Subgroups — C₂×C₃×#63648 #13163149

Order 1728.

1516 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63648	C₂	1	4	yes	maximal, direct product factor
5	C₂×#63648	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×#821	—	3	4	no	maximal
7	C₂³×C₃×C₃⋊D₃	—	2	1	no	—
8	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₃⋊Dic₃	—	2	1	no	—
10	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
11	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
12	C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	1	4	yes	complemented
13	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
14	C₂×C₃³×C₈	—	2	2	no	—
15	C₂×C₃³×C₈	C₂²	1	2	yes	complemented
16	C₃×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
17	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
18	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₃×D₁₂	—	3	4	no	—
20	C₂²×C₃²×C₈	—	2	4	no	—
21	C₂²×C₃²×C₈	D₃	1	4	yes	complemented
22	C₂²×C₃²×C₈	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₃×C₄⋊Dic₃	—	3	4	no	—
25	#63648	C₂×C₃	1	4	yes	direct product factor
26	C₃×#821	—	3	16	no	—
27	C₂³×C₃³	D₄	1	1	yes	characteristic
28	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
29	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
30	C₂²×C₃×C₃⋊D₃	—	4	2	no	—
31	C₂²×C₃×C₃⋊D₃	—	4	2	no	—
32	C₂×C₃³×C₄	C₂×C₄	1	2	yes	—
33	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
34	C₂×C₃³×C₄	D₄	1	2	yes	—
35	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
36	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
37	C₂×C₃×C₃⋊Dic₃	—	4	2	no	—
38	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
39	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
40	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	4	yes	complemented
41	C₃³×C₈	—	2	2	no	—
42	C₂×C₃×#102	—	9	1	no	—
43	C₂×#821	—	3	4	no	—
44	C₂³×C₃⋊D₃	—	2	1	no	—
45	C₂³×C₃×D₃	—	6	4	no	—
46	C₂²×C₃²×C₄	—	2	4	no	—
47	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
48	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
49	C₂²×C₃⋊Dic₃	—	2	1	no	—
50	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
51	C₂×C₄⋊(C₃⋊D₃)	—	2	2	no	—
52	C₂×C₄⋊(C₃⋊D₃)	C₃×C₄	1	4	yes	complemented
53	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
54	C₂²×C₃×Dic₃	—	6	4	no	—
55	C₂×C₃×D₁₂	—	3	16	no	—
56	C₂×C₃×D₁₂	—	3	8	no	—
57	C₂×C₃×D₁₂	—	6	4	no	—
58	C₂×C₃×D₁₂	—	6	8	no	—
59	C₂×C₃²×C₈	—	2	16	no	—
60	C₂×C₃²×C₈	—	2	8	no	—
61	C₂×C₃²×C₈	—	2	8	no	—
62	C₂×C₃²×C₈	—	2	2	no	—
63	C₂×C₃²×C₈	C₂×D₃	1	8	yes	complemented
64	C₂×C₃²×C₈	C₂²×C₃	1	2	yes	complemented
65	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
66	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	complemented
67	C₃×C₄⋊Dic₃	—	3	8	no	—
68	C₃×C₄⋊Dic₃	—	6	4	no	—
69	C₂²×C₃³	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₃³	D₈	1	2	yes	—
71	C₂²×C₃³	SD₁₆	1	2	yes	—
72	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
73	C₂×C₃×C₃⋊D₃	—	2	4	no	—
74	C₂×C₃×C₃⋊D₃	—	4	8	no	—
75	C₂×C₃×C₃⋊D₃	—	4	2	no	—
76	C₂×C₃×C₃⋊D₃	—	4	2	no	—
77	C₃³×C₄	C₂²⋊C₄	1	2	yes	—
78	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
79	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
80	C₃×C₃⋊Dic₃	—	4	2	no	—
81	C₂²×C₃×D₄	—	9	1	no	—
82	C₂²×D₁₂	—	3	4	no	—
83	C₂²×C₃×C₈	—	2	4	no	—
84	C₂²×C₃×C₈	C₃×D₃	1	4	yes	complemented
85	C₂²×C₃×C₈	C₃⋊D₃	1	1	yes	characteristic, complemented
86	C₂×C₃×C₄⋊C₄	—	9	1	no	—
87	C₂×C₄⋊Dic₃	—	3	4	no	—
88	C₃×#102	—	9	4	no	—
89	#821	—	3	16	no	—
90	C₂³×C₃²	—	2	4	no	—
91	C₂³×C₃²	D₁₂	1	4	yes	—
92	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
93	C₂²×C₃⋊D₃	—	2	4	no	—
94	C₂²×C₃⋊D₃	—	2	2	no	—
95	C₂²×C₃⋊D₃	—	4	2	no	—
96	C₂²×C₃⋊D₃	—	4	2	no	—
97	C₂²×C₃×D₃	—	6	16	no	—
98	C₂²×C₃×D₃	—	6	8	no	—
99	C₂²×C₃×D₃	—	12	8	no	—
100	C₂²×C₃×D₃	—	12	8	no	—
101	C₂×C₃²×C₄	—	2	8	no	—
102	C₂×C₃²×C₄	—	2	4	no	—
103	C₂×C₃²×C₄	—	2	8	no	—
104	C₂×C₃²×C₄	—	2	4	no	—
105	C₂×C₃²×C₄	C₄×D₃	1	8	yes	—
106	C₂×C₃²×C₄	D₁₂	1	4	yes	—
107	C₂×C₃²×C₄	#67	1	8	yes	—
108	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
109	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
111	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
112	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
113	C₂×C₃⋊Dic₃	—	2	2	no	—
114	C₂×C₃⋊Dic₃	—	4	2	no	—
115	C₄⋊(C₃⋊D₃)	—	2	4	no	—
116	C₄⋊(C₃⋊D₃)	—	2	2	no	—
117	C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	1	4	yes	complemented
118	C₂×C₃×Dic₃	—	6	8	no	—
119	C₂×C₃×Dic₃	—	12	8	no	—
120	C₃×D₁₂	—	3	16	no	—
121	C₃×D₁₂	—	6	16	no	—
122	C₃×D₁₂	—	6	8	no	—
123	C₃²×C₈	—	2	16	no	—
124	C₃²×C₈	—	2	8	no	—
125	C₃²×C₈	—	2	2	no	—
126	C₂×#102	—	9	1	no	Sylow
127	C₂×C₃³	#102	1	4	yes	complemented
128	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₃³	C₂×D₈	1	1	yes	characteristic
130	C₂×C₃³	C₂×SD₁₆	1	1	yes	characteristic
131	C₃×C₃⋊D₃	—	4	4	no	—
132	C₂⁴×C₃	—	18	1	no	—
133	C₂³×D₃	—	6	4	no	—
134	C₂×C₃×D₄	—	9	4	no	—
135	C₂×C₃×D₄	—	9	2	no	—
136	C₂×C₃×D₄	—	18	1	no	—
137	C₂×C₃×D₄	—	18	2	no	—
138	C₂²×C₃×C₄	—	2	4	no	—
139	C₂²×C₃×C₄	—	18	1	no	—
140	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
141	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
142	C₂²×Dic₃	—	6	4	no	—
143	C₂×D₁₂	—	3	16	no	—
144	C₂×D₁₂	—	3	8	no	—
145	C₂×D₁₂	—	6	4	no	—
146	C₂×D₁₂	—	6	8	no	—
147	C₂×C₃×C₈	—	2	16	no	—
148	C₂×C₃×C₈	—	2	8	no	—
149	C₂×C₃×C₈	—	2	2	no	—
150	C₂×C₃×C₈	—	2	8	no	—
151	C₂×C₃×C₈	C₂×C₃×D₃	1	8	yes	complemented
152	C₂×C₃×C₈	C₂×C₃⋊D₃	1	2	yes	complemented
153	C₃×C₄⋊C₄	—	9	2	no	—
154	C₃×C₄⋊C₄	—	18	1	no	—
155	C₄⋊Dic₃	—	3	8	no	—
156	C₄⋊Dic₃	—	6	4	no	—
157	C₂²×C₃²	—	2	8	no	—
158	C₂²×C₃²	—	2	8	no	—
159	C₂²×C₃²	—	2	8	no	—
160	C₂²×C₃²	—	2	4	no	—
161	C₂²×C₃²	#204	1	8	yes	—
162	C₂²×C₃²	D₂₄	1	8	yes	—
163	C₂²×C₃²	(C₂×D₃)⋊C₄	1	8	yes	—
164	C₂²×C₃²	C₃×C₂²⋊C₄	1	2	yes	—
165	C₂²×C₃²	C₃×D₈	1	2	yes	—
166	C₂²×C₃²	C₃×SD₁₆	1	2	yes	—
167	C₂²×C₃²	C₂×D₁₂	1	4	yes	—
168	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
169	C₂×C₃⋊D₃	—	2	4	no	—
170	C₂×C₃⋊D₃	—	4	8	no	—
171	C₂×C₃⋊D₃	—	4	2	no	—
172	C₂×C₃⋊D₃	—	4	2	no	—
173	C₂×C₃×D₃	—	6	16	no	—
174	C₂×C₃×D₃	—	12	32	no	—
175	C₂×C₃×D₃	—	12	8	no	—
176	C₂×C₃×D₃	—	12	8	no	—
177	C₃²×C₄	—	2	8	no	—
178	C₃²×C₄	—	2	4	no	—
179	C₃²×C₄	—	2	4	no	—
180	C₃²×C₄	(C₂×D₃)⋊C₄	1	8	yes	—
181	C₃²×C₄	C₃×C₂²⋊C₄	1	2	yes	—
182	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
183	C₃²×C₄	C₂×#67	1	4	yes	—
184	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
185	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
186	C₃⋊Dic₃	—	4	2	no	—
187	C₃×Dic₃	—	12	8	no	—
188	C₂²×D₄	—	9	1	no	—
189	C₂²×C₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
190	C₂×C₄⋊C₄	—	9	1	no	—
191	#102	—	9	4	no	—
192	C₃³	C₂×#102	1	1	yes	characteristic, complemented, Sylow
193	C₂³×C₃	—	2	4	no	—
194	C₂³×C₃	—	18	4	no	—
195	C₂³×C₃	—	18	2	no	—
196	C₂³×C₃	—	36	2	no	—
197	C₂³×C₃	—	36	2	no	—
198	C₂³×C₃	C₃×D₁₂	1	4	yes	—
199	C₂³×C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
200	C₂²×D₃	—	6	16	no	—
201	C₂²×D₃	—	6	8	no	—
202	C₂²×D₃	—	12	8	no	—
203	C₂²×D₃	—	12	8	no	—
204	C₃×D₄	—	9	4	no	—
205	C₃×D₄	—	18	4	no	—
206	C₃×D₄	—	18	2	no	—
207	C₂×C₃×C₄	—	2	8	no	—
208	C₂×C₃×C₄	—	2	4	no	—
209	C₂×C₃×C₄	—	2	8	no	—
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	18	2	no	—
212	C₂×C₃×C₄	—	36	2	no	—
213	C₂×C₃×C₄	C₃×C₄×D₃	1	8	yes	—
214	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
215	C₂×C₃×C₄	C₃×#67	1	8	yes	—
216	C₂×C₃×C₄	C₄×C₃⋊D₃	1	2	yes	—
217	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
218	C₂×C₃×C₄	#638	1	2	yes	—
219	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
220	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
221	C₂×Dic₃	—	6	8	no	—
222	C₂×Dic₃	—	12	8	no	—
223	D₁₂	—	3	16	no	—
224	D₁₂	—	6	16	no	—
225	D₁₂	—	6	8	no	—
226	C₃×C₈	—	2	16	no	—
227	C₃×C₈	—	2	8	no	—
228	C₃×C₈	—	2	2	no	—
229	C₂×C₃²	—	2	4	no	—
230	C₂×C₃²	—	2	4	no	—
231	C₂×C₃²	—	2	4	no	—
232	C₂×C₃²	—	2	16	no	—
233	C₂×C₃²	#821	1	16	yes	complemented
234	C₂×C₃²	C₃×#102	1	4	yes	complemented
235	C₂×C₃²	C₂×#204	1	4	yes	—
236	C₂×C₃²	C₂×D₂₄	1	4	yes	—
237	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
238	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₃²	C₂×C₃×D₈	1	1	yes	characteristic
240	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
241	C₃⋊D₃	—	4	4	no	—
242	C₃×D₃	—	12	16	no	—
243	C₂⁴	—	18	1	no	—
244	C₂×D₄	—	9	4	no	—
245	C₂×D₄	—	9	2	no	—
246	C₂×D₄	—	18	1	no	—
247	C₂×D₄	—	18	2	no	—
248	C₂²×C₄	—	18	1	no	—
249	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
252	C₄⋊C₄	—	9	2	no	—
253	C₄⋊C₄	—	18	1	no	—
254	C₂²×C₃	—	2	8	no	—
255	C₂²×C₃	—	2	8	no	—
256	C₂²×C₃	—	2	8	no	—
257	C₂²×C₃	—	2	4	no	—
258	C₂²×C₃	—	18	4	no	—
259	C₂²×C₃	—	36	2	no	—
260	C₂²×C₃	—	36	2	no	—
261	C₂²×C₃	—	36	8	no	—
262	C₂²×C₃	C₃×#204	1	8	yes	—
263	C₂²×C₃	C₃×D₂₄	1	8	yes	—
264	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	8	yes	—
265	C₂²×C₃	#3744	1	2	yes	—
266	C₂²×C₃	#3745	1	2	yes	—
267	C₂²×C₃	#3752	1	2	yes	—
268	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
269	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
270	C₂×D₃	—	6	16	no	—
271	C₂×D₃	—	12	8	no	—
272	C₂×D₃	—	12	8	no	—
273	C₂×D₃	—	12	32	no	—
274	C₃×C₄	—	2	8	no	—
275	C₃×C₄	—	2	4	no	—
276	C₃×C₄	—	2	4	no	—
277	C₃×C₄	—	36	2	no	—
278	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	8	yes	—
279	C₃×C₄	#3752	1	2	yes	—
280	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
281	C₃×C₄	C₂×C₃×#67	1	4	yes	—
282	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
283	C₃×C₄	C₂×#638	1	1	yes	characteristic
284	Dic₃	—	12	8	no	—
285	C₃²	—	2	4	no	—
286	C₃²	C₂×#821	1	4	yes	complemented
287	C₃²	C₂×C₃×#102	1	1	yes	characteristic, complemented
288	C₂³	—	18	4	no	—
289	C₂³	—	18	2	no	—
290	C₂³	—	36	2	no	—
291	C₂³	—	36	2	no	—
292	C₂³	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
293	D₄	—	9	4	no	—
294	D₄	—	18	4	no	—
295	D₄	—	18	2	no	—
296	C₂×C₄	—	18	2	no	—
297	C₂×C₄	—	36	2	no	—
298	C₂×C₄	C₃×C₄×C₃⋊D₃	1	2	yes	—
299	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
300	C₂×C₄	C₃×#638	1	2	yes	—
301	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
302	C₈	—	2	2	no	—
303	C₂×C₃	—	2	4	no	—
304	C₂×C₃	—	2	4	no	—
305	C₂×C₃	—	2	4	no	—
306	C₂×C₃	—	2	16	no	—
307	C₂×C₃	—	36	4	no	—
308	C₂×C₃	C₃×#821	1	16	yes	complemented
309	C₂×C₃	#63648	1	4	yes	direct product factor
310	C₂×C₃	C₂×C₃×#204	1	4	yes	—
311	C₂×C₃	C₂×C₃×D₂₄	1	4	yes	—
312	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	4	yes	—
313	C₂×C₃	C₂×#3744	1	1	yes	characteristic
314	C₂×C₃	C₂×#3745	1	1	yes	characteristic
315	C₂×C₃	C₂×#3752	1	1	yes	characteristic
316	D₃	—	12	16	no	—
317	C₂²	—	18	4	no	—
318	C₂²	—	36	2	no	—
319	C₂²	—	36	2	no	—
320	C₂²	—	36	8	no	—
321	C₂²	C₃×#3744	1	2	yes	—
322	C₂²	C₃×#3745	1	2	yes	—
323	C₂²	C₃×#3752	1	2	yes	—
324	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
325	C₄	—	36	2	no	—
326	C₄	C₃×#3752	1	2	yes	—
327	C₄	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
328	C₄	C₂×C₃×#638	1	1	yes	characteristic
329	C₃	—	2	4	no	—
330	C₃	C₂×C₃×#821	1	4	yes	complemented
331	C₃	C₂×#63648	1	1	yes	characteristic, direct product factor
332	C₂	—	36	4	no	—
333	C₂	C₃×#63648	1	4	yes	direct product factor
334	C₂	C₂×C₃×#3744	1	1	yes	characteristic
335	C₂	C₂×C₃×#3745	1	1	yes	characteristic
336	C₂	C₂×C₃×#3752	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₄⋊(C₃⋊D₃)
commutator	C₃²×C₄	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×C₈	C₂
socle	C₂³×C₃³	D₄
prime radical	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂²×C₃×C₈	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#102
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃³×C₈	C₂	semidirect
3. C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	semidirect
4. C₃×#63648	C₂	direct (N × H)
5. C₂×#63648	C₃	direct (N × H)
12. C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	semidirect
15. C₂×C₃³×C₈	C₂²	semidirect
17. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
21. C₂²×C₃²×C₈	D₃	semidirect
22. C₂²×C₃²×C₈	C₂×C₃	semidirect
23. C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	semidirect
25. #63648	C₂×C₃	direct (N × H)
40. C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	semidirect
52. C₂×C₄⋊(C₃⋊D₃)	C₃×C₄	semidirect
63. C₂×C₃²×C₈	C₂×D₃	semidirect
64. C₂×C₃²×C₈	C₂²×C₃	semidirect
66. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
84. C₂²×C₃×C₈	C₃×D₃	semidirect
85. C₂²×C₃×C₈	C₃⋊D₃	semidirect
117. C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	semidirect
127. C₂×C₃³	#102	semidirect
151. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
152. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
189. C₂²×C₈	C₃×C₃⋊D₃	semidirect
192. C₃³	C₂×#102	semidirect
233. C₂×C₃²	#821	semidirect
234. C₂×C₃²	C₃×#102	semidirect
251. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
286. C₃²	C₂×#821	semidirect
287. C₃²	C₂×C₃×#102	semidirect
308. C₂×C₃	C₃×#821	semidirect
309. C₂×C₃	#63648	direct (N × H)
330. C₃	C₂×C₃×#821	semidirect
331. C₃	C₂×#63648	direct (N × H)
333. C₂	C₃×#63648	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×C₄⋊(C₃⋊D₃)	2
C₂²×C₃³×C₈	2
C₂×C₃×C₄⋊(C₃⋊Dic₃)	2
C₃×#63648	2
C₂×#63648	3
C₂×C₃×#821	3

Subgroups — C2×C3×#63648 #13163149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63648 #13163149