Subgroups — C₃×#33766 #10652373

Order 768.

584 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3058	C₂	1	1	yes	maximal, characteristic
3	C₃×#2237	C₂	1	2	yes	maximal, complemented
4	C₃×#2234	C₂	1	2	yes	maximal, complemented
5	C₃×#2220	C₂	1	2	yes	maximal, complemented
6	C₃×#2217	C₂	1	2	yes	maximal, complemented
7	C₃×#2187	C₂	1	2	yes	maximal, complemented
8	C₃×#2185	C₂	1	2	yes	maximal, complemented
9	C₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	#33766	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
12	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×#131	C₂²	1	1	yes	characteristic
14	C₃×#536	—	2	1	no	—
15	C₃×#535	—	2	1	no	—
16	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
17	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₃×#470	—	2	1	no	—
21	C₃×#470	—	2	1	no	—
22	C₃×#469	—	2	1	no	—
23	C₃×#469	—	2	1	no	—
24	C₃×#467	C₂²	1	2	yes	—
25	C₃×#467	C₂²	1	2	yes	complemented
26	C₃×#466	C₂²	1	2	yes	—
27	C₃×#466	C₂²	1	2	yes	—
28	C₃×#427	C₂²	1	1	yes	characteristic
29	C₃×#427	C₂²	1	1	yes	characteristic, complemented
30	C₃×#419	—	2	1	no	—
31	C₃×#418	—	2	1	no	—
32	C₃×#367	C₂²	1	2	yes	complemented
33	C₃×#366	C₂²	1	2	yes	complemented
34	C₃×#358	C₂²	1	2	yes	complemented
35	C₃×#358	C₂²	1	2	yes	complemented
36	C₃×#357	C₂²	1	2	yes	—
37	C₃×#357	C₂²	1	2	yes	—
38	C₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
39	C₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	#3059	C₂×C₃	1	1	yes	characteristic, complemented
41	#3058	C₂×C₃	1	1	yes	characteristic
42	#2237	C₂×C₃	1	2	yes	complemented
43	#2234	C₂×C₃	1	2	yes	complemented
44	#2220	C₂×C₃	1	2	yes	complemented
45	#2217	C₂×C₃	1	2	yes	complemented
46	#2187	C₂×C₃	1	2	yes	complemented
47	#2185	C₂×C₃	1	2	yes	complemented
48	#2113	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₃×#41	D₄	1	1	yes	characteristic
50	C₂²×C₃×Q₈	—	2	1	no	—
51	C₂²×C₃×D₄	—	2	1	no	—
52	C₂×C₃×Q₁₆	—	2	1	no	—
53	C₂×C₃×Q₁₆	—	4	1	no	—
54	C₂×C₃×Q₁₆	—	4	1	no	—
55	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
56	C₂×C₃×D₈	—	2	1	no	—
57	C₂×C₃×D₈	—	4	1	no	—
58	C₂×C₃×D₈	—	4	1	no	—
59	C₂×C₃×D₈	C₂³	1	2	yes	—
60	C₃×#131	—	4	1	no	—
61	C₃×#131	—	4	1	no	—
62	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
63	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
64	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
65	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
68	C₃×C₄⋊Q₈	—	4	1	no	—
69	C₃×#127	—	4	1	no	—
70	C₃×#124	—	4	1	no	—
71	C₃×#124	—	4	1	no	—
72	C₃×#123	—	4	1	no	—
73	C₃×#123	—	4	1	no	—
74	C₃×C₂²⋊Q₈	—	2	2	no	—
75	C₃×C₂²⋊Q₈	—	2	2	no	—
76	C₃×#121	—	2	2	no	—
77	C₃×#121	—	2	2	no	—
78	C₃×#120	—	4	1	no	—
79	C₃×#120	—	4	1	no	—
80	C₃×#117	—	2	1	no	—
81	C₃×#117	—	2	1	no	—
82	C₃×SD₃₂	—	4	2	no	—
83	C₃×SD₃₂	—	4	2	no	—
84	C₃×M₃₂	—	4	1	no	—
85	C₂×C₃×C₁₆	—	4	1	no	—
86	C₂×C₃×C₁₆	C₂³	1	2	yes	—
87	C₂×C₃×C₁₆	C₂³	1	2	yes	—
88	C₃×#107	C₂³	1	2	yes	—
89	C₃×#107	C₂³	1	2	yes	—
90	C₃×#106	—	2	1	no	—
91	C₃×#106	—	2	1	no	—
92	C₃×#103	—	2	2	no	—
93	C₃×#103	—	2	2	no	—
94	C₃×#102	—	2	2	no	—
95	C₃×#102	—	2	2	no	—
96	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic
98	C₂×#131	C₂²×C₃	1	1	yes	characteristic
99	#536	—	2	1	no	—
100	#535	—	2	1	no	—
101	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
102	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
103	C₂×M₃₂	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂²×C₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
105	#470	—	2	1	no	—
106	#470	—	2	1	no	—
107	#469	—	2	1	no	—
108	#469	—	2	1	no	—
109	#467	C₂²×C₃	1	2	yes	—
110	#467	C₂²×C₃	1	2	yes	complemented
111	#466	C₂²×C₃	1	2	yes	—
112	#466	C₂²×C₃	1	2	yes	—
113	#427	C₂²×C₃	1	1	yes	characteristic
114	#427	C₂²×C₃	1	1	yes	characteristic, complemented
115	#419	—	2	1	no	—
116	#418	—	2	1	no	—
117	#367	C₂²×C₃	1	2	yes	complemented
118	#366	C₂²×C₃	1	2	yes	complemented
119	#358	C₂²×C₃	1	2	yes	complemented
120	#358	C₂²×C₃	1	2	yes	complemented
121	#357	C₂²×C₃	1	2	yes	—
122	#357	C₂²×C₃	1	2	yes	—
123	C₂²⋊C₁₆	C₂²×C₃	1	2	yes	—
124	C₂²⋊C₁₆	C₂²×C₃	1	2	yes	complemented
125	C₂⁴×C₃	—	4	1	no	—
126	C₃×#41	—	4	1	no	—
127	C₃×#41	—	4	1	no	—
128	C₂×C₃×Q₈	—	2	2	no	—
129	C₂×C₃×Q₈	—	4	2	no	—
130	C₂×C₃×Q₈	—	4	2	no	—
131	C₂×C₃×Q₈	—	4	1	no	—
132	C₂×C₃×Q₈	D₈	1	1	yes	characteristic
133	C₂×C₃×D₄	—	2	2	no	—
134	C₂×C₃×D₄	—	4	2	no	—
135	C₂×C₃×D₄	—	4	2	no	—
136	C₂×C₃×D₄	—	4	2	no	—
137	C₂×C₃×D₄	—	4	2	no	—
138	C₂×C₃×D₄	—	4	1	no	—
139	C₂×C₃×D₄	D₈	1	1	yes	characteristic
140	C₂×C₃×D₄	D₈	1	1	yes	characteristic
141	C₂×C₃×D₄	D₈	1	1	yes	characteristic
142	C₂²×C₃×C₄	—	4	1	no	—
143	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
146	C₃×Q₁₆	—	2	2	no	—
147	C₃×Q₁₆	—	2	2	no	—
148	C₃×Q₁₆	—	4	2	no	—
149	C₃×D₈	—	2	2	no	—
150	C₃×D₈	—	2	2	no	—
151	C₃×D₈	—	4	2	no	—
152	C₃×M₁₆	—	4	1	no	—
153	C₃×M₁₆	—	4	1	no	—
154	C₃×M₁₆	—	4	1	no	—
155	C₂×C₃×C₈	—	2	1	no	—
156	C₂×C₃×C₈	—	2	1	no	—
157	C₂×C₃×C₈	—	2	1	no	—
158	C₂×C₃×C₈	—	2	1	no	—
159	C₂×C₃×C₈	—	2	1	no	—
160	C₂×C₃×C₈	—	2	1	no	—
161	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
165	C₃×C₄⋊C₄	—	2	2	no	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₄⋊C₄	—	4	2	no	—
168	C₃×C₄⋊C₄	—	4	2	no	—
169	C₃×C₂²⋊C₄	—	4	1	no	—
170	C₃×C₂²⋊C₄	—	4	1	no	—
171	C₃×C₂²⋊C₄	—	4	2	no	—
172	C₃×C₂²⋊C₄	—	4	2	no	—
173	C₃×C₂²⋊C₄	—	4	2	no	—
174	C₃×C₂²⋊C₄	—	4	2	no	—
175	C₃×C₄²	—	4	1	no	—
176	C₃×C₄²	—	4	1	no	—
177	C₃×C₁₆	—	2	2	no	—
178	C₃×C₁₆	—	2	2	no	—
179	C₂×#41	C₃×D₄	1	1	yes	characteristic
180	C₂²×Q₈	—	2	1	no	—
181	C₂²×D₄	—	2	1	no	—
182	C₂×Q₁₆	—	2	1	no	—
183	C₂×Q₁₆	—	4	1	no	—
184	C₂×Q₁₆	—	4	1	no	—
185	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
186	C₂×D₈	—	2	1	no	—
187	C₂×D₈	—	4	1	no	—
188	C₂×D₈	—	4	1	no	—
189	C₂×D₈	C₂³×C₃	1	2	yes	—
190	#131	—	4	1	no	—
191	#131	—	4	1	no	—
192	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
193	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
194	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
195	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
196	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
197	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
198	C₄⋊Q₈	—	4	1	no	—
199	#127	—	4	1	no	—
200	#124	—	4	1	no	—
201	#124	—	4	1	no	—
202	#123	—	4	1	no	—
203	#123	—	4	1	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	#121	—	2	2	no	—
207	#121	—	2	2	no	—
208	#120	—	4	1	no	—
209	#120	—	4	1	no	—
210	#117	—	2	1	no	—
211	#117	—	2	1	no	—
212	SD₃₂	—	4	2	no	—
213	SD₃₂	—	4	2	no	—
214	M₃₂	—	4	1	no	—
215	C₂×C₁₆	—	4	1	no	—
216	C₂×C₁₆	C₂³×C₃	1	2	yes	—
217	C₂×C₁₆	C₂³×C₃	1	2	yes	—
218	#107	C₂³×C₃	1	2	yes	—
219	#107	C₂³×C₃	1	2	yes	—
220	#106	—	2	1	no	—
221	#106	—	2	1	no	—
222	#103	—	2	2	no	—
223	#103	—	2	2	no	—
224	#102	—	2	2	no	—
225	#102	—	2	2	no	—
226	C₂³×C₃	—	4	2	no	—
227	C₂³×C₃	—	8	2	no	—
228	C₂³×C₃	—	16	2	no	—
229	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
230	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
231	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
232	C₃×Q₈	—	4	1	no	—
233	C₃×Q₈	—	4	2	no	—
234	C₃×Q₈	—	4	2	no	—
235	C₃×Q₈	—	8	2	no	—
236	C₃×D₄	—	4	1	no	—
237	C₃×D₄	—	4	1	no	—
238	C₃×D₄	—	4	1	no	—
239	C₃×D₄	—	4	2	no	—
240	C₃×D₄	—	4	2	no	—
241	C₃×D₄	—	8	2	no	—
242	C₃×D₄	—	16	2	no	—
243	C₃×D₄	—	16	2	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	4	2	no	—
251	C₂×C₃×C₄	—	4	2	no	—
252	C₂×C₃×C₄	—	4	2	no	—
253	C₂×C₃×C₄	—	8	2	no	—
254	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
258	C₃×C₈	—	2	1	no	—
259	C₃×C₈	—	2	1	no	—
260	C₃×C₈	—	2	1	no	—
261	C₃×C₈	H(5,𝔽₂)	1	1	yes	characteristic
262	C₃×C₈	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂⁴	—	4	1	no	—
264	#41	—	4	1	no	—
265	#41	—	4	1	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	—	4	1	no	—
270	C₂×Q₈	C₃×D₈	1	1	yes	characteristic
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	C₃×D₈	1	1	yes	characteristic
278	C₂×D₄	C₃×D₈	1	1	yes	characteristic
279	C₂×D₄	C₃×D₈	1	1	yes	characteristic
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
284	Q₁₆	—	2	2	no	—
285	Q₁₆	—	2	2	no	—
286	Q₁₆	—	4	2	no	—
287	D₈	—	2	2	no	—
288	D₈	—	2	2	no	—
289	D₈	—	4	2	no	—
290	M₁₆	—	4	1	no	—
291	M₁₆	—	4	1	no	—
292	M₁₆	—	4	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
300	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
301	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
302	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₄²	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₁₆	—	2	2	no	—
316	C₁₆	—	2	2	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	8	2	no	—
324	C₂²×C₃	—	8	2	no	—
325	C₂²×C₃	—	8	2	no	—
326	C₂²×C₃	—	16	4	no	—
327	C₂²×C₃	C₂²×D₈	1	1	yes	characteristic
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	2	1	no	—
330	C₃×C₄	—	2	1	no	—
331	C₃×C₄	—	8	2	no	—
332	C₃×C₄	—	8	2	no	—
333	C₃×C₄	—	8	2	no	—
334	C₃×C₄	#534	1	1	yes	characteristic
335	C₃×C₄	#575	1	1	yes	characteristic
336	C₂³	—	4	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	16	2	no	—
339	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
340	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
341	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
342	Q₈	—	4	1	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	8	2	no	—
346	D₄	—	4	1	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	16	2	no	—
353	D₄	—	16	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
365	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
366	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
367	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	C₃×H(5,𝔽₂)	1	1	yes	characteristic
372	C₈	C₃×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₃	—	4	1	no	—
374	C₂×C₃	—	4	1	no	—
375	C₂×C₃	—	4	1	no	—
376	C₂×C₃	—	16	2	no	—
377	C₂×C₃	#3186	1	1	yes	characteristic
378	C₂×C₃	#3416	1	2	yes	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	16	4	no	—
389	C₂²	C₂²×C₃×D₈	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₄	C₃×#534	1	1	yes	characteristic
397	C₄	C₃×#575	1	1	yes	characteristic
398	C₃	#33766	1	1	yes	characteristic, direct product factor, Sylow
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	4	1	no	—
402	C₂	—	16	2	no	—
403	C₂	C₃×#3186	1	1	yes	characteristic
404	C₂	C₃×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃
prime radical	C₃×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41 ◁ C₂×C₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3059	C₂	semidirect
3. C₃×#2237	C₂	semidirect
4. C₃×#2234	C₂	semidirect
5. C₃×#2220	C₂	semidirect
6. C₃×#2217	C₂	semidirect
7. C₃×#2187	C₂	semidirect
8. C₃×#2185	C₂	semidirect
9. C₃×#2113	C₂	semidirect
10. #33766	C₃	direct (N × H)
11. C₂²×C₃×Q₁₆	C₂²	semidirect
18. C₂×C₃×M₃₂	C₂²	semidirect
19. C₂²×C₃×C₁₆	C₂²	semidirect
25. C₃×#467	C₂²	semidirect
29. C₃×#427	C₂²	semidirect
32. C₃×#367	C₂²	semidirect
33. C₃×#366	C₂²	semidirect
34. C₃×#358	C₂²	semidirect
35. C₃×#358	C₂²	semidirect
39. C₃×C₂²⋊C₁₆	C₂²	semidirect
40. #3059	C₂×C₃	semidirect
42. #2237	C₂×C₃	semidirect
43. #2234	C₂×C₃	semidirect
44. #2220	C₂×C₃	semidirect
45. #2217	C₂×C₃	semidirect
46. #2187	C₂×C₃	semidirect
47. #2185	C₂×C₃	semidirect
48. #2113	C₂×C₃	semidirect
96. C₂²×Q₁₆	C₂²×C₃	semidirect
103. C₂×M₃₂	C₂²×C₃	semidirect
104. C₂²×C₁₆	C₂²×C₃	semidirect
110. #467	C₂²×C₃	semidirect
114. #427	C₂²×C₃	semidirect
117. #367	C₂²×C₃	semidirect
118. #366	C₂²×C₃	semidirect
119. #358	C₂²×C₃	semidirect
120. #358	C₂²×C₃	semidirect
124. C₂²⋊C₁₆	C₂²×C₃	semidirect
398. C₃	#33766	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3059	2
C₃×#3058	2
C₃×#2237	2
C₃×#2234	2
C₃×#2220	2
C₃×#2217	2
C₃×#2187	2
C₃×#2185	2
C₃×#2113	2
#33766	3

Subgroups — C3×#33766 #10652373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33766 #10652373