂²×C₃	1	4	yes	complemented
74	#3752	C₂²×C₃	1	8	yes	complemented
75	#3750	C₂²×C₃	1	8	yes	complemented
76	C₃×#217	—	3	16	no	—
77	C₃×(C₂×D₃)⋊C₄	—	3	32	no	—
78	C₃×Dic₃⋊C₄	—	3	32	no	—
79	C₂²×C₃³	—	2	8	no	—
80	C₂²×C₃³	—	2	4	no	—
81	C₂²×C₃³	C₂×D₄	1	4	yes	—
82	C₂²×C₃³	C₂×D₄	1	2	yes	—
83	C₂²×C₃³	#41	1	4	yes	—
84	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
85	C₂×C₃×C₃⋊D₃	—	2	2	no	—
86	C₂×C₃×C₃⋊D₃	—	2	4	no	—
87	C₂×C₃×C₃⋊D₃	—	4	4	no	—
88	C₃³×C₄	—	2	4	no	—
89	C₃×C₃⋊Dic₃	—	2	2	no	—
90	C₃×C₃⋊Dic₃	—	2	4	no	—
91	C₂²×C₃×D₄	—	9	1	no	—
92	C₂³×C₃×C₄	—	2	4	no	—
93	C₂³×C₃×C₄	C₃×D₃	1	4	yes	complemented
94	C₂³×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic, complemented
95	C₂²×#67	—	3	4	no	—
96	C₃×#123	—	9	8	no	—
97	C₂×C₃×C₄⋊C₄	—	9	2	no	—
98	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
99	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
100	C₂×#217	—	3	4	no	—
101	#929	—	3	32	no	—
102	C₂×(C₂×D₃)⋊C₄	—	3	8	no	—
103	C₂×Dic₃⋊C₄	—	3	8	no	—
104	C₂³×C₃²	—	2	32	no	—
105	C₂³×C₃²	—	2	16	no	—
106	C₂³×C₃²	—	2	4	no	—
107	C₂³×C₃²	—	2	16	no	—
108	C₂³×C₃²	—	2	8	no	—
109	C₂³×C₃²	—	2	4	no	—
110	C₂³×C₃²	#67	1	16	yes	—
111	C₂³×C₃²	C₃×D₄	1	4	yes	—
112	C₂³×C₃²	C₂²×D₃	1	8	yes	—
113	C₂³×C₃²	C₂²×D₃	1	4	yes	—
114	C₂³×C₃²	C₂³×C₃	1	2	yes	—
115	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
116	C₂²×C₃⋊D₃	—	2	2	no	—
117	C₂²×C₃⋊D₃	—	2	4	no	—
118	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
119	C₂²×C₃×D₃	—	3	8	no	—
120	C₂²×C₃×D₃	—	6	16	no	—
121	C₂²×C₃×D₃	—	6	8	no	—
122	C₂×C₃²×C₄	—	2	32	no	—
123	C₂×C₃²×C₄	—	2	64	no	—
124	C₂×C₃²×C₄	—	2	16	no	—
125	C₂×C₃²×C₄	—	2	32	no	—
126	C₂×C₃²×C₄	—	2	4	no	—
127	C₂×C₃²×C₄	—	2	8	no	—
128	C₂×C₃²×C₄	—	2	16	no	—
129	C₂×C₃²×C₄	C₂²×D₃	1	16	yes	—
130	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
131	#638	—	2	8	no	—
132	C₂×C₃⋊Dic₃	—	2	2	no	—
133	C₂×C₃⋊Dic₃	—	2	4	no	—
134	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
135	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
136	C₃×#67	—	6	32	no	—
137	C₂×C₃×Dic₃	—	3	8	no	—
138	C₂×C₃×Dic₃	—	3	16	no	—
139	C₂×C₃×Dic₃	—	6	16	no	—
140	C₂×C₃×Dic₃	—	6	8	no	—
141	C₂×#123	—	9	1	no	Sylow
142	C₂×C₃³	—	2	4	no	—
143	C₂×C₃³	#123	1	4	yes	complemented
144	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₃³	C₂×#41	1	2	yes	—
146	C₃×C₃⋊D₃	—	4	2	no	—
147	C₂⁴×C₃	—	2	4	no	—
148	C₂⁴×C₃	—	9	1	no	—
149	C₂⁴×C₃	C₂×C₃×D₃	1	4	yes	—
150	C₂⁴×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
151	C₂³×D₃	—	3	4	no	—
152	C₂×C₃×D₄	—	9	4	no	—
153	C₂×C₃×D₄	—	18	4	no	—
154	C₂²×C₃×C₄	—	2	32	no	—
155	C₂²×C₃×C₄	—	2	16	no	—
156	C₂²×C₃×C₄	—	2	4	no	—
157	C₂²×C₃×C₄	—	2	8	no	—
158	C₂²×C₃×C₄	—	2	16	no	—
159	C₂²×C₃×C₄	—	9	2	no	—
160	C₂²×C₃×C₄	—	9	1	no	—
161	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
162	C₂²×C₃×C₄	C₂×C₃×D₃	1	16	yes	complemented
163	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
164	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	4	yes	complemented
165	C₂×#67	—	3	16	no	—
166	C₂×#67	—	6	16	no	—
167	C₂²×Dic₃	—	3	4	no	—
168	C₂²×Dic₃	—	3	8	no	—
169	C₃×C₄⋊C₄	—	9	8	no	—
170	C₃×C₂²⋊C₄	—	9	4	no	—
171	C₃×C₂²⋊C₄	—	9	8	no	—
172	#217	—	3	16	no	—
173	(C₂×D₃)⋊C₄	—	3	32	no	—
174	Dic₃⋊C₄	—	3	32	no	—
175	C₂²×C₃²	—	2	64	no	—
176	C₂²×C₃²	—	2	32	no	—
177	C₂²×C₃²	—	2	32	no	—
178	C₂²×C₃²	—	2	8	no	—
179	C₂²×C₃²	—	2	16	no	—
180	C₂²×C₃²	—	2	4	no	—
181	C₂²×C₃²	—	2	4	no	—
182	C₂²×C₃²	—	2	16	no	—
183	C₂²×C₃²	—	2	16	no	—
184	C₂²×C₃²	—	2	8	no	—
185	C₂²×C₃²	#235	1	16	yes	—
186	C₂²×C₃²	C₂×#67	1	16	yes	—
187	C₂²×C₃²	C₂×#67	1	8	yes	—
188	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
189	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
190	C₂²×C₃²	C₃×#41	1	4	yes	—
191	C₂²×C₃²	C₂³×D₃	1	4	yes	—
192	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
193	C₂×C₃⋊D₃	—	2	2	no	—
194	C₂×C₃⋊D₃	—	2	4	no	—
195	C₂×C₃⋊D₃	—	4	4	no	—
196	C₂×C₃×D₃	—	6	16	no	—
197	C₂×C₃×D₃	—	6	8	no	—
198	C₂×C₃×D₃	—	12	16	no	—
199	C₃²×C₄	—	2	32	no	—
200	C₃²×C₄	—	2	16	no	—
201	C₃²×C₄	—	2	4	no	—
202	C₃⋊Dic₃	—	2	2	no	—
203	C₃⋊Dic₃	—	2	4	no	—
204	C₃×Dic₃	—	6	16	no	—
205	C₃×Dic₃	—	6	8	no	—
206	C₂²×D₄	—	9	1	no	—
207	C₂³×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
208	#123	—	9	8	no	—
209	C₂×C₄⋊C₄	—	9	2	no	—
210	C₂×C₂²⋊C₄	—	9	1	no	—
211	C₂×C₂²⋊C₄	—	9	2	no	—
212	C₃³	C₂×#123	1	1	yes	characteristic, complemented, Sylow
213	C₂³×C₃	—	2	32	no	—
214	C₂³×C₃	—	2	16	no	—
215	C₂³×C₃	—	2	4	no	—
216	C₂³×C₃	—	2	16	no	—
217	C₂³×C₃	—	2	8	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	9	2	no	—
220	C₂³×C₃	—	18	4	no	—
221	C₂³×C₃	—	18	2	no	—
222	C₂³×C₃	C₃×#67	1	16	yes	—
223	C₂³×C₃	#638	1	4	yes	—
224	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
225	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
226	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
227	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
228	C₂²×D₃	—	3	8	no	—
229	C₂²×D₃	—	6	16	no	—
230	C₂²×D₃	—	6	8	no	—
231	C₃×D₄	—	18	8	no	—
232	C₂×C₃×C₄	—	2	32	no	—
233	C₂×C₃×C₄	—	2	64	no	—
234	C₂×C₃×C₄	—	2	16	no	—
235	C₂×C₃×C₄	—	2	32	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	8	no	—
238	C₂×C₃×C₄	—	2	16	no	—
239	C₂×C₃×C₄	—	9	4	no	—
240	C₂×C₃×C₄	—	9	2	no	—
241	C₂×C₃×C₄	—	18	4	no	—
242	C₂×C₃×C₄	—	18	2	no	—
243	C₂×C₃×C₄	C₂²×C₃×D₃	1	16	yes	—
244	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	4	yes	—
245	#67	—	6	32	no	—
246	C₂×Dic₃	—	3	8	no	—
247	C₂×Dic₃	—	3	16	no	—
248	C₂×Dic₃	—	6	16	no	—
249	C₂×Dic₃	—	6	8	no	—
250	C₂×C₃²	—	2	32	no	—
251	C₂×C₃²	—	2	16	no	—
252	C₂×C₃²	—	2	4	no	—
253	C₂×C₃²	—	2	16	no	—
254	C₂×C₃²	—	2	8	no	—
255	C₂×C₃²	—	2	4	no	—
256	C₂×C₃²	#929	1	16	yes	complemented
257	C₂×C₃²	C₃×#123	1	4	yes	complemented
258	C₂×C₃²	C₂×#235	1	8	yes	—
259	C₂×C₃²	C₂²×#67	1	4	yes	—
260	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
261	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
262	C₃⋊D₃	—	4	2	no	—
263	C₃×D₃	—	12	8	no	—
264	C₂⁴	—	9	1	no	—
265	C₂⁴	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
266	C₂×D₄	—	9	4	no	—
267	C₂×D₄	—	18	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	9	2	no	—
270	C₂²×C₄	—	9	1	no	—
271	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
272	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
273	C₄⋊C₄	—	9	8	no	—
274	C₂²⋊C₄	—	9	4	no	—
275	C₂²⋊C₄	—	9	8	no	—
276	C₂²×C₃	—	2	64	no	—
277	C₂²×C₃	—	2	32	no	—
278	C₂²×C₃	—	2	32	no	—
279	C₂²×C₃	—	2	16	no	—
280	C₂²×C₃	—	2	4	no	—
281	C₂²×C₃	—	2	8	no	—
282	C₂²×C₃	—	2	4	no	—
283	C₂²×C₃	—	2	16	no	—
284	C₂²×C₃	—	2	16	no	—
285	C₂²×C₃	—	2	8	no	—
286	C₂²×C₃	—	18	4	no	—
287	C₂²×C₃	—	18	2	no	—
288	C₂²×C₃	—	36	4	no	—
289	C₂²×C₃	C₃×#235	1	16	yes	—
290	C₂²×C₃	C₂×C₃×#67	1	16	yes	—
291	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
292	C₂²×C₃	#3828	1	4	yes	—
293	C₂²×C₃	C₂×#638	1	4	yes	—
294	C₂²×C₃	C₂×#638	1	2	yes	—
295	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
296	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
297	C₂×D₃	—	6	16	no	—
298	C₂×D₃	—	6	8	no	—
299	C₂×D₃	—	12	16	no	—
300	C₃×C₄	—	2	32	no	—
301	C₃×C₄	—	2	16	no	—
302	C₃×C₄	—	2	4	no	—
303	C₃×C₄	—	18	4	no	—
304	C₃×C₄	—	18	2	no	—
305	Dic₃	—	6	16	no	—
306	Dic₃	—	6	8	no	—
307	C₃²	—	2	4	no	—
308	C₃²	C₂×#929	1	4	yes	complemented
309	C₃²	C₂×C₃×#123	1	1	yes	characteristic, complemented
310	C₂³	—	2	4	no	—
311	C₂³	—	9	2	no	—
312	C₂³	—	18	4	no	—
313	C₂³	—	18	2	no	—
314	C₂³	C₃×#638	1	4	yes	—
315	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
316	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
317	D₄	—	18	8	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	9	4	no	—
321	C₂×C₄	—	9	2	no	—
322	C₂×C₄	—	18	4	no	—
323	C₂×C₄	—	18	2	no	—
324	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	4	yes	—
325	C₂×C₃	—	2	32	no	—
326	C₂×C₃	—	2	16	no	—
327	C₂×C₃	—	2	4	no	—
328	C₂×C₃	—	2	16	no	—
329	C₂×C₃	—	2	8	no	—
330	C₂×C₃	—	2	4	no	—
331	C₂×C₃	—	36	2	no	—
332	C₂×C₃	C₃×#929	1	16	yes	complemented
333	C₂×C₃	#64138	1	4	yes	direct product factor
334	C₂×C₃	C₂×C₃×#235	1	8	yes	—
335	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
336	C₂×C₃	C₂×#3828	1	2	yes	—
337	C₂×C₃	C₂²×#638	1	1	yes	characteristic
338	D₃	—	12	8	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	18	4	no	—
342	C₂²	—	18	2	no	—
343	C₂²	—	36	4	no	—
344	C₂²	C₃×#3828	1	4	yes	—
345	C₂²	C₂×C₃×#638	1	4	yes	—
346	C₂²	C₂×C₃×#638	1	2	yes	—
347	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
348	C₄	—	2	4	no	—
349	C₄	—	18	4	no	—
350	C₄	—	18	2	no	—
351	C₃	—	2	4	no	—
352	C₃	C₂×C₃×#929	1	4	yes	complemented
353	C₃	C₂×#64138	1	1	yes	characteristic, direct product factor
354	C₂	—	2	4	no	—
355	C₂	—	36	2	no	—
356	C₂	C₃×#64138	1	4	yes	direct product factor
357	C₂	C₂×C₃×#3828	1	2	yes	—
358	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	C₂³×C₃³×C₄	C₂
socle	C₂³×C₃³	C₂³
prime radical	C₂²×C₃×#638	C₂
hypercenter	C₂³×C₃×C₄	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#123
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃³×C₄	C₂	semidirect
3. C₂×C₃×#3757	C₂	semidirect
4. C₃×#64138	C₂	direct (N × H)
5. C₂×C₃×#3752	C₂	semidirect
6. C₂×C₃×#3750	C₂	semidirect
7. C₂×#64138	C₃	direct (N × H)
13. C₂²×C₃³×C₄	C₂²	semidirect
18. C₃×#3757	C₂²	semidirect
19. C₃×#3752	C₂²	semidirect
20. C₃×#3750	C₂²	semidirect
22. C₂³×C₃²×C₄	D₃	semidirect
23. C₂³×C₃²×C₄	C₂×C₃	semidirect
26. C₂×#3757	C₂×C₃	semidirect
27. #64138	C₂×C₃	direct (N × H)
28. C₂×#3752	C₂×C₃	semidirect
29. C₂×#3750	C₂×C₃	semidirect
62. C₂²×C₃²×C₄	C₂×D₃	semidirect
64. C₂²×C₃²×C₄	C₂²×C₃	semidirect
73. #3757	C₂²×C₃	semidirect
74. #3752	C₂²×C₃	semidirect
75. #3750	C₂²×C₃	semidirect
93. C₂³×C₃×C₄	C₃×D₃	semidirect
94. C₂³×C₃×C₄	C₃⋊D₃	semidirect
143. C₂×C₃³	#123	semidirect
162. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
164. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
207. C₂³×C₄	C₃×C₃⋊D₃	semidirect
212. C₃³	C₂×#123	semidirect
256. C₂×C₃²	#929	semidirect
257. C₂×C₃²	C₃×#123	semidirect
272. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
308. C₃²	C₂×#929	semidirect
309. C₃²	C₂×C₃×#123	semidirect
332. C₂×C₃	C₃×#929	semidirect
333. C₂×C₃	#64138	direct (N × H)
352. C₃	C₂×C₃×#929	semidirect
353. C₃	C₂×#64138	direct (N × H)
356. C₂	C₃×#64138	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×C₃³×C₄	2
C₂²×C₃×#638	2
C₂×C₃×#3757	2
C₃×#64138	2
C₂×C₃×#3752	2
C₂×C₃×#3750	2
C₂×#64138	3
C₂×C₃×#929	3

Subgroups — C2×C3×#64138 #13179540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64138 #13179540