Subgroups — C₃×#10592874 #13163202

Order 1728.

1124 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64153	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3755	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64149	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×#3754	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3744	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#10592874	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃×#5175	—	3	4	no	maximal
10	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×#638	—	2	2	no	—
13	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
14	C₂×C₃×#634	C₂²	1	1	yes	characteristic
15	C₃³×SD₁₆	—	2	2	no	—
16	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
17	C₃×#3755	—	2	2	no	—
18	C₃×#3754	—	2	2	no	—
19	C₃×#3750	—	2	2	no	—
20	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
22	C₃×#3744	—	2	2	no	—
23	C₂×C₃²×SD₁₆	—	2	4	no	—
24	C₂×C₃²×SD₁₆	D₃	1	4	yes	complemented
25	C₂×C₃²×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
26	#64153	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#3755	C₂×C₃	1	1	yes	characteristic, complemented
28	#64149	C₂×C₃	1	1	yes	characteristic
29	C₂×#3754	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×#3744	C₂×C₃	1	1	yes	characteristic, complemented
31	C₃×#944	—	3	4	no	—
32	C₂×C₃×#215	—	3	4	no	—
33	C₃×#940	—	3	4	no	—
34	C₂×C₃×#214	—	3	4	no	—
35	C₂×C₃×#204	—	3	4	no	—
36	C₈×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
37	C₃×C₈×Dic₃	—	3	4	no	—
38	C₂³×C₃³	—	2	1	no	—
39	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
40	C₃³×Q₈	—	2	1	no	—
41	C₃³×Q₈	—	2	1	no	—
42	C₃³×D₄	—	2	1	no	—
43	C₃³×D₄	—	2	1	no	—
44	C₂×C₃³×C₄	—	2	1	no	—
45	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
46	C₃×#638	—	4	4	no	—
47	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
48	C₂×C₃×C₃⋊Dic₃	D₄	1	2	yes	—
49	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
50	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
51	C₃×#634	—	2	1	no	—
52	C₃×#634	—	2	1	no	—
53	C₃³×C₈	D₄	1	2	yes	complemented
54	C₃×C₃⋊(C₃⋊C₈)	D₄	1	2	yes	complemented
55	C₃×#492	—	9	1	no	—
56	#5175	—	3	4	no	—
57	C₂×C₃²×Q₈	—	2	4	no	—
58	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
59	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃²×D₄	—	2	4	no	—
61	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
62	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
63	C₂×#638	—	2	2	no	—
64	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
65	C₂×#634	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₃×#67	—	6	8	no	—
67	C₂×C₃×D₁₂	—	3	4	no	—
68	C₂×C₃×Dic₆	—	3	4	no	—
69	C₃²×SD₁₆	—	2	16	no	—
70	C₃²×SD₁₆	—	2	8	no	—
71	C₃²×SD₁₆	—	2	2	no	—
72	C₂×C₃²×C₈	—	2	4	no	—
73	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
74	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
75	#3755	—	2	2	no	—
76	#3754	—	2	2	no	—
77	#3750	—	2	2	no	—
78	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
80	#3744	—	2	2	no	—
81	C₃×#215	—	6	8	no	—
82	C₃×#214	—	6	8	no	—
83	C₃×Dic₃⋊C₄	—	6	8	no	—
84	C₃×C₄×Dic₃	—	3	4	no	—
85	C₂×C₃×C₃⋊C₈	—	3	4	no	—
86	C₃×#204	—	6	8	no	—
87	C₂²×C₃³	—	4	1	no	—
88	C₂²×C₃³	—	4	2	no	—
89	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₃⋊D₃	—	4	1	no	—
91	C₂×C₃×C₃⋊D₃	—	4	2	no	—
92	C₃³×C₄	—	4	1	no	—
93	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
94	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
95	C₃×C₃⋊Dic₃	—	4	1	no	—
96	C₃×C₃⋊Dic₃	SD₁₆	1	4	yes	complemented
97	C₂×C₃×SD₁₆	—	2	4	no	—
98	C₂×C₃×SD₁₆	—	9	1	no	—
99	C₂×C₃×SD₁₆	—	9	1	no	—
100	C₂×C₃×SD₁₆	—	9	1	no	—
101	C₂×C₃×SD₁₆	C₃×D₃	1	4	yes	complemented
102	C₂×C₃×SD₁₆	C₃⋊D₃	1	1	yes	characteristic, complemented
103	C₃×C₄⋊Q₈	—	9	1	no	—
104	C₃×#127	—	9	1	no	—
105	#944	—	3	4	no	—
106	C₂×#215	—	3	4	no	—
107	#940	—	3	4	no	—
108	C₂×#214	—	3	4	no	—
109	C₂×#204	—	3	4	no	—
110	C₃×C₄×C₈	—	9	1	no	—
111	C₈×Dic₃	—	3	4	no	—
112	C₂³×C₃²	—	2	1	no	—
113	C₂³×C₃²	—	2	4	no	—
114	C₂³×C₃²	—	4	4	no	—
115	C₂²×C₃⋊D₃	—	2	1	no	—
116	C₂²×C₃×D₃	—	6	4	no	—
117	C₃²×Q₈	—	2	8	no	—
118	C₃²×Q₈	—	2	4	no	—
119	C₃²×Q₈	—	2	1	no	—
120	C₃²×Q₈	—	2	1	no	—
121	C₃²×Q₈	—	2	4	no	—
122	C₃²×Q₈	—	4	4	no	—
123	C₃²×D₄	—	2	8	no	—
124	C₃²×D₄	—	2	4	no	—
125	C₃²×D₄	—	2	1	no	—
126	C₃²×D₄	—	2	1	no	—
127	C₃²×D₄	—	2	4	no	—
128	C₃²×D₄	—	4	4	no	—
129	C₂×C₃²×C₄	—	2	1	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	4	4	no	—
133	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
134	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
135	#638	—	4	4	no	—
136	C₂×C₃⋊Dic₃	—	2	1	no	—
137	C₂×C₃⋊Dic₃	C₃×D₄	1	2	yes	—
138	C₄⋊(C₃⋊D₃)	—	2	1	no	—
139	C₄⋊(C₃⋊D₃)	—	2	1	no	—
140	#634	—	2	1	no	—
141	#634	—	2	1	no	—
142	C₃×#67	—	12	16	no	—
143	C₂×C₃×Dic₃	—	3	8	no	—
144	C₂×C₃×Dic₃	—	6	4	no	—
145	C₃×D₁₂	—	6	4	no	—
146	C₃×D₁₂	—	6	4	no	—
147	C₃×Dic₆	—	6	4	no	—
148	C₃×Dic₆	—	6	4	no	—
149	C₃²×C₈	—	2	8	no	—
150	C₃²×C₈	#67	1	8	yes	complemented
151	C₃²×C₈	C₃×D₄	1	2	yes	complemented
152	C₃⋊(C₃⋊C₈)	C₃×D₄	1	2	yes	complemented
153	C₃×C₃⋊C₈	—	3	8	no	—
154	#492	—	9	1	no	Sylow
155	C₂×C₃³	—	8	1	no	—
156	C₂×C₃³	#127	1	1	yes	characteristic
157	C₂×C₃³	C₂×SD₁₆	1	2	yes	—
158	C₃×C₃⋊D₃	—	8	1	no	—
159	C₂×C₃×Q₈	—	2	4	no	—
160	C₂×C₃×Q₈	—	9	1	no	—
161	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
162	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
163	C₂×C₃×D₄	—	2	4	no	—
164	C₂×C₃×D₄	—	9	1	no	—
165	C₂×C₃×D₄	—	18	2	no	—
166	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
167	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
168	C₂×#67	—	6	8	no	—
169	C₂×D₁₂	—	3	4	no	—
170	C₂×Dic₆	—	3	4	no	—
171	C₃×SD₁₆	—	2	16	no	—
172	C₃×SD₁₆	—	2	8	no	—
173	C₃×SD₁₆	—	2	2	no	—
174	C₃×SD₁₆	—	18	2	no	—
175	C₃×SD₁₆	—	18	2	no	—
176	C₃×SD₁₆	—	18	2	no	—
177	C₂×C₃×C₈	—	2	4	no	—
178	C₂×C₃×C₈	—	9	1	no	—
179	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
180	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
181	C₃×C₄⋊C₄	—	18	2	no	—
182	C₃×C₄²	—	9	1	no	—
183	#215	—	6	8	no	—
184	#214	—	6	8	no	—
185	Dic₃⋊C₄	—	6	8	no	—
186	C₄×Dic₃	—	3	4	no	—
187	C₂×C₃⋊C₈	—	3	4	no	—
188	#204	—	6	8	no	—
189	C₂²×C₃²	—	2	4	no	—
190	C₂²×C₃²	—	4	8	no	—
191	C₂²×C₃²	—	4	4	no	—
192	C₂²×C₃²	—	4	1	no	—
193	C₂²×C₃²	—	4	2	no	—
194	C₂²×C₃²	—	4	8	no	—
195	C₂²×C₃²	—	8	8	no	—
196	C₂²×C₃²	D₃×D₄	1	4	yes	—
197	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
198	C₂×C₃⋊D₃	—	4	1	no	—
199	C₂×C₃⋊D₃	—	4	2	no	—
200	C₂×C₃×D₃	—	12	8	no	—
201	C₂×C₃×D₃	—	12	4	no	—
202	C₃²×C₄	—	2	4	no	—
203	C₃²×C₄	—	2	4	no	—
204	C₃²×C₄	—	4	8	no	—
205	C₃²×C₄	—	4	4	no	—
206	C₃²×C₄	—	4	1	no	—
207	C₃²×C₄	D₃×D₄	1	4	yes	—
208	C₃²×C₄	C₂×#67	1	4	yes	—
209	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
210	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
211	C₃⋊Dic₃	—	4	1	no	—
212	C₃⋊Dic₃	C₃×SD₁₆	1	4	yes	complemented
213	C₃×Dic₃	—	3	16	no	—
214	C₃×Dic₃	—	12	4	no	—
215	C₂×SD₁₆	—	9	1	no	—
216	C₂×SD₁₆	—	9	1	no	—
217	C₂×SD₁₆	—	9	1	no	—
218	C₂×SD₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
219	C₄⋊Q₈	—	9	1	no	—
220	#127	—	9	1	no	—
221	C₄×C₈	—	9	1	no	—
222	C₃³	#492	1	1	yes	characteristic, complemented, Sylow
223	C₂³×C₃	—	2	4	no	—
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	—	4	4	no	—
226	C₂³×C₃	—	18	1	no	—
227	C₂²×D₃	—	6	4	no	—
228	C₃×Q₈	—	2	8	no	—
229	C₃×Q₈	—	2	4	no	—
230	C₃×Q₈	—	2	4	no	—
231	C₃×Q₈	—	2	1	no	—
232	C₃×Q₈	—	2	1	no	—
233	C₃×Q₈	—	4	4	no	—
234	C₃×Q₈	—	18	1	no	—
235	C₃×Q₈	—	18	1	no	—
236	C₃×D₄	—	2	8	no	—
237	C₃×D₄	—	2	4	no	—
238	C₃×D₄	—	2	4	no	—
239	C₃×D₄	—	2	1	no	—
240	C₃×D₄	—	2	1	no	—
241	C₃×D₄	—	4	4	no	—
242	C₃×D₄	—	18	1	no	—
243	C₃×D₄	—	18	1	no	—
244	C₃×D₄	—	36	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	4	4	no	—
249	C₂×C₃×C₄	—	9	2	no	—
250	C₂×C₃×C₄	—	18	1	no	—
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
252	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
253	#67	—	12	16	no	—
254	C₂×Dic₃	—	3	8	no	—
255	C₂×Dic₃	—	6	4	no	—
256	D₁₂	—	6	4	no	—
257	D₁₂	—	6	4	no	—
258	Dic₆	—	6	4	no	—
259	Dic₆	—	6	4	no	—
260	C₃×C₈	—	2	8	no	—
261	C₃×C₈	—	9	2	no	—
262	C₃×C₈	C₃×#67	1	8	yes	complemented
263	C₃×C₈	#638	1	2	yes	complemented
264	C₃⋊C₈	—	3	8	no	—
265	C₂×C₃²	—	2	8	no	—
266	C₂×C₃²	—	2	4	no	—
267	C₂×C₃²	—	8	8	no	—
268	C₂×C₃²	—	8	4	no	—
269	C₂×C₃²	—	8	1	no	—
270	C₂×C₃²	D₃×SD₁₆	1	8	yes	—
271	C₂×C₃²	#940	1	4	yes	—
272	C₂×C₃²	C₃×#127	1	1	yes	characteristic
273	C₂×C₃²	C₂×C₃×SD₁₆	1	2	yes	—
274	C₃⋊D₃	—	8	1	no	—
275	C₃×D₃	—	24	4	no	—
276	C₂×Q₈	—	9	1	no	—
277	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
278	C₂×D₄	—	9	1	no	—
279	C₂×D₄	—	18	2	no	—
280	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
281	SD₁₆	—	2	2	no	—
282	SD₁₆	—	18	2	no	—
283	SD₁₆	—	18	2	no	—
284	SD₁₆	—	18	2	no	—
285	C₂×C₈	—	9	1	no	—
286	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
287	C₄⋊C₄	—	18	2	no	—
288	C₄²	—	9	1	no	—
289	C₂²×C₃	—	2	4	no	—
290	C₂²×C₃	—	4	8	no	—
291	C₂²×C₃	—	4	8	no	—
292	C₂²×C₃	—	4	4	no	—
293	C₂²×C₃	—	4	2	no	—
294	C₂²×C₃	—	4	1	no	—
295	C₂²×C₃	—	8	8	no	—
296	C₂²×C₃	—	36	2	no	—
297	C₂²×C₃	—	36	1	no	—
298	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
299	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
300	C₂×D₃	—	12	8	no	—
301	C₂×D₃	—	12	4	no	—
302	C₃×C₄	—	2	4	no	—
303	C₃×C₄	—	2	4	no	—
304	C₃×C₄	—	4	8	no	—
305	C₃×C₄	—	4	4	no	—
306	C₃×C₄	—	4	1	no	—
307	C₃×C₄	—	9	4	no	—
308	C₃×C₄	—	36	1	no	—
309	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
310	C₃×C₄	C₂×C₃×#67	1	4	yes	—
311	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
312	C₃×C₄	C₂×#638	1	1	yes	characteristic
313	Dic₃	—	3	16	no	—
314	Dic₃	—	12	4	no	—
315	C₃²	—	2	4	no	—
316	C₃²	#5175	1	4	yes	complemented
317	C₃²	C₃×#492	1	1	yes	characteristic, complemented
318	C₂³	—	2	1	no	—
319	C₂³	—	18	1	no	—
320	Q₈	—	2	1	no	—
321	Q₈	—	2	1	no	—
322	Q₈	—	18	1	no	—
323	Q₈	—	18	1	no	—
324	D₄	—	2	1	no	—
325	D₄	—	2	1	no	—
326	D₄	—	18	1	no	—
327	D₄	—	18	1	no	—
328	D₄	—	36	4	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	9	2	no	—
331	C₂×C₄	—	18	1	no	—
332	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
333	C₈	—	9	2	no	—
334	C₈	C₃×#638	1	2	yes	complemented
335	C₂×C₃	—	2	8	no	—
336	C₂×C₃	—	2	4	no	—
337	C₂×C₃	—	8	8	no	—
338	C₂×C₃	—	8	4	no	—
339	C₂×C₃	—	8	1	no	—
340	C₂×C₃	—	72	1	no	—
341	C₂×C₃	C₃×D₃×SD₁₆	1	8	yes	—
342	C₂×C₃	C₃×#940	1	4	yes	—
343	C₂×C₃	SD₁₆×C₃⋊D₃	1	2	yes	—
344	C₂×C₃	#64149	1	1	yes	characteristic
345	D₃	—	24	4	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	36	2	no	—
349	C₂²	—	36	1	no	—
350	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
351	C₄	—	4	1	no	—
352	C₄	—	9	4	no	—
353	C₄	—	36	1	no	—
354	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
355	C₄	C₂×C₃×#638	1	1	yes	characteristic
356	C₃	—	2	4	no	—
357	C₃	C₃×#5175	1	4	yes	complemented
358	C₃	#10592874	1	1	yes	characteristic, direct product factor
359	C₂	—	8	1	no	—
360	C₂	—	72	1	no	—
361	C₂	C₃×SD₁₆×C₃⋊D₃	1	2	yes	—
362	C₂	C₃×#64149	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₄×C₃⋊D₃
commutator, cosocle	C₂×C₃²×C₄	C₂³×C₃
Frattini	C₂×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₂×C₃³×SD₁₆	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₃×#64149	C₂
hypercenter	C₂×C₃×SD₁₆	C₃⋊D₃
hypocenter	C₃²	C₃×#492
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃³×SD₁₆	C₂	semidirect
2. C₃×#64153	C₂	semidirect
3. C₂×C₃×#3755	C₂	semidirect
5. C₂×C₃×#3754	C₂	semidirect
6. C₂×C₃×#3744	C₂	semidirect
7. C₃×C₈×C₃⋊Dic₃	C₂	semidirect
8. #10592874	C₃	direct (N × H)
24. C₂×C₃²×SD₁₆	D₃	semidirect
25. C₂×C₃²×SD₁₆	C₂×C₃	semidirect
26. #64153	C₂×C₃	semidirect
27. C₂×#3755	C₂×C₃	semidirect
29. C₂×#3754	C₂×C₃	semidirect
30. C₂×#3744	C₂×C₃	semidirect
36. C₈×C₃⋊Dic₃	C₂×C₃	semidirect
53. C₃³×C₈	D₄	semidirect
54. C₃×C₃⋊(C₃⋊C₈)	D₄	semidirect
96. C₃×C₃⋊Dic₃	SD₁₆	semidirect
101. C₂×C₃×SD₁₆	C₃×D₃	semidirect
102. C₂×C₃×SD₁₆	C₃⋊D₃	semidirect
150. C₃²×C₈	#67	semidirect
151. C₃²×C₈	C₃×D₄	semidirect
152. C₃⋊(C₃⋊C₈)	C₃×D₄	semidirect
212. C₃⋊Dic₃	C₃×SD₁₆	semidirect
218. C₂×SD₁₆	C₃×C₃⋊D₃	semidirect
222. C₃³	#492	semidirect
262. C₃×C₈	C₃×#67	semidirect
263. C₃×C₈	#638	semidirect
316. C₃²	#5175	semidirect
317. C₃²	C₃×#492	semidirect
334. C₈	C₃×#638	semidirect
357. C₃	C₃×#5175	semidirect
358. C₃	#10592874	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃³×SD₁₆	2
C₃×#64153	2
C₂×C₃×#3755	2
C₃×#64149	2
C₂×C₃×#3754	2
C₂×C₃×#3744	2
C₃×C₈×C₃⋊Dic₃	2
#10592874	3
C₃×#5175	3

Subgroups — C3×#10592874 #13163202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10592874 #13163202