Subgroups — #13179672

Order 1728.

4732 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×D₄×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₃⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#6312	C₂	1	2	yes	maximal, complemented
5	C₂×#88859	C₂	1	2	yes	maximal, complemented
6	#11723934	C₂	1	1	yes	maximal, characteristic, complemented
7	#11723933	C₂	1	1	yes	maximal, characteristic, complemented
8	#11723922	C₂	1	2	yes	maximal, complemented
9	C₂²⋊C₄×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
10	C₄×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic, complemented
11	#11723913	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596016	—	3	13	no	maximal
13	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	—
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃³×C₄	C₂²	1	2	yes	complemented
16	C₂×#6312	C₂²	1	2	yes	—
17	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
18	D₄×C₃⋊(C₃⋊D₃)	C₄	1	8	yes	complemented
19	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
22	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
23	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₃³×C₂²⋊C₄	C₂²	1	2	yes	complemented
25	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
26	#88864	C₂²	1	2	yes	complemented
27	#88859	C₂²	1	1	yes	characteristic
28	#88859	C₂²	1	1	yes	characteristic
29	#88859	C₂²	1	2	yes	—
30	#88859	C₂²	1	2	yes	complemented
31	#88859	C₂²	1	2	yes	complemented
32	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic, complemented
33	#88857	C₂²	1	1	yes	characteristic, complemented
34	#88857	C₂²	1	1	yes	characteristic, complemented
35	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
37	C₂×D₄×C₃⋊D₃	—	3	13	no	—
38	C₃²×C₄×D₄	D₃	1	13	yes	complemented
39	D₄×C₃⋊Dic₃	—	3	13	no	—
40	C₄×#638	—	3	26	no	—
41	C₂×#3752	—	3	26	no	—
42	#64102	—	3	13	no	—
43	#64101	—	3	13	no	—
44	#64090	—	3	26	no	—
45	C₂²⋊C₄×C₃⋊D₃	—	3	26	no	—
46	C₄×C₄⋊(C₃⋊D₃)	—	3	13	no	—
47	#64081	—	3	13	no	—
48	C₂³×C₃³	C₂³	1	2	yes	—
49	C₂²×C₃⋊(C₃⋊D₃)	—	4	2	no	—
50	C₂²×C₃⋊(C₃⋊D₃)	—	4	2	no	—
51	C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	1	8	yes	complemented
52	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
53	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	2	yes	—
54	C₃³×D₄	C₂×C₄	1	4	yes	complemented
55	C₂×C₃³×C₄	—	4	2	no	—
56	C₂×C₃³×C₄	C₂³	1	2	yes	—
57	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
58	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
59	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
60	#6312	C₂×C₄	1	8	yes	complemented
61	C₂×C₃⋊(C₃⋊Dic₃)	—	4	2	no	—
62	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
63	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
64	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
65	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
66	C₄⋊(C₃⋊(C₃⋊D₃))	C₂×C₄	1	4	yes	complemented
67	C₄×C₃⋊(C₃⋊D₃)	—	4	2	no	—
68	C₄×C₃⋊(C₃⋊D₃)	—	4	2	no	—
69	C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	1	4	yes	complemented
70	#5545	—	9	13	no	—
71	C₂³×C₃⋊D₃	—	3	26	no	—
72	C₂×C₃²×D₄	C₂×D₃	1	13	yes	—
73	C₂²×C₃²×C₄	C₂×D₃	1	26	yes	complemented
74	C₂×#638	—	3	26	no	—
75	C₂²×C₃⋊Dic₃	—	3	26	no	—
76	D₄×C₃⋊D₃	—	3	104	no	—
77	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
78	C₂×C₄×C₃⋊D₃	—	3	13	no	—
79	C₂×C₄×C₃⋊D₃	—	3	26	no	—
80	C₂×C₄×C₃⋊D₃	—	3	26	no	—
81	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	complemented
82	C₃²×C₂²⋊C₄	C₂×D₃	1	26	yes	complemented
83	C₃²×C₄²	C₂×D₃	1	13	yes	complemented
84	#3757	—	3	26	no	—
85	#3752	—	3	13	no	—
86	#3752	—	3	13	no	—
87	#3752	—	3	26	no	—
88	#3752	—	3	26	no	—
89	#3752	—	3	26	no	—
90	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
91	#3750	—	3	13	no	—
92	#3750	—	3	13	no	—
93	C₄×C₃⋊Dic₃	—	3	13	no	—
94	C₄×C₃⋊Dic₃	—	3	26	no	—
95	C₂²×C₃³	—	2	2	no	—
96	C₂²×C₃³	—	2	2	no	—
97	C₂²×C₃³	C₂²×C₄	1	4	yes	—
98	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
99	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
100	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
101	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
102	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
103	C₂×C₃⋊(C₃⋊D₃)	—	4	8	no	—
104	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	2	yes	—
105	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	4	yes	—
106	C₃³×C₄	—	2	1	no	—
107	C₃³×C₄	—	2	2	no	—
108	C₃³×C₄	—	2	1	no	—
109	C₃³×C₄	C₂²×C₄	1	2	yes	—
110	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
111	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
112	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
113	C₃⋊(C₃⋊Dic₃)	C₂²×C₄	1	2	yes	—
114	C₂×D₃×D₄	—	9	13	no	—
115	C₃×C₄×D₄	C₃⋊D₃	1	13	yes	complemented
116	D₄×Dic₃	—	9	13	no	—
117	C₄×#67	—	9	26	no	—
118	C₂×(C₂×D₃)⋊C₄	—	9	26	no	—
119	#893	—	9	13	no	—
120	#892	—	9	13	no	—
121	#67⋊C₄	—	9	26	no	—
122	D₃×C₂²⋊C₄	—	9	26	no	—
123	C₄×D₁₂	—	9	13	no	—
124	#872	—	9	13	no	—
125	C₂³×C₃²	C₂²×D₃	1	26	yes	—
126	C₂²×C₃⋊D₃	—	3	13	no	—
127	C₂²×C₃⋊D₃	—	3	26	no	—
128	C₂²×C₃⋊D₃	—	3	104	no	—
129	C₂²×C₃⋊D₃	—	12	26	no	—
130	C₂²×C₃⋊D₃	—	12	26	no	—
131	C₃²×D₄	C₄×D₃	1	52	yes	complemented
132	C₂×C₃²×C₄	—	4	26	no	—
133	C₂×C₃²×C₄	C₂²×D₃	1	26	yes	—
134	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
135	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
136	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
137	#638	—	3	104	no	—
138	C₂×C₃⋊Dic₃	—	3	13	no	—
139	C₂×C₃⋊Dic₃	—	3	13	no	—
140	C₂×C₃⋊Dic₃	—	3	13	no	—
141	C₂×C₃⋊Dic₃	—	3	26	no	—
142	C₂×C₃⋊Dic₃	—	12	26	no	—
143	C₄⋊(C₃⋊D₃)	—	3	52	no	—
144	C₄×C₃⋊D₃	—	3	52	no	—
145	C₄×C₃⋊D₃	—	12	26	no	—
146	C₄×C₃⋊D₃	—	12	26	no	—
147	#518	—	27	1	no	Sylow
148	C₂×C₃³	—	2	4	no	—
149	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
152	C₃⋊(C₃⋊D₃)	—	2	2	no	—
153	C₃⋊(C₃⋊D₃)	—	2	4	no	—
154	C₂³×D₃	—	9	26	no	—
155	C₂×C₃×D₄	C₂×C₃⋊D₃	1	13	yes	—
156	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	26	yes	complemented
157	C₂×#67	—	9	26	no	—
158	C₂²×Dic₃	—	9	26	no	—
159	D₃×D₄	—	9	104	no	—
160	C₂×D₁₂	—	9	13	no	—
161	C₂×C₄×D₃	—	9	13	no	—
162	C₂×C₄×D₃	—	9	26	no	—
163	C₂×C₄×D₃	—	9	26	no	—
164	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
165	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	26	yes	complemented
166	C₃×C₄²	C₂×C₃⋊D₃	1	13	yes	complemented
167	#217	—	9	26	no	—
168	(C₂×D₃)⋊C₄	—	9	13	no	—
169	(C₂×D₃)⋊C₄	—	9	13	no	—
170	(C₂×D₃)⋊C₄	—	9	26	no	—
171	(C₂×D₃)⋊C₄	—	9	26	no	—
172	(C₂×D₃)⋊C₄	—	9	26	no	—
173	C₄⋊Dic₃	—	9	13	no	—
174	Dic₃⋊C₄	—	9	13	no	—
175	Dic₃⋊C₄	—	9	13	no	—
176	C₄×Dic₃	—	9	13	no	—
177	C₄×Dic₃	—	9	26	no	—
178	C₂²×C₃²	—	2	26	no	—
179	C₂²×C₃²	—	2	26	no	—
180	C₂²×C₃²	C₂×C₄×D₃	1	52	yes	—
181	C₂²×C₃²	C₂³×D₃	1	13	yes	—
182	C₂×C₃⋊D₃	—	3	26	no	—
183	C₂×C₃⋊D₃	—	3	52	no	—
184	C₂×C₃⋊D₃	—	6	26	no	—
185	C₂×C₃⋊D₃	—	6	13	no	—
186	C₂×C₃⋊D₃	—	6	26	no	—
187	C₂×C₃⋊D₃	—	6	13	no	—
188	C₂×C₃⋊D₃	—	12	104	no	—
189	C₃²×C₄	—	2	26	no	—
190	C₃²×C₄	—	2	13	no	—
191	C₃²×C₄	—	2	13	no	—
192	C₃²×C₄	C₂×C₄×D₃	1	26	yes	—
193	C₃⋊Dic₃	—	3	26	no	—
194	C₃⋊Dic₃	—	6	13	no	—
195	C₃⋊Dic₃	—	6	26	no	—
196	C₃⋊Dic₃	—	6	13	no	—
197	C₂²×D₄	—	27	1	no	—
198	C₄×D₄	—	27	1	no	—
199	C₄×D₄	—	27	2	no	—
200	C₄×D₄	—	27	1	no	—
201	C₄×D₄	—	27	2	no	—
202	C₄×D₄	—	27	1	no	—
203	C₄×D₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
204	#117	—	27	1	no	—
205	#117	—	27	1	no	—
206	C₂×C₂²⋊C₄	—	27	2	no	—
207	C₂×C₂²⋊C₄	—	27	2	no	—
208	C₃³	#518	1	1	yes	characteristic, complemented, Sylow
209	C₂³×C₃	C₂²×C₃⋊D₃	1	26	yes	—
210	C₂²×D₃	—	9	13	no	—
211	C₂²×D₃	—	9	26	no	—
212	C₂²×D₃	—	9	104	no	—
213	C₂²×D₃	—	36	26	no	—
214	C₂²×D₃	—	36	26	no	—
215	C₃×D₄	C₄×C₃⋊D₃	1	52	yes	complemented
216	C₂×C₃×C₄	—	4	26	no	—
217	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	26	yes	—
218	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
219	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
220	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
221	#67	—	9	104	no	—
222	C₂×Dic₃	—	9	13	no	—
223	C₂×Dic₃	—	9	13	no	—
224	C₂×Dic₃	—	9	13	no	—
225	C₂×Dic₃	—	9	26	no	—
226	C₂×Dic₃	—	36	26	no	—
227	D₁₂	—	9	52	no	—
228	C₄×D₃	—	9	52	no	—
229	C₄×D₃	—	36	26	no	—
230	C₄×D₃	—	36	26	no	—
231	C₂×C₃²	—	2	52	no	—
232	C₂×C₃²	C₂²×C₄×D₃	1	13	yes	—
233	C₂×C₃²	#1004	1	13	yes	—
234	C₂×C₃²	#1009	1	13	yes	—
235	C₃⋊D₃	—	6	52	no	—
236	C₃⋊D₃	—	6	26	no	—
237	C₂⁴	—	27	2	no	—
238	C₂×D₄	—	27	2	no	—
239	C₂×D₄	—	27	8	no	—
240	C₂×D₄	—	27	1	no	—
241	C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
242	C₂²×C₄	—	27	1	no	—
243	C₂²×C₄	—	27	2	no	—
244	C₂²×C₄	—	27	2	no	—
245	C₂²×C₄	—	27	2	no	—
246	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
247	C₄⋊C₄	—	27	1	no	—
248	C₄⋊C₄	—	27	1	no	—
249	C₄⋊C₄	—	27	1	no	—
250	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
251	C₂²⋊C₄	—	27	2	no	—
252	C₂²⋊C₄	—	27	2	no	—
253	C₂²⋊C₄	—	27	1	no	—
254	C₂²⋊C₄	—	27	1	no	—
255	C₂²⋊C₄	—	27	2	no	—
256	C₂²⋊C₄	—	27	2	no	—
257	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
258	C₄²	—	27	2	no	—
259	C₄²	—	27	1	no	—
260	C₄²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
261	C₂²×C₃	—	2	26	no	—
262	C₂²×C₃	—	2	26	no	—
263	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	52	yes	—
264	C₂²×C₃	C₂³×C₃⋊D₃	1	13	yes	—
265	C₂×D₃	—	9	26	no	—
266	C₂×D₃	—	9	52	no	—
267	C₂×D₃	—	18	26	no	—
268	C₂×D₃	—	18	13	no	—
269	C₂×D₃	—	18	26	no	—
270	C₂×D₃	—	18	13	no	—
271	C₂×D₃	—	36	104	no	—
272	C₃×C₄	—	2	26	no	—
273	C₃×C₄	—	2	13	no	—
274	C₃×C₄	—	2	13	no	—
275	C₃×C₄	C₂×C₄×C₃⋊D₃	1	26	yes	—
276	Dic₃	—	9	26	no	—
277	Dic₃	—	18	13	no	—
278	Dic₃	—	18	26	no	—
279	Dic₃	—	18	13	no	—
280	C₃²	#5545	1	13	yes	complemented
281	C₂³	—	27	1	no	—
282	C₂³	—	27	2	no	—
283	C₂³	—	27	8	no	—
284	C₂³	—	108	2	no	—
285	C₂³	—	108	2	no	—
286	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
287	D₄	—	27	8	no	—
288	D₄	—	27	4	no	—
289	D₄	C₄×C₃⋊(C₃⋊D₃)	1	4	yes	complemented
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	27	1	no	—
292	C₂×C₄	—	27	4	no	—
293	C₂×C₄	—	27	1	no	—
294	C₂×C₄	—	27	2	no	—
295	C₂×C₄	—	27	1	no	—
296	C₂×C₄	—	108	2	no	—
297	C₂×C₄	—	108	2	no	—
298	C₂×C₄	—	108	2	no	—
299	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
300	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
301	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
302	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
303	C₂×C₃	—	2	52	no	—
304	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	13	yes	—
305	C₂×C₃	#64361	1	13	yes	—
306	C₂×C₃	#64366	1	13	yes	—
307	D₃	—	18	26	no	—
308	D₃	—	18	52	no	—
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	27	2	no	—
312	C₂²	—	27	4	no	—
313	C₂²	—	54	2	no	—
314	C₂²	—	54	1	no	—
315	C₂²	—	54	2	no	—
316	C₂²	—	54	1	no	—
317	C₂²	—	108	8	no	—
318	C₂²	C₂×C₄×C₃⋊(C₃⋊D₃)	1	4	yes	—
319	C₂²	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
320	C₄	—	2	1	no	—
321	C₄	—	2	2	no	—
322	C₄	—	2	1	no	—
323	C₄	—	27	2	no	—
324	C₄	—	54	1	no	—
325	C₄	—	54	2	no	—
326	C₄	—	54	1	no	—
327	C₄	C₂×C₄×C₃⋊(C₃⋊D₃)	1	2	yes	—
328	C₃	#10596016	1	13	yes	complemented
329	C₂	—	2	4	no	—
330	C₂	—	54	2	no	—
331	C₂	—	54	4	no	—
332	C₂	C₂²×C₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
333	C₂	#11724679	1	1	yes	characteristic
334	C₂	#11724684	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×C₃⋊(C₃⋊D₃)
commutator	C₂×C₃³	C₂³×C₄
Fitting	C₃³×C₄×D₄	C₂
socle, cosocle	C₂²×C₃³	C₂⁴
prime radical	C₂×D₄×C₃⋊(C₃⋊D₃)	C₂
hypercenter	C₄×D₄	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#518
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₃³×C₄×D₄	C₂	semidirect
3. D₄×C₃⋊(C₃⋊Dic₃)	C₂	semidirect
4. C₄×#6312	C₂	semidirect
5. C₂×#88859	C₂	semidirect
6. #11723934	C₂	semidirect
7. #11723933	C₂	semidirect
8. #11723922	C₂	semidirect
9. C₂²⋊C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
10. C₄×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	semidirect
11. #11723913	C₂	semidirect
15. C₂²×C₃³×C₄	C₂²	semidirect
17. C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
18. D₄×C₃⋊(C₃⋊D₃)	C₄	semidirect
21. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
22. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
23. C₃³×C₄⋊C₄	C₂²	semidirect
24. C₃³×C₂²⋊C₄	C₂²	semidirect
25. C₃³×C₄²	C₂²	semidirect
26. #88864	C₂²	semidirect
30. #88859	C₂²	semidirect
31. #88859	C₂²	semidirect
32. C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	semidirect
33. #88857	C₂²	semidirect
34. #88857	C₂²	semidirect
35. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
36. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
38. C₃²×C₄×D₄	D₃	semidirect
51. C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	semidirect
54. C₃³×D₄	C₂×C₄	semidirect
60. #6312	C₂×C₄	semidirect
66. C₄⋊(C₃⋊(C₃⋊D₃))	C₂×C₄	semidirect
69. C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	semidirect
73. C₂²×C₃²×C₄	C₂×D₃	semidirect
81. C₃²×C₄⋊C₄	C₂×D₃	semidirect
82. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
83. C₃²×C₄²	C₂×D₃	semidirect
115. C₃×C₄×D₄	C₃⋊D₃	semidirect
131. C₃²×D₄	C₄×D₃	semidirect
156. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
164. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
165. C₃×C₂²⋊C₄	C₂×C₃⋊D₃	semidirect
166. C₃×C₄²	C₂×C₃⋊D₃	semidirect
203. C₄×D₄	C₃⋊(C₃⋊D₃)	semidirect
208. C₃³	#518	semidirect
215. C₃×D₄	C₄×C₃⋊D₃	semidirect
246. C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
250. C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
257. C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
260. C₄²	C₂×C₃⋊(C₃⋊D₃)	semidirect
280. C₃²	#5545	semidirect
289. D₄	C₄×C₃⋊(C₃⋊D₃)	semidirect
328. C₃	#10596016	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₃⋊(C₃⋊D₃)	2
C₃³×C₄×D₄	2
D₄×C₃⋊(C₃⋊Dic₃)	2
C₄×#6312	2
C₂×#88859	2
#11723934	2
#11723933	2
#11723922	2
C₂²⋊C₄×C₃⋊(C₃⋊D₃)	2
C₄×C₄⋊(C₃⋊(C₃⋊D₃))	2
#11723913	2
#10596016	3