Subgroups — #137×C₃⋊(C₃⋊D₃) #13179901

Order 1728.

3612 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	#11723992	C₂	1	1	yes	maximal, characteristic, complemented
5	#11723983	C₂	1	1	yes	maximal, characteristic, complemented
6	#11723959	C₂	1	2	yes	maximal, complemented
7	Q₁₆×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
8	#11723956	C₂	1	2	yes	maximal, complemented
9	SD₁₆×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
10	#11723950	C₂	1	1	yes	maximal, characteristic, complemented
11	M₁₆×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃⋊D₃×#137	—	3	13	no	maximal
13	C₃³×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
15	#89080	C₂²	1	1	yes	characteristic
16	Q₈×C₃⋊(C₃⋊D₃)	—	2	1	no	—
17	Q₈×C₃⋊(C₃⋊D₃)	—	2	1	no	—
18	Q₈×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	—
19	Q₈×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
20	Q₈×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
21	#89078	—	2	1	no	—
22	#89078	C₂²	1	1	yes	characteristic
23	D₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
24	D₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
25	#89076	—	2	1	no	—
26	#89076	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
28	C₂×C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
29	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
30	C₂×#6308	—	2	1	no	—
31	C₂×#6308	C₂²	1	1	yes	characteristic, complemented
32	C₃³×Q₁₆	C₂²	1	2	yes	complemented
33	C₃³×SD₁₆	C₂²	1	2	yes	complemented
34	C₃³×M₁₆	C₂²	1	1	yes	characteristic, complemented
35	#88863	C₂²	1	2	yes	complemented
36	#88863	C₂²	1	2	yes	complemented
37	#88862	C₂²	1	2	yes	complemented
38	#88861	C₂²	1	2	yes	complemented
39	#88855	C₂²	1	1	yes	characteristic, complemented
40	#88853	C₂²	1	2	yes	complemented
41	#88851	C₂²	1	2	yes	complemented
42	#88850	C₂²	1	2	yes	complemented
43	C₈×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	—
44	#41×C₃⋊D₃	—	3	13	no	—
45	C₂×Q₈×C₃⋊D₃	—	3	13	no	—
46	C₃²×#137	D₃	1	13	yes	complemented
47	#64160	—	3	13	no	—
48	#64151	—	3	13	no	—
49	#64127	—	3	26	no	—
50	Q₁₆×C₃⋊D₃	—	3	26	no	—
51	#64124	—	3	26	no	—
52	SD₁₆×C₃⋊D₃	—	3	26	no	—
53	#64118	—	3	13	no	—
54	M₁₆×C₃⋊D₃	—	3	13	no	—
55	C₂²×C₃⋊(C₃⋊D₃)	—	2	1	no	—
56	C₂²×C₃⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
57	C₃³×Q₈	—	2	1	no	—
58	C₃³×Q₈	C₂³	1	2	yes	—
59	C₃³×Q₈	C₂³	1	1	yes	characteristic
60	C₃³×D₄	—	2	1	no	—
61	C₃³×D₄	C₂³	1	1	yes	characteristic
62	C₂×C₃³×C₄	—	2	1	no	—
63	C₂×C₃³×C₄	—	2	1	no	—
64	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
65	#6312	—	2	1	no	—
66	#6312	—	2	1	no	—
67	#6312	—	2	1	no	—
68	C₂×C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
69	C₂×C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
70	C₂×C₃⋊(C₃⋊Dic₃)	D₄	1	1	yes	characteristic
71	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	1	no	—
72	C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	1	1	yes	characteristic
73	C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
74	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
75	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
76	C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
77	C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
78	C₄×C₃⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
79	C₄×C₃⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
80	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
81	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
82	#6308	—	2	1	no	—
83	#6308	—	2	2	no	—
84	#6308	—	2	2	no	—
85	#6308	—	2	1	no	—
86	#6308	C₂³	1	2	yes	—
87	#6308	C₂³	1	1	yes	characteristic
88	C₃³×C₈	C₂³	1	2	yes	—
89	C₃⋊(C₃⋊(C₃⋊C₈))	C₂³	1	2	yes	—
90	D₃×#137	—	9	13	no	—
91	C₃²×#41	C₂×D₃	1	13	yes	—
92	C₂×C₃²×Q₈	C₂×D₃	1	13	yes	complemented
93	#3832	—	3	13	no	—
94	Q₈×C₃⋊D₃	—	3	26	no	—
95	Q₈×C₃⋊D₃	—	3	26	no	—
96	Q₈×C₃⋊D₃	—	3	13	no	—
97	Q₈×C₃⋊D₃	—	6	13	no	—
98	Q₈×C₃⋊D₃	—	6	13	no	—
99	#3830	—	3	13	no	—
100	#3830	—	6	13	no	—
101	D₄×C₃⋊D₃	—	3	13	no	—
102	D₄×C₃⋊D₃	—	6	13	no	—
103	#3828	—	3	13	no	—
104	#3828	—	6	13	no	—
105	C₂×C₄×C₃⋊D₃	—	3	13	no	—
106	C₂×C₄×C₃⋊D₃	—	6	13	no	—
107	C₂×C₄×C₃⋊D₃	—	6	13	no	—
108	C₂×#634	—	3	13	no	—
109	C₂×#634	—	6	13	no	—
110	C₃²×Q₁₆	C₂×D₃	1	26	yes	complemented
111	C₃²×SD₁₆	C₂×D₃	1	26	yes	complemented
112	C₃²×M₁₆	C₂×D₃	1	13	yes	complemented
113	#3756	—	3	26	no	—
114	#3756	—	3	26	no	—
115	#3755	—	3	26	no	—
116	#3754	—	3	26	no	—
117	#3748	—	3	13	no	—
118	#3746	—	3	26	no	—
119	#3744	—	3	26	no	—
120	#3743	—	3	26	no	—
121	C₈×C₃⋊D₃	—	3	26	no	—
122	C₂²×C₃³	—	2	1	no	—
123	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
125	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
126	C₂×C₃⋊(C₃⋊D₃)	—	4	2	no	—
127	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	1	yes	characteristic
129	C₃³×C₄	—	2	2	no	—
130	C₃³×C₄	—	2	1	no	—
131	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
132	C₃³×C₄	C₂⁴	1	1	yes	characteristic
133	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
134	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
135	C₃⋊(C₃⋊Dic₃)	C₂×D₄	1	1	yes	characteristic
136	C₃⋊(C₃⋊Dic₃)	C₂×D₄	1	1	yes	characteristic
137	D₃×#41	—	9	13	no	—
138	C₂×D₃×Q₈	—	9	13	no	—
139	C₃×#137	C₃⋊D₃	1	13	yes	complemented
140	#951	—	9	13	no	—
141	#942	—	9	13	no	—
142	#918	—	9	26	no	—
143	D₃×Q₁₆	—	9	26	no	—
144	#915	—	9	26	no	—
145	D₃×SD₁₆	—	9	26	no	—
146	#909	—	9	13	no	—
147	D₃×M₁₆	—	9	13	no	—
148	C₂²×C₃⋊D₃	—	3	13	no	—
149	C₂²×C₃⋊D₃	—	6	13	no	—
150	C₃²×Q₈	—	2	13	no	—
151	C₃²×Q₈	C₂²×D₃	1	26	yes	—
152	C₃²×Q₈	C₂²×D₃	1	13	yes	—
153	C₃²×D₄	—	2	13	no	—
154	C₃²×D₄	C₂²×D₃	1	13	yes	—
155	C₂×C₃²×C₄	—	2	13	no	—
156	C₂×C₃²×C₄	—	2	13	no	—
157	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
158	#638	—	6	13	no	—
159	#638	—	6	13	no	—
160	#638	—	6	13	no	—
161	C₂×C₃⋊Dic₃	—	3	13	no	—
162	C₂×C₃⋊Dic₃	—	6	13	no	—
163	C₂×C₃⋊Dic₃	—	6	13	no	—
164	C₄⋊(C₃⋊D₃)	—	3	13	no	—
165	C₄⋊(C₃⋊D₃)	—	6	13	no	—
166	C₄×C₃⋊D₃	—	3	13	no	—
167	C₄×C₃⋊D₃	—	3	13	no	—
168	C₄×C₃⋊D₃	—	3	13	no	—
169	C₄×C₃⋊D₃	—	3	13	no	—
170	C₄×C₃⋊D₃	—	6	13	no	—
171	C₄×C₃⋊D₃	—	6	13	no	—
172	C₄×C₃⋊D₃	—	6	26	no	—
173	C₄×C₃⋊D₃	—	6	26	no	—
174	C₄×C₃⋊D₃	—	6	13	no	—
175	#634	—	3	26	no	—
176	#634	—	3	13	no	—
177	#634	—	6	26	no	—
178	#634	—	6	26	no	—
179	#634	—	6	13	no	—
180	#634	—	6	13	no	—
181	C₃²×C₈	C₂²×D₃	1	26	yes	—
182	C₃⋊(C₃⋊C₈)	—	3	26	no	—
183	C₂×#137	—	27	1	no	Sylow
184	C₂×C₃³	—	2	1	no	—
185	C₂×C₃³	—	4	1	no	—
186	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
187	C₃⋊(C₃⋊D₃)	—	2	1	no	—
188	C₃⋊(C₃⋊D₃)	—	4	1	no	—
189	C₃⋊(C₃⋊D₃)	#137	1	2	yes	direct product factor
190	C₃×#41	C₂×C₃⋊D₃	1	13	yes	—
191	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	13	yes	complemented
192	#239	—	9	13	no	—
193	D₃×Q₈	—	9	26	no	—
194	D₃×Q₈	—	9	26	no	—
195	D₃×Q₈	—	9	13	no	—
196	D₃×Q₈	—	18	13	no	—
197	D₃×Q₈	—	18	13	no	—
198	#237	—	9	13	no	—
199	#237	—	18	13	no	—
200	D₃×D₄	—	9	13	no	—
201	D₃×D₄	—	18	13	no	—
202	#235	—	9	13	no	—
203	#235	—	18	13	no	—
204	C₂×C₄×D₃	—	9	13	no	—
205	C₂×C₄×D₃	—	18	13	no	—
206	C₂×C₄×D₃	—	18	13	no	—
207	C₂×Dic₆	—	9	13	no	—
208	C₂×Dic₆	—	18	13	no	—
209	C₃×Q₁₆	C₂×C₃⋊D₃	1	26	yes	complemented
210	C₃×SD₁₆	C₂×C₃⋊D₃	1	26	yes	complemented
211	C₃×M₁₆	C₂×C₃⋊D₃	1	13	yes	complemented
212	#216	—	9	26	no	—
213	#216	—	9	26	no	—
214	#215	—	9	26	no	—
215	#214	—	9	26	no	—
216	#208	—	9	13	no	—
217	Dic₁₂	—	9	26	no	—
218	#204	—	9	26	no	—
219	ΓL(1,𝔽₂₅)	—	9	26	no	—
220	D₃×C₈	—	9	26	no	—
221	C₂²×C₃²	—	2	13	no	—
222	C₂²×C₃²	D₃×D₄	1	13	yes	—
223	C₂×C₃⋊D₃	—	3	13	no	—
224	C₂×C₃⋊D₃	—	3	13	no	—
225	C₂×C₃⋊D₃	—	6	26	no	—
226	C₂×C₃⋊D₃	—	6	13	no	—
227	C₂×C₃⋊D₃	—	12	26	no	—
228	C₃²×C₄	—	2	26	no	—
229	C₃²×C₄	—	2	13	no	—
230	C₃²×C₄	D₃×D₄	1	13	yes	—
231	C₃²×C₄	C₂³×D₃	1	13	yes	—
232	C₃⋊Dic₃	—	3	13	no	—
233	C₃⋊Dic₃	—	3	13	no	—
234	C₃⋊Dic₃	—	6	26	no	—
235	C₃⋊Dic₃	—	6	13	no	—
236	C₂×#41	—	27	1	no	—
237	C₂²×Q₈	—	27	1	no	—
238	#137	—	27	1	no	—
239	#137	—	27	1	no	—
240	#137	—	27	2	no	—
241	#137	—	27	2	no	—
242	#137	—	27	1	no	—
243	#137	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
244	C₂×Q₁₆	—	27	2	no	—
245	C₂×SD₁₆	—	27	2	no	—
246	C₂×M₁₆	—	27	1	no	—
247	C₃³	C₂×#137	1	1	yes	characteristic, complemented, Sylow
248	C₂²×D₃	—	9	13	no	—
249	C₂²×D₃	—	18	13	no	—
250	C₃×Q₈	—	2	13	no	—
251	C₃×Q₈	C₂²×C₃⋊D₃	1	26	yes	—
252	C₃×Q₈	C₂²×C₃⋊D₃	1	13	yes	—
253	C₃×D₄	—	2	13	no	—
254	C₃×D₄	C₂²×C₃⋊D₃	1	13	yes	—
255	C₂×C₃×C₄	—	2	13	no	—
256	C₂×C₃×C₄	—	2	13	no	—
257	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
258	#67	—	18	13	no	—
259	#67	—	18	13	no	—
260	#67	—	18	13	no	—
261	C₂×Dic₃	—	9	13	no	—
262	C₂×Dic₃	—	18	13	no	—
263	C₂×Dic₃	—	18	13	no	—
264	D₁₂	—	9	13	no	—
265	D₁₂	—	18	13	no	—
266	C₄×D₃	—	9	13	no	—
267	C₄×D₃	—	9	13	no	—
268	C₄×D₃	—	9	13	no	—
269	C₄×D₃	—	9	13	no	—
270	C₄×D₃	—	18	13	no	—
271	C₄×D₃	—	18	13	no	—
272	C₄×D₃	—	18	26	no	—
273	C₄×D₃	—	18	26	no	—
274	C₄×D₃	—	18	13	no	—
275	Dic₆	—	9	26	no	—
276	Dic₆	—	9	13	no	—
277	Dic₆	—	18	26	no	—
278	Dic₆	—	18	26	no	—
279	Dic₆	—	18	13	no	—
280	Dic₆	—	18	13	no	—
281	C₃×C₈	C₂²×C₃⋊D₃	1	26	yes	—
282	C₃⋊C₈	—	9	26	no	—
283	C₂×C₃²	—	2	13	no	—
284	C₂×C₃²	—	4	13	no	—
285	C₂×C₃²	C₂×D₃×D₄	1	13	yes	—
286	C₃⋊D₃	—	3	26	no	—
287	C₃⋊D₃	—	6	13	no	—
288	C₃⋊D₃	—	12	13	no	—
289	#41	—	27	1	no	—
290	#41	—	27	1	no	—
291	#41	—	27	1	no	—
292	#41	—	54	1	no	—
293	#41	—	54	1	no	—
294	#41	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
295	C₂×Q₈	—	27	2	no	—
296	C₂×Q₈	—	27	1	no	—
297	C₂×Q₈	—	27	2	no	—
298	C₂×Q₈	—	27	1	no	—
299	C₂×Q₈	—	54	1	no	—
300	C₂×Q₈	—	54	1	no	—
301	C₂×Q₈	—	54	1	no	—
302	C₂×Q₈	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
303	C₂×D₄	—	27	1	no	—
304	C₂×D₄	—	54	1	no	—
305	C₂²×C₄	—	27	1	no	—
306	C₂²×C₄	—	54	1	no	—
307	C₂²×C₄	—	54	1	no	—
308	Q₁₆	—	27	2	no	—
309	Q₁₆	—	27	2	no	—
310	Q₁₆	—	27	2	no	—
311	Q₁₆	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
312	SD₁₆	—	27	2	no	—
313	SD₁₆	—	27	2	no	—
314	SD₁₆	—	27	2	no	—
315	SD₁₆	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
316	M₁₆	—	27	1	no	—
317	M₁₆	—	27	2	no	—
318	M₁₆	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
319	C₂×C₈	—	27	2	no	—
320	C₂²×C₃	—	2	13	no	—
321	C₂²×C₃	D₄×C₃⋊D₃	1	13	yes	—
322	C₂×D₃	—	9	13	no	—
323	C₂×D₃	—	9	13	no	—
324	C₂×D₃	—	18	26	no	—
325	C₂×D₃	—	18	13	no	—
326	C₂×D₃	—	36	26	no	—
327	C₃×C₄	—	2	26	no	—
328	C₃×C₄	—	2	13	no	—
329	C₃×C₄	D₄×C₃⋊D₃	1	13	yes	—
330	C₃×C₄	C₂³×C₃⋊D₃	1	13	yes	—
331	Dic₃	—	9	13	no	—
332	Dic₃	—	9	13	no	—
333	Dic₃	—	18	26	no	—
334	Dic₃	—	18	13	no	—
335	C₃²	D₃×#137	1	13	yes	complemented
336	C₂³	—	27	1	no	—
337	C₂³	—	54	1	no	—
338	Q₈	—	2	1	no	—
339	Q₈	—	27	2	no	—
340	Q₈	—	27	1	no	—
341	Q₈	—	54	2	no	—
342	Q₈	—	54	2	no	—
343	Q₈	—	54	1	no	—
344	Q₈	—	54	1	no	—
345	Q₈	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
346	Q₈	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
347	D₄	—	2	1	no	—
348	D₄	—	27	1	no	—
349	D₄	—	54	1	no	—
350	D₄	—	54	1	no	—
351	D₄	—	54	1	no	—
352	D₄	—	54	1	no	—
353	D₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	27	1	no	—
357	C₂×C₄	—	27	1	no	—
358	C₂×C₄	—	27	1	no	—
359	C₂×C₄	—	27	1	no	—
360	C₂×C₄	—	27	1	no	—
361	C₂×C₄	—	54	1	no	—
362	C₂×C₄	—	54	1	no	—
363	C₂×C₄	—	54	2	no	—
364	C₂×C₄	—	54	2	no	—
365	C₂×C₄	—	54	1	no	—
366	C₂×C₄	—	54	1	no	—
367	C₂×C₄	—	54	1	no	—
368	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
369	C₈	—	27	2	no	—
370	C₈	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
371	C₂×C₃	—	2	13	no	—
372	C₂×C₃	—	4	13	no	—
373	C₂×C₃	C₂×D₄×C₃⋊D₃	1	13	yes	—
374	D₃	—	9	26	no	—
375	D₃	—	18	13	no	—
376	D₃	—	36	13	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	27	1	no	—
379	C₂²	—	27	1	no	—
380	C₂²	—	54	2	no	—
381	C₂²	—	54	1	no	—
382	C₂²	—	108	2	no	—
383	C₂²	D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	27	1	no	—
387	C₄	—	27	1	no	—
388	C₄	—	54	1	no	—
389	C₄	—	54	2	no	—
390	C₄	D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
391	C₄	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
392	C₃	C₃⋊D₃×#137	1	13	yes	complemented
393	C₂	—	2	1	no	—
394	C₂	—	4	1	no	—
395	C₂	—	27	2	no	—
396	C₂	—	54	1	no	—
397	C₂	—	108	1	no	—
398	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)
commutator, cosocle	C₃³×C₄	C₂⁴
Frattini	C₄	C₂³×C₃⋊(C₃⋊D₃)
Fitting	C₃³×#137	C₂
socle	C₂×C₃³	C₂²×D₄
prime radical	#41×C₃⋊(C₃⋊D₃)	C₂
hypercenter	#137	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	C₂×#137
LCS	G ▷ C₃³×C₄ ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #137

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×C₃⋊(C₃⋊D₃)	C₂	semidirect
3. C₃³×#137	C₂	semidirect
4. #11723992	C₂	semidirect
5. #11723983	C₂	semidirect
6. #11723959	C₂	semidirect
7. Q₁₆×C₃⋊(C₃⋊D₃)	C₂	semidirect
8. #11723956	C₂	semidirect
9. SD₁₆×C₃⋊(C₃⋊D₃)	C₂	semidirect
10. #11723950	C₂	semidirect
11. M₁₆×C₃⋊(C₃⋊D₃)	C₂	semidirect
14. C₂×C₃³×Q₈	C₂²	semidirect
20. Q₈×C₃⋊(C₃⋊D₃)	C₂²	semidirect
31. C₂×#6308	C₂²	semidirect
32. C₃³×Q₁₆	C₂²	semidirect
33. C₃³×SD₁₆	C₂²	semidirect
34. C₃³×M₁₆	C₂²	semidirect
35. #88863	C₂²	semidirect
36. #88863	C₂²	semidirect
37. #88862	C₂²	semidirect
38. #88861	C₂²	semidirect
39. #88855	C₂²	semidirect
40. #88853	C₂²	semidirect
41. #88851	C₂²	semidirect
42. #88850	C₂²	semidirect
46. C₃²×#137	D₃	semidirect
92. C₂×C₃²×Q₈	C₂×D₃	semidirect
110. C₃²×Q₁₆	C₂×D₃	semidirect
111. C₃²×SD₁₆	C₂×D₃	semidirect
112. C₃²×M₁₆	C₂×D₃	semidirect
139. C₃×#137	C₃⋊D₃	semidirect
189. C₃⋊(C₃⋊D₃)	#137	direct (N × H)
191. C₂×C₃×Q₈	C₂×C₃⋊D₃	semidirect
209. C₃×Q₁₆	C₂×C₃⋊D₃	semidirect
210. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
211. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
243. #137	C₃⋊(C₃⋊D₃)	direct (N × H)
247. C₃³	C₂×#137	semidirect
302. C₂×Q₈	C₂×C₃⋊(C₃⋊D₃)	semidirect
311. Q₁₆	C₂×C₃⋊(C₃⋊D₃)	semidirect
315. SD₁₆	C₂×C₃⋊(C₃⋊D₃)	semidirect
318. M₁₆	C₂×C₃⋊(C₃⋊D₃)	semidirect
335. C₃²	D₃×#137	semidirect
392. C₃	C₃⋊D₃×#137	semidirect

Maximal subgroups

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

subgroup	index
#41×C₃⋊(C₃⋊D₃)	2
C₂×Q₈×C₃⋊(C₃⋊D₃)	2
C₃³×#137	2
#11723992	2
#11723983	2
#11723959	2
Q₁₆×C₃⋊(C₃⋊D₃)	2
#11723956	2
SD₁₆×C₃⋊(C₃⋊D₃)	2
#11723950	2
M₁₆×C₃⋊(C₃⋊D₃)	2
C₃⋊D₃×#137	3

Subgroups — #137×C3⋊(C3⋊D3) #13179901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #137×C₃⋊(C₃⋊D₃) #13179901