Subgroups — C₃²×C₄×#204 #13162127

Order 1728.

908 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	C₂×C₃²×#204	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃²×C₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#821	C₂	1	1	yes	maximal, characteristic
6	C₃²×#817	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#816	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₄×SD₁₆	—	3	1	no	maximal
9	C₃×C₄×#204	C₃	1	4	yes	maximal, direct product factor
10	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
11	C₂×C₃²×C₄×D₃	—	2	1	no	—
12	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
13	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
15	C₃³×C₄²	C₂²	1	1	yes	characteristic
16	C₃²×(C₂×D₃)⋊C₄	—	2	1	no	—
17	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₃²×Dic₃⋊C₄	—	2	1	no	—
20	C₃²×C₄×Dic₃	—	2	1	no	—
21	C₃²×#204	C₄	1	4	yes	direct product factor
22	C₂×C₃²×SD₁₆	—	3	1	no	—
23	C₃²×C₄×Q₈	—	3	1	no	—
24	C₃²×C₄×D₄	—	3	1	no	—
25	C₂×C₃×#204	C₂×C₃	1	4	yes	—
26	C₃×C₄×D₁₂	C₂×C₃	1	4	yes	—
27	C₃×C₄×Dic₆	C₂×C₃	1	4	yes	complemented
28	C₃²×#106	—	3	1	no	—
29	C₃²×#103	—	3	1	no	—
30	C₃²×#102	—	3	1	no	—
31	C₃²×C₄×C₈	—	2	4	no	—
32	C₃²×C₄×C₈	D₃	1	1	yes	characteristic, complemented
33	C₃²×C₄×C₈	C₂×C₃	1	4	yes	complemented
34	C₃×#821	C₂×C₃	1	4	yes	—
35	C₃×#817	C₂×C₃	1	4	yes	complemented
36	C₃×#816	C₂×C₃	1	4	yes	complemented
37	C₂²×C₃²×D₃	—	2	1	no	—
38	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
39	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
40	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
41	C₂×C₃²×Dic₃	—	2	1	no	—
42	C₂×C₃²×Dic₃	—	2	1	no	—
43	C₂×C₃²×Dic₃	—	2	1	no	—
44	C₃²×D₁₂	—	2	1	no	—
45	C₃²×D₁₂	C₂×C₄	1	2	yes	—
46	C₃²×C₄×D₃	—	4	2	no	—
47	C₃²×Dic₆	—	2	1	no	—
48	C₃²×Dic₆	C₂×C₄	1	2	yes	complemented
49	C₃³×C₈	—	2	1	no	—
50	C₃³×C₈	C₂×C₄	1	2	yes	complemented
51	C₃×C₄×SD₁₆	—	3	4	no	—
52	C₄×#204	C₃²	1	1	yes	characteristic, direct product factor
53	C₂×C₃²×Q₈	—	3	1	no	—
54	C₂×C₃²×D₄	—	3	1	no	—
55	C₂²×C₃²×C₄	—	6	1	no	—
56	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
57	C₂×C₃×C₄×D₃	—	2	4	no	—
58	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
59	C₃²×SD₁₆	—	3	4	no	—
60	C₂×C₃²×C₈	—	2	4	no	—
61	C₂×C₃²×C₈	—	2	4	no	—
62	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
64	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
65	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
66	C₃²×C₄⋊C₄	—	3	1	no	—
67	C₃²×C₄⋊C₄	—	3	1	no	—
68	C₃²×C₄⋊C₄	—	6	1	no	—
69	C₃²×C₂²⋊C₄	—	6	1	no	—
70	C₃²×C₄²	—	2	4	no	—
71	C₃²×C₄²	—	6	1	no	—
72	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
73	C₃²×C₄²	C₂²×C₃	1	4	yes	—
74	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
75	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
76	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
77	C₃×Dic₃⋊C₄	—	2	4	no	—
78	C₃×C₄×Dic₃	—	2	4	no	—
79	C₃×#204	C₃×C₄	1	16	yes	direct product factor
80	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
81	C₂×C₃²×D₃	—	2	2	no	—
82	C₂×C₃²×D₃	—	4	1	no	—
83	C₂×C₃²×D₃	—	4	1	no	—
84	C₃³×C₄	—	2	1	no	—
85	C₃³×C₄	SD₁₆	1	2	yes	complemented
86	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
87	C₃³×C₄	#41	1	1	yes	characteristic
88	C₃²×Dic₃	—	2	2	no	—
89	C₃²×Dic₃	—	4	1	no	—
90	C₃²×Dic₃	—	4	1	no	—
91	C₂×C₃×SD₁₆	—	3	4	no	—
92	C₃×C₄×Q₈	—	3	4	no	—
93	C₃×C₄×D₄	—	3	4	no	—
94	C₂×#204	C₂×C₃²	1	1	yes	characteristic
95	C₄×D₁₂	C₂×C₃²	1	1	yes	characteristic
96	C₄×Dic₆	C₂×C₃²	1	1	yes	characteristic, complemented
97	C₃×#106	—	3	4	no	—
98	C₃×#103	—	3	4	no	—
99	C₃×#102	—	3	4	no	—
100	C₃×C₄×C₈	—	2	4	no	—
101	C₃×C₄×C₈	C₃×D₃	1	4	yes	complemented
102	C₃×C₄×C₈	C₂×C₃²	1	1	yes	characteristic, complemented
103	#821	C₂×C₃²	1	1	yes	characteristic
104	#817	C₂×C₃²	1	1	yes	characteristic, complemented
105	#816	C₂×C₃²	1	1	yes	characteristic, complemented
106	C₂³×C₃²	—	6	1	no	—
107	C₂²×C₃×D₃	—	2	4	no	—
108	C₃²×Q₈	—	3	2	no	—
109	C₃²×Q₈	—	6	1	no	—
110	C₃²×D₄	—	3	2	no	—
111	C₃²×D₄	—	6	1	no	—
112	C₂×C₃²×C₄	—	2	4	no	—
113	C₂×C₃²×C₄	—	2	4	no	—
114	C₂×C₃²×C₄	—	2	4	no	—
115	C₂×C₃²×C₄	—	6	1	no	—
116	C₂×C₃²×C₄	—	6	1	no	—
117	C₂×C₃²×C₄	—	6	1	no	—
118	C₂×C₃²×C₄	—	12	2	no	—
119	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
120	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
121	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
122	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
123	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
124	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
125	C₂×C₃×Dic₃	—	2	4	no	—
126	C₂×C₃×Dic₃	—	2	4	no	—
127	C₂×C₃×Dic₃	—	2	4	no	—
128	C₃×D₁₂	—	2	4	no	—
129	C₃×D₁₂	C₂×C₃×C₄	1	8	yes	—
130	C₃×C₄×D₃	—	4	8	no	—
131	C₃×Dic₆	—	2	4	no	—
132	C₃×Dic₆	C₂×C₃×C₄	1	8	yes	complemented
133	C₃²×C₈	—	2	8	no	—
134	C₃²×C₈	—	2	1	no	—
135	C₃²×C₈	—	2	4	no	—
136	C₃²×C₈	—	2	8	no	—
137	C₃²×C₈	C₄×D₃	1	2	yes	complemented
138	C₃²×C₈	C₂×C₃×C₄	1	8	yes	complemented
139	C₄×SD₁₆	—	3	1	no	Sylow
140	C₂×C₃³	C₄×D₄	1	1	yes	characteristic
141	C₂×C₃³	C₂×SD₁₆	1	1	yes	characteristic
142	C₂×C₃³	#135	1	1	yes	characteristic
143	C₃²×D₃	—	4	2	no	—
144	C₂×C₃×Q₈	—	3	4	no	—
145	C₂×C₃×D₄	—	3	4	no	—
146	C₂²×C₃×C₄	—	6	4	no	—
147	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
148	C₂×C₄×D₃	—	2	1	no	—
149	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
150	C₃×SD₁₆	—	3	16	no	—
151	C₂×C₃×C₈	—	2	4	no	—
152	C₂×C₃×C₈	—	2	4	no	—
153	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
154	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
155	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
156	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
157	C₃×C₄⋊C₄	—	3	4	no	—
158	C₃×C₄⋊C₄	—	3	4	no	—
159	C₃×C₄⋊C₄	—	6	4	no	—
160	C₃×C₂²⋊C₄	—	6	4	no	—
161	C₃×C₄²	—	2	4	no	—
162	C₃×C₄²	—	6	4	no	—
163	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
164	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
165	(C₂×D₃)⋊C₄	—	2	1	no	—
166	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
167	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
168	Dic₃⋊C₄	—	2	1	no	—
169	C₄×Dic₃	—	2	1	no	—
170	#204	C₃²×C₄	1	4	yes	direct product factor
171	C₂²×C₃²	—	2	4	no	—
172	C₂²×C₃²	—	6	2	no	—
173	C₂²×C₃²	—	12	1	no	—
174	C₂²×C₃²	—	12	1	no	—
175	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
176	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
177	C₂×C₃×D₃	—	2	8	no	—
178	C₂×C₃×D₃	—	4	4	no	—
179	C₂×C₃×D₃	—	4	4	no	—
180	C₃²×C₄	—	2	8	no	—
181	C₃²×C₄	—	2	1	no	—
182	C₃²×C₄	—	2	4	no	—
183	C₃²×C₄	—	2	8	no	—
184	C₃²×C₄	—	2	4	no	—
185	C₃²×C₄	—	2	4	no	—
186	C₃²×C₄	—	6	2	no	—
187	C₃²×C₄	—	12	1	no	—
188	C₃²×C₄	—	12	1	no	—
189	C₃²×C₄	#204	1	2	yes	direct product factor
190	C₃²×C₄	C₃×SD₁₆	1	8	yes	complemented
191	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
192	C₃²×C₄	#235	1	1	yes	characteristic
193	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
194	C₃²×C₄	C₃×#41	1	4	yes	—
195	C₃×Dic₃	—	2	8	no	—
196	C₃×Dic₃	—	4	4	no	—
197	C₃×Dic₃	—	4	4	no	—
198	C₂×SD₁₆	—	3	1	no	—
199	C₄×Q₈	—	3	1	no	—
200	C₄×D₄	—	3	1	no	—
201	#106	—	3	1	no	—
202	#103	—	3	1	no	—
203	#102	—	3	1	no	—
204	C₄×C₈	C₃²×D₃	1	1	yes	characteristic, complemented
205	C₃³	C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
206	C₂³×C₃	—	6	4	no	—
207	C₂²×D₃	—	2	1	no	—
208	C₃×Q₈	—	3	8	no	—
209	C₃×Q₈	—	6	4	no	—
210	C₃×D₄	—	3	8	no	—
211	C₃×D₄	—	6	4	no	—
212	C₂×C₃×C₄	—	2	4	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	2	4	no	—
215	C₂×C₃×C₄	—	6	4	no	—
216	C₂×C₃×C₄	—	6	4	no	—
217	C₂×C₃×C₄	—	6	4	no	—
218	C₂×C₃×C₄	—	12	8	no	—
219	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
220	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
221	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
222	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
224	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
225	C₂×Dic₃	—	2	1	no	—
226	C₂×Dic₃	—	2	1	no	—
227	C₂×Dic₃	—	2	1	no	—
228	D₁₂	—	2	1	no	—
229	D₁₂	C₂×C₃²×C₄	1	2	yes	—
230	C₄×D₃	—	4	2	no	—
231	Dic₆	—	2	1	no	—
232	Dic₆	C₂×C₃²×C₄	1	2	yes	complemented
233	C₃×C₈	—	2	8	no	—
234	C₃×C₈	—	2	4	no	—
235	C₃×C₈	—	2	1	no	—
236	C₃×C₈	—	2	8	no	—
237	C₃×C₈	C₃×C₄×D₃	1	8	yes	complemented
238	C₃×C₈	C₂×C₃²×C₄	1	2	yes	complemented
239	C₂×C₃²	—	2	4	no	—
240	C₂×C₃²	—	2	4	no	—
241	C₂×C₃²	—	2	4	no	—
242	C₂×C₃²	—	12	2	no	—
243	C₂×C₃²	C₄×D₁₂	1	1	yes	characteristic
244	C₂×C₃²	C₂×#204	1	1	yes	characteristic
245	C₂×C₃²	#904	1	1	yes	characteristic
246	C₂×C₃²	C₃×C₄×D₄	1	4	yes	—
247	C₂×C₃²	C₂×C₃×SD₁₆	1	4	yes	—
248	C₂×C₃²	C₃×#135	1	4	yes	—
249	C₃×D₃	—	4	8	no	—
250	C₂×Q₈	—	3	1	no	—
251	C₂×D₄	—	3	1	no	—
252	C₂²×C₄	—	6	1	no	—
253	SD₁₆	—	3	4	no	—
254	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
255	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
256	C₄⋊C₄	—	3	1	no	—
257	C₄⋊C₄	—	3	1	no	—
258	C₄⋊C₄	—	6	1	no	—
259	C₂²⋊C₄	—	6	1	no	—
260	C₄²	—	6	1	no	—
261	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
262	C₂²×C₃	—	2	4	no	—
263	C₂²×C₃	—	6	8	no	—
264	C₂²×C₃	—	12	4	no	—
265	C₂²×C₃	—	12	4	no	—
266	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
267	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
268	C₂×D₃	—	2	2	no	—
269	C₂×D₃	—	4	1	no	—
270	C₂×D₃	—	4	1	no	—
271	C₃×C₄	—	2	8	no	—
272	C₃×C₄	—	2	4	no	—
273	C₃×C₄	—	2	1	no	—
274	C₃×C₄	—	2	4	no	—
275	C₃×C₄	—	2	4	no	—
276	C₃×C₄	—	2	8	no	—
277	C₃×C₄	—	6	8	no	—
278	C₃×C₄	—	12	4	no	—
279	C₃×C₄	—	12	4	no	—
280	C₃×C₄	C₃×#204	1	8	yes	direct product factor
281	C₃×C₄	C₃²×SD₁₆	1	2	yes	complemented
282	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
283	C₃×C₄	C₃×#235	1	4	yes	—
284	C₃×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
285	C₃×C₄	C₃²×#41	1	1	yes	characteristic
286	Dic₃	—	2	2	no	—
287	Dic₃	—	4	1	no	—
288	Dic₃	—	4	1	no	—
289	C₃²	—	2	4	no	—
290	C₃²	C₄×#204	1	1	yes	characteristic, direct product factor
291	C₃²	C₃×C₄×SD₁₆	1	4	yes	complemented
292	C₂³	—	6	1	no	—
293	Q₈	—	3	2	no	—
294	Q₈	—	6	1	no	—
295	D₄	—	3	2	no	—
296	D₄	—	6	1	no	—
297	C₂×C₄	—	6	1	no	—
298	C₂×C₄	—	6	1	no	—
299	C₂×C₄	—	6	1	no	—
300	C₂×C₄	—	12	2	no	—
301	C₂×C₄	C₃²×D₁₂	1	1	yes	characteristic
302	C₂×C₄	C₃²×D₁₂	1	1	yes	characteristic
303	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
304	C₈	—	2	1	no	—
305	C₈	C₃²×C₄×D₃	1	2	yes	complemented
306	C₂×C₃	—	2	4	no	—
307	C₂×C₃	—	2	4	no	—
308	C₂×C₃	—	2	4	no	—
309	C₂×C₃	—	12	8	no	—
310	C₂×C₃	C₃×C₄×D₁₂	1	4	yes	—
311	C₂×C₃	C₂×C₃×#204	1	4	yes	—
312	C₂×C₃	C₃×#904	1	4	yes	—
313	C₂×C₃	C₃²×C₄×D₄	1	1	yes	characteristic
314	C₂×C₃	C₂×C₃²×SD₁₆	1	1	yes	characteristic
315	C₂×C₃	C₃²×#135	1	1	yes	characteristic
316	D₃	—	4	2	no	—
317	C₂²	—	6	2	no	—
318	C₂²	—	12	1	no	—
319	C₂²	—	12	1	no	—
320	C₂²	C₂×C₃²×D₁₂	1	1	yes	characteristic
321	C₄	—	2	1	no	—
322	C₄	—	6	2	no	—
323	C₄	—	12	1	no	—
324	C₄	—	12	1	no	—
325	C₄	C₃²×#204	1	2	yes	direct product factor
326	C₄	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
327	C₄	C₃²×#235	1	1	yes	characteristic
328	C₃	—	2	4	no	—
329	C₃	C₃×C₄×#204	1	4	yes	direct product factor
330	C₃	C₃²×C₄×SD₁₆	1	1	yes	characteristic, complemented
331	C₂	—	12	2	no	—
332	C₂	C₃²×C₄×D₁₂	1	1	yes	characteristic
333	C₂	C₂×C₃²×#204	1	1	yes	characteristic
334	C₂	C₃²×#904	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	D₁₂
commutator	C₃×C₄	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₃³×C₄×C₈	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃²×D₁₂	C₂²
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₃²×C₄×C₈	D₃
hypocenter	C₃	C₃²×C₄×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₃²×C₄² ◁ C₃²×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₃²×C₄×Dic₆	C₂	semidirect
4. C₃³×C₄×C₈	C₂	semidirect
6. C₃²×#817	C₂	semidirect
7. C₃²×#816	C₂	semidirect
9. C₃×C₄×#204	C₃	direct (N × H)
21. C₃²×#204	C₄	direct (N × H)
27. C₃×C₄×Dic₆	C₂×C₃	semidirect
32. C₃²×C₄×C₈	D₃	semidirect
33. C₃²×C₄×C₈	C₂×C₃	semidirect
35. C₃×#817	C₂×C₃	semidirect
36. C₃×#816	C₂×C₃	semidirect
48. C₃²×Dic₆	C₂×C₄	semidirect
50. C₃³×C₈	C₂×C₄	semidirect
52. C₄×#204	C₃²	direct (N × H)
79. C₃×#204	C₃×C₄	direct (N × H)
85. C₃³×C₄	SD₁₆	semidirect
96. C₄×Dic₆	C₂×C₃²	semidirect
101. C₃×C₄×C₈	C₃×D₃	semidirect
102. C₃×C₄×C₈	C₂×C₃²	semidirect
104. #817	C₂×C₃²	semidirect
105. #816	C₂×C₃²	semidirect
132. C₃×Dic₆	C₂×C₃×C₄	semidirect
137. C₃²×C₈	C₄×D₃	semidirect
138. C₃²×C₈	C₂×C₃×C₄	semidirect
170. #204	C₃²×C₄	direct (N × H)
189. C₃²×C₄	#204	direct (N × H)
190. C₃²×C₄	C₃×SD₁₆	semidirect
204. C₄×C₈	C₃²×D₃	semidirect
205. C₃³	C₄×SD₁₆	semidirect
232. Dic₆	C₂×C₃²×C₄	semidirect
237. C₃×C₈	C₃×C₄×D₃	semidirect
238. C₃×C₈	C₂×C₃²×C₄	semidirect
280. C₃×C₄	C₃×#204	direct (N × H)
281. C₃×C₄	C₃²×SD₁₆	semidirect
290. C₃²	C₄×#204	direct (N × H)
291. C₃²	C₃×C₄×SD₁₆	semidirect
305. C₈	C₃²×C₄×D₃	semidirect
325. C₄	C₃²×#204	direct (N × H)
329. C₃	C₃×C₄×#204	direct (N × H)
330. C₃	C₃²×C₄×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#204	2
C₃²×C₄×D₁₂	2
C₃²×C₄×Dic₆	2
C₃³×C₄×C₈	2
C₃²×#821	2
C₃²×#817	2
C₃²×#816	2
C₃²×C₄×SD₁₆	3
C₃×C₄×#204	3

Subgroups — C32×C4×#204 #13162127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄×#204 #13162127