Subgroups — #13179771

Order 1728.

2744 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#11723987	C₂	1	1	yes	maximal, characteristic, complemented
3	#11723985	C₂	1	1	yes	maximal, characteristic, complemented
4	#11723970	C₂	1	1	yes	maximal, characteristic
5	#11723965	C₂	1	1	yes	maximal, characteristic, complemented
6	#11723939	C₂	1	1	yes	maximal, characteristic, complemented
7	#11723939	C₂	1	1	yes	maximal, characteristic, complemented
8	#11723937	C₂	1	1	yes	maximal, characteristic, complemented
9	#11723931	C₂	1	1	yes	maximal, characteristic, complemented
10	#11723930	C₂	1	1	yes	maximal, characteristic, complemented
11	#11723929	C₂	1	1	yes	maximal, characteristic, complemented
12	#11723926	C₂	1	1	yes	maximal, characteristic
13	#11723924	C₂	1	1	yes	maximal, characteristic
14	#11723920	C₂	1	1	yes	maximal, characteristic, complemented
15	#11723920	C₂	1	1	yes	maximal, characteristic, complemented
16	#10596117	—	3	13	no	maximal
17	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
19	C₂×#6312	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
21	C₂×#6308	C₂²	1	1	yes	characteristic
22	C₂×#6308	C₂²	1	1	yes	characteristic
23	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	#88864	C₂²	1	1	yes	characteristic
29	#88864	C₂²	1	1	yes	characteristic
30	#88864	C₂²	1	1	yes	characteristic
31	#88859	C₂²	1	1	yes	characteristic
32	#88859	C₂²	1	1	yes	characteristic
33	#88859	C₂²	1	1	yes	characteristic
34	#88859	C₂²	1	1	yes	characteristic
35	#88859	C₂²	1	1	yes	characteristic
36	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic
37	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic
38	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic
39	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic
40	#88857	C₂²	1	1	yes	characteristic
41	#88857	C₂²	1	1	yes	characteristic
42	#88857	C₂²	1	1	yes	characteristic
43	#88857	C₂²	1	1	yes	characteristic
44	#88857	C₂²	1	1	yes	characteristic
45	#88857	C₂²	1	1	yes	characteristic
46	#88857	C₂²	1	1	yes	characteristic
47	#88857	C₂²	1	1	yes	characteristic
48	#88857	C₂²	1	1	yes	characteristic
49	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
50	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
51	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
52	C₃²×C₂²⋊Q₈	D₃	1	13	yes	complemented
53	#64155	—	3	13	no	—
54	#64153	—	3	13	no	—
55	#64138	—	3	13	no	—
56	#64133	—	3	13	no	—
57	#64107	—	3	13	no	—
58	#64107	—	3	13	no	—
59	#64105	—	3	13	no	—
60	#64099	—	3	13	no	—
61	#64098	—	3	13	no	—
62	#64097	—	3	13	no	—
63	#64094	—	3	13	no	—
64	#64092	—	3	13	no	—
65	#64088	—	3	13	no	—
66	#64088	—	3	13	no	—
67	C₂³×C₃³	C₂³	1	1	yes	characteristic
68	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
69	C₃³×Q₈	—	4	1	no	—
70	C₂×C₃³×C₄	—	4	1	no	—
71	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
72	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
73	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
74	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
75	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
76	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
77	#6312	—	4	1	no	—
78	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
79	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
80	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
81	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
82	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
83	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
84	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
85	C₄×C₃⋊(C₃⋊D₃)	—	4	1	no	—
86	#6308	—	4	1	no	—
87	#6308	—	4	1	no	—
88	#5646	—	9	13	no	—
89	C₂×C₃²×Q₈	C₂×D₃	1	13	yes	—
90	C₂²×C₃²×C₄	C₂×D₃	1	13	yes	—
91	C₂×#638	—	3	13	no	—
92	C₂×C₄×C₃⋊D₃	—	3	13	no	—
93	C₂×#634	—	3	13	no	—
94	C₂×#634	—	3	13	no	—
95	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	—
96	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	—
97	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	—
98	C₃²×C₂²⋊C₄	C₂×D₃	1	13	yes	—
99	C₃²×C₂²⋊C₄	C₂×D₃	1	13	yes	—
100	#3757	—	3	13	no	—
101	#3757	—	3	13	no	—
102	#3757	—	3	13	no	—
103	#3752	—	3	13	no	—
104	#3752	—	3	13	no	—
105	#3752	—	3	13	no	—
106	#3752	—	3	13	no	—
107	#3752	—	3	13	no	—
108	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
109	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
110	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
111	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
112	#3750	—	3	13	no	—
113	#3750	—	3	13	no	—
114	#3750	—	3	13	no	—
115	#3750	—	3	13	no	—
116	#3750	—	3	13	no	—
117	#3750	—	3	13	no	—
118	#3750	—	3	13	no	—
119	#3750	—	3	13	no	—
120	#3750	—	3	13	no	—
121	C₄×C₃⋊Dic₃	—	3	13	no	—
122	C₄×C₃⋊Dic₃	—	3	13	no	—
123	C₄×C₃⋊Dic₃	—	3	13	no	—
124	C₂²×C₃³	—	2	1	no	—
125	C₂²×C₃³	—	2	1	no	—
126	C₂²×C₃³	—	2	1	no	—
127	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
128	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
129	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
130	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
131	C₃³×C₄	—	2	1	no	—
132	C₃³×C₄	—	2	1	no	—
133	C₃³×C₄	—	2	1	no	—
134	C₃³×C₄	—	2	1	no	—
135	C₃³×C₄	—	2	1	no	—
136	C₃³×C₄	—	2	1	no	—
137	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
138	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
139	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
140	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
141	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
142	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
143	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
144	C₃×C₂²⋊Q₈	C₃⋊D₃	1	13	yes	complemented
145	#946	—	9	13	no	—
146	#944	—	9	13	no	—
147	#929	—	9	13	no	—
148	#924	—	9	13	no	—
149	#898	—	9	13	no	—
150	#898	—	9	13	no	—
151	#896	—	9	13	no	—
152	#890	—	9	13	no	—
153	#889	—	9	13	no	—
154	#888	—	9	13	no	—
155	#885	—	9	13	no	—
156	#883	—	9	13	no	—
157	#879	—	9	13	no	—
158	#879	—	9	13	no	—
159	C₂³×C₃²	C₂²×D₃	1	13	yes	—
160	C₂²×C₃⋊D₃	—	3	13	no	—
161	C₃²×Q₈	—	4	13	no	—
162	C₂×C₃²×C₄	—	4	13	no	—
163	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
164	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
165	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
166	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
167	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
168	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
169	#638	—	12	13	no	—
170	C₂×C₃⋊Dic₃	—	3	13	no	—
171	C₂×C₃⋊Dic₃	—	3	13	no	—
172	C₂×C₃⋊Dic₃	—	3	13	no	—
173	C₂×C₃⋊Dic₃	—	3	13	no	—
174	C₂×C₃⋊Dic₃	—	3	13	no	—
175	C₂×C₃⋊Dic₃	—	3	13	no	—
176	C₂×C₃⋊Dic₃	—	3	13	no	—
177	C₄×C₃⋊D₃	—	12	13	no	—
178	#634	—	12	13	no	—
179	#634	—	12	13	no	—
180	#563	—	27	1	no	Sylow
181	C₂×C₃³	—	4	1	no	—
182	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
185	C₃⋊(C₃⋊D₃)	—	4	1	no	—
186	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	13	yes	—
187	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
188	C₂×#67	—	9	13	no	—
189	C₂×C₄×D₃	—	9	13	no	—
190	C₂×Dic₆	—	9	13	no	—
191	C₂×Dic₆	—	9	13	no	—
192	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
193	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
194	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
195	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
196	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
197	#217	—	9	13	no	—
198	#217	—	9	13	no	—
199	#217	—	9	13	no	—
200	(C₂×D₃)⋊C₄	—	9	13	no	—
201	(C₂×D₃)⋊C₄	—	9	13	no	—
202	(C₂×D₃)⋊C₄	—	9	13	no	—
203	(C₂×D₃)⋊C₄	—	9	13	no	—
204	(C₂×D₃)⋊C₄	—	9	13	no	—
205	C₄⋊Dic₃	—	9	13	no	—
206	C₄⋊Dic₃	—	9	13	no	—
207	C₄⋊Dic₃	—	9	13	no	—
208	C₄⋊Dic₃	—	9	13	no	—
209	Dic₃⋊C₄	—	9	13	no	—
210	Dic₃⋊C₄	—	9	13	no	—
211	Dic₃⋊C₄	—	9	13	no	—
212	Dic₃⋊C₄	—	9	13	no	—
213	Dic₃⋊C₄	—	9	13	no	—
214	Dic₃⋊C₄	—	9	13	no	—
215	Dic₃⋊C₄	—	9	13	no	—
216	Dic₃⋊C₄	—	9	13	no	—
217	Dic₃⋊C₄	—	9	13	no	—
218	C₄×Dic₃	—	9	13	no	—
219	C₄×Dic₃	—	9	13	no	—
220	C₄×Dic₃	—	9	13	no	—
221	C₂²×C₃²	—	2	13	no	—
222	C₂²×C₃²	—	2	13	no	—
223	C₂²×C₃²	—	2	13	no	—
224	C₂²×C₃²	C₂³×D₃	1	13	yes	—
225	C₂×C₃⋊D₃	—	6	13	no	—
226	C₂×C₃⋊D₃	—	6	13	no	—
227	C₂×C₃⋊D₃	—	6	13	no	—
228	C₃²×C₄	—	2	13	no	—
229	C₃²×C₄	—	2	13	no	—
230	C₃²×C₄	—	2	13	no	—
231	C₃²×C₄	—	2	13	no	—
232	C₃²×C₄	—	2	13	no	—
233	C₃²×C₄	—	2	13	no	—
234	C₃⋊Dic₃	—	6	13	no	—
235	C₃⋊Dic₃	—	6	13	no	—
236	C₃⋊Dic₃	—	6	13	no	—
237	C₃⋊Dic₃	—	6	13	no	—
238	C₃⋊Dic₃	—	6	13	no	—
239	C₃⋊Dic₃	—	6	13	no	—
240	C₃⋊Dic₃	—	6	13	no	—
241	C₄⋊Q₈	—	27	1	no	—
242	C₄⋊Q₈	—	27	1	no	—
243	#126	—	27	1	no	—
244	#126	—	27	1	no	—
245	#126	—	27	1	no	—
246	#126	—	27	1	no	—
247	#125	—	27	1	no	—
248	#125	—	27	1	no	—
249	#124	—	27	1	no	—
250	#123	—	27	1	no	—
251	#123	—	27	1	no	—
252	C₂²⋊Q₈	—	27	1	no	—
253	C₂²⋊Q₈	—	27	1	no	—
254	C₂²⋊Q₈	—	27	1	no	—
255	C₂²⋊Q₈	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
256	C₃³	#563	1	1	yes	characteristic, complemented, Sylow
257	C₂³×C₃	C₂²×C₃⋊D₃	1	13	yes	—
258	C₂²×D₃	—	9	13	no	—
259	C₃×Q₈	—	4	13	no	—
260	C₂×C₃×C₄	—	4	13	no	—
261	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
262	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
263	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
264	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
265	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
266	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
267	#67	—	36	13	no	—
268	C₂×Dic₃	—	9	13	no	—
269	C₂×Dic₃	—	9	13	no	—
270	C₂×Dic₃	—	9	13	no	—
271	C₂×Dic₃	—	9	13	no	—
272	C₂×Dic₃	—	9	13	no	—
273	C₂×Dic₃	—	9	13	no	—
274	C₂×Dic₃	—	9	13	no	—
275	C₄×D₃	—	36	13	no	—
276	Dic₆	—	36	13	no	—
277	Dic₆	—	36	13	no	—
278	C₂×C₃²	—	4	13	no	—
279	C₂×C₃²	#1004	1	13	yes	—
280	C₂×C₃²	#1007	1	13	yes	—
281	C₂×C₃²	#1010	1	13	yes	—
282	C₃⋊D₃	—	12	13	no	—
283	C₂×Q₈	—	27	1	no	—
284	C₂×Q₈	—	27	1	no	—
285	C₂×Q₈	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
286	C₂×D₄	—	27	1	no	—
287	C₂²×C₄	—	27	1	no	—
288	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
289	C₄⋊C₄	—	27	1	no	—
290	C₄⋊C₄	—	27	1	no	—
291	C₄⋊C₄	—	27	1	no	—
292	C₄⋊C₄	—	27	1	no	—
293	C₄⋊C₄	—	27	1	no	—
294	C₄⋊C₄	—	27	1	no	—
295	C₄⋊C₄	—	27	1	no	—
296	C₄⋊C₄	—	27	1	no	—
297	C₄⋊C₄	—	27	1	no	—
298	C₄⋊C₄	—	27	1	no	—
299	C₄⋊C₄	—	27	1	no	—
300	C₄⋊C₄	—	27	1	no	—
301	C₄⋊C₄	—	27	1	no	—
302	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
303	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
304	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
305	C₂²⋊C₄	—	27	1	no	—
306	C₂²⋊C₄	—	27	1	no	—
307	C₂²⋊C₄	—	27	1	no	—
308	C₂²⋊C₄	—	27	1	no	—
309	C₂²⋊C₄	—	27	1	no	—
310	C₂²⋊C₄	—	27	1	no	—
311	C₂²⋊C₄	—	27	1	no	—
312	C₂²⋊C₄	—	27	1	no	—
313	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
314	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
315	C₄²	—	27	1	no	—
316	C₄²	—	27	1	no	—
317	C₄²	—	27	1	no	—
318	C₂²×C₃	—	2	13	no	—
319	C₂²×C₃	—	2	13	no	—
320	C₂²×C₃	—	2	13	no	—
321	C₂²×C₃	C₂³×C₃⋊D₃	1	13	yes	—
322	C₂×D₃	—	18	13	no	—
323	C₂×D₃	—	18	13	no	—
324	C₂×D₃	—	18	13	no	—
325	C₃×C₄	—	2	13	no	—
326	C₃×C₄	—	2	13	no	—
327	C₃×C₄	—	2	13	no	—
328	C₃×C₄	—	2	13	no	—
329	C₃×C₄	—	2	13	no	—
330	C₃×C₄	—	2	13	no	—
331	Dic₃	—	18	13	no	—
332	Dic₃	—	18	13	no	—
333	Dic₃	—	18	13	no	—
334	Dic₃	—	18	13	no	—
335	Dic₃	—	18	13	no	—
336	Dic₃	—	18	13	no	—
337	Dic₃	—	18	13	no	—
338	C₃²	#5646	1	13	yes	complemented
339	C₂³	—	27	1	no	—
340	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
341	Q₈	—	4	1	no	—
342	Q₈	—	108	1	no	—
343	Q₈	—	108	1	no	—
344	D₄	—	108	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	27	1	no	—
347	C₂×C₄	—	27	1	no	—
348	C₂×C₄	—	27	1	no	—
349	C₂×C₄	—	27	1	no	—
350	C₂×C₄	—	27	1	no	—
351	C₂×C₄	—	27	1	no	—
352	C₂×C₄	—	27	1	no	—
353	C₂×C₄	—	108	1	no	—
354	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
359	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
360	C₂×C₃	—	4	13	no	—
361	C₂×C₃	#64361	1	13	yes	—
362	C₂×C₃	#64364	1	13	yes	—
363	C₂×C₃	#64367	1	13	yes	—
364	D₃	—	36	13	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	54	1	no	—
369	C₂²	—	54	1	no	—
370	C₂²	—	54	1	no	—
371	C₂²	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	54	1	no	—
379	C₄	—	54	1	no	—
380	C₄	—	54	1	no	—
381	C₄	—	54	1	no	—
382	C₄	—	54	1	no	—
383	C₄	—	54	1	no	—
384	C₄	—	54	1	no	—
385	C₃	#10596117	1	13	yes	complemented
386	C₂	—	4	1	no	—
387	C₂	—	108	1	no	—
388	C₂	#11724679	1	1	yes	characteristic
389	C₂	#11724682	1	1	yes	characteristic
390	C₂	#11724685	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×C₃⋊(C₃⋊D₃)
commutator, socle, cosocle	C₂²×C₃³	C₂⁴
Fitting	C₃³×C₂²⋊Q₈	C₂
prime radical	C₂×#6312	C₂²
hypercenter	C₂²⋊Q₈	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#563
LCS	G ▷ C₂²×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₂²⋊Q₈	C₂	semidirect
2. #11723987	C₂	semidirect
3. #11723985	C₂	semidirect
5. #11723965	C₂	semidirect
6. #11723939	C₂	semidirect
7. #11723939	C₂	semidirect
8. #11723937	C₂	semidirect
9. #11723931	C₂	semidirect
10. #11723930	C₂	semidirect
11. #11723929	C₂	semidirect
14. #11723920	C₂	semidirect
15. #11723920	C₂	semidirect
52. C₃²×C₂²⋊Q₈	D₃	semidirect
144. C₃×C₂²⋊Q₈	C₃⋊D₃	semidirect
255. C₂²⋊Q₈	C₃⋊(C₃⋊D₃)	semidirect
256. C₃³	#563	semidirect
338. C₃²	#5646	semidirect
385. C₃	#10596117	semidirect

Maximal subgroups

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

subgroup	index
C₃³×C₂²⋊Q₈	2
#11723987	2
#11723985	2
#11723970	2
#11723965	2
#11723939	2
#11723937	2
#11723931	2
#11723930	2
#11723929	2
#11723926	2
#11723924	2
#11723920	2
#10596117	3