Subgroups — C₃×#33786 #10652393

Order 768.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2246	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2210	C₂	1	2	yes	maximal, complemented
8	C₃×#2206	C₂	1	2	yes	maximal, complemented
9	C₃×#2186	C₂	1	2	yes	maximal, complemented
10	C₃×#2184	C₂	1	2	yes	maximal, complemented
11	C₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	#33786	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×AGL(1,ℤ/8)	—	2	1	no	—
14	C₂×C₃×#135	C₂²	1	1	yes	characteristic
15	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic
16	C₃×#540	—	2	1	no	—
17	C₃×#535	—	2	1	no	—
18	C₂×C₃×SD₃₂	C₂²	1	2	yes	complemented
19	C₂×C₃×D₁₆	C₂²	1	2	yes	—
20	C₂×C₃×D₁₆	C₂²	1	2	yes	—
21	C₂×C₃×D₁₆	C₂²	1	2	yes	complemented
22	C₃×#499	C₂²	1	1	yes	characteristic, complemented
23	C₃×#496	—	2	1	no	—
24	C₃×#496	—	2	1	no	—
25	C₃×#495	C₂²	1	1	yes	characteristic
26	C₃×#495	C₂²	1	1	yes	characteristic
27	C₃×#493	C₂²	1	1	yes	characteristic
28	C₃×#493	C₂²	1	1	yes	characteristic
29	C₃×#493	C₂²	1	1	yes	characteristic, complemented
30	C₃×#490	—	2	1	no	—
31	C₃×#469	—	2	1	no	—
32	C₃×#466	C₂²	1	2	yes	—
33	C₃×#442	—	2	1	no	—
34	C₃×C₄×D₈	C₂²	1	2	yes	complemented
35	C₃×#405	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
37	C₃×#358	C₂²	1	2	yes	complemented
38	C₃×#357	C₂²	1	2	yes	—
39	C₃×#357	C₂²	1	2	yes	—
40	C₃×#357	C₂²	1	2	yes	complemented
41	C₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
42	C₃×#346	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
44	#3176	C₂×C₃	1	1	yes	characteristic, complemented
45	#3155	C₂×C₃	1	1	yes	characteristic, complemented
46	#2250	C₂×C₃	1	1	yes	characteristic, complemented
47	#2246	C₂×C₃	1	1	yes	characteristic, complemented
48	#2244	C₂×C₃	1	1	yes	characteristic, complemented
49	#2242	C₂×C₃	1	1	yes	characteristic, complemented
50	#2210	C₂×C₃	1	2	yes	complemented
51	#2206	C₂×C₃	1	2	yes	complemented
52	#2186	C₂×C₃	1	2	yes	complemented
53	#2184	C₂×C₃	1	2	yes	complemented
54	#2164	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₃×#41	—	2	1	no	—
56	C₂²×C₃×D₄	—	2	1	no	—
57	C₃×AGL(1,ℤ/8)	—	4	4	no	—
58	C₃×#135	—	4	2	no	—
59	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₃×SD₁₆	—	2	1	no	—
61	C₂×C₃×SD₁₆	—	2	1	no	—
62	C₂×C₃×SD₁₆	—	2	1	no	—
63	C₂×C₃×D₈	—	2	1	no	—
64	C₂×C₃×D₈	—	2	1	no	—
65	C₂×C₃×D₈	—	2	1	no	—
66	C₂×C₃×D₈	—	2	1	no	—
67	C₂×C₃×D₈	—	4	2	no	—
68	C₂×C₃×D₈	C₂³	1	2	yes	—
69	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
73	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
74	C₃×#127	—	2	1	no	—
75	C₃×#127	—	2	1	no	—
76	C₃×#127	—	2	1	no	—
77	C₃×#125	—	2	1	no	—
78	C₃×#124	—	2	1	no	—
79	C₃×#124	—	2	1	no	—
80	C₃×#123	—	4	2	no	—
81	C₃×#121	—	2	2	no	—
82	C₃×#121	—	4	2	no	—
83	C₃×#121	—	4	2	no	—
84	C₃×#120	—	4	2	no	—
85	C₃×C₄×D₄	—	2	2	no	—
86	C₃×#117	D₄	1	1	yes	characteristic
87	C₃×SD₃₂	—	4	2	no	—
88	C₃×D₁₆	—	4	2	no	—
89	C₃×D₁₆	—	4	2	no	—
90	C₃×D₁₆	—	4	2	no	—
91	C₂×C₃×C₁₆	C₂³	1	2	yes	—
92	C₂×C₃×C₁₆	C₂³	1	2	yes	—
93	C₃×#107	C₂³	1	2	yes	—
94	C₃×#106	—	2	1	no	—
95	C₃×#102	—	2	2	no	—
96	C₃×#102	—	2	2	no	—
97	C₃×#97	D₄	1	1	yes	characteristic
98	C₃×#97	D₄	1	1	yes	characteristic
99	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
100	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
101	C₂×AGL(1,ℤ/8)	—	2	1	no	—
102	C₂×#135	C₂²×C₃	1	1	yes	characteristic
103	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic
104	#540	—	2	1	no	—
105	#535	—	2	1	no	—
106	C₂×SD₃₂	C₂²×C₃	1	2	yes	complemented
107	C₂×D₁₆	C₂²×C₃	1	2	yes	—
108	C₂×D₁₆	C₂²×C₃	1	2	yes	—
109	C₂×D₁₆	C₂²×C₃	1	2	yes	complemented
110	#499	C₂²×C₃	1	1	yes	characteristic, complemented
111	#496	—	2	1	no	—
112	#496	—	2	1	no	—
113	#495	C₂²×C₃	1	1	yes	characteristic
114	#495	C₂²×C₃	1	1	yes	characteristic
115	#493	C₂²×C₃	1	1	yes	characteristic
116	#493	C₂²×C₃	1	1	yes	characteristic
117	#493	C₂²×C₃	1	1	yes	characteristic, complemented
118	#490	—	2	1	no	—
119	#469	—	2	1	no	—
120	#466	C₂²×C₃	1	2	yes	—
121	#442	—	2	1	no	—
122	C₄×D₈	C₂²×C₃	1	2	yes	complemented
123	#405	C₂²×C₃	1	1	yes	characteristic
124	C₄⋊C₁₆	C₂²×C₃	1	2	yes	complemented
125	#358	C₂²×C₃	1	2	yes	complemented
126	#357	C₂²×C₃	1	2	yes	—
127	#357	C₂²×C₃	1	2	yes	—
128	#357	C₂²×C₃	1	2	yes	complemented
129	C₂²⋊C₁₆	C₂²×C₃	1	2	yes	—
130	#346	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₄×C₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₂⁴×C₃	—	4	1	no	—
133	C₃×#41	—	4	2	no	—
134	C₃×#41	—	4	2	no	—
135	C₂×C₃×Q₈	—	2	1	no	—
136	C₂×C₃×D₄	—	2	2	no	—
137	C₂×C₃×D₄	—	2	1	no	—
138	C₂×C₃×D₄	—	2	1	no	—
139	C₂×C₃×D₄	—	2	1	no	—
140	C₂×C₃×D₄	—	4	2	no	—
141	C₂×C₃×D₄	—	4	2	no	—
142	C₂×C₃×D₄	—	4	1	no	—
143	C₂×C₃×D₄	—	4	2	no	—
144	C₂×C₃×D₄	—	4	1	no	—
145	C₂×C₃×D₄	—	4	2	no	—
146	C₂×C₃×D₄	—	4	2	no	—
147	C₂×C₃×D₄	—	4	2	no	—
148	C₂²×C₃×C₄	—	4	1	no	—
149	C₂²×C₃×C₄	—	4	2	no	—
150	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
151	C₃×Q₁₆	—	2	2	no	—
152	C₃×SD₁₆	—	4	2	no	—
153	C₃×SD₁₆	—	4	2	no	—
154	C₃×SD₁₆	—	4	2	no	—
155	C₃×D₈	—	2	2	no	—
156	C₃×D₈	—	2	2	no	—
157	C₃×D₈	—	2	2	no	—
158	C₃×D₈	—	2	2	no	—
159	C₃×D₈	—	2	2	no	—
160	C₃×D₈	—	4	2	no	—
161	C₃×D₈	—	4	2	no	—
162	C₃×D₈	—	4	2	no	—
163	C₃×D₈	—	4	2	no	—
164	C₃×M₁₆	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	4	2	no	—
172	C₃×C₄⋊C₄	D₈	1	2	yes	—
173	C₃×C₂²⋊C₄	—	4	2	no	—
174	C₃×C₂²⋊C₄	—	4	2	no	—
175	C₃×C₂²⋊C₄	—	4	2	no	—
176	C₃×C₂²⋊C₄	—	4	2	no	—
177	C₃×C₂²⋊C₄	D₈	1	2	yes	—
178	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
179	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
180	C₃×C₁₆	—	2	2	no	—
181	C₃×C₁₆	—	2	2	no	—
182	C₂×#41	—	2	1	no	—
183	C₂²×D₄	—	2	1	no	—
184	AGL(1,ℤ/8)	—	4	4	no	—
185	#135	—	4	2	no	—
186	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
187	C₂×SD₁₆	—	2	1	no	—
188	C₂×SD₁₆	—	2	1	no	—
189	C₂×SD₁₆	—	2	1	no	—
190	C₂×D₈	—	2	1	no	—
191	C₂×D₈	—	2	1	no	—
192	C₂×D₈	—	2	1	no	—
193	C₂×D₈	—	2	1	no	—
194	C₂×D₈	—	4	2	no	—
195	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
196	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
197	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
198	C₂×D₈	C₂³×C₃	1	2	yes	—
199	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
200	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
201	#127	—	2	1	no	—
202	#127	—	2	1	no	—
203	#127	—	2	1	no	—
204	#125	—	2	1	no	—
205	#124	—	2	1	no	—
206	#124	—	2	1	no	—
207	#123	—	4	2	no	—
208	#121	—	2	2	no	—
209	#121	—	4	2	no	—
210	#121	—	4	2	no	—
211	#120	—	4	2	no	—
212	C₄×D₄	—	2	2	no	—
213	#117	C₃×D₄	1	1	yes	characteristic
214	SD₃₂	—	4	2	no	—
215	D₁₆	—	4	2	no	—
216	D₁₆	—	4	2	no	—
217	D₁₆	—	4	2	no	—
218	C₂×C₁₆	C₂³×C₃	1	2	yes	—
219	C₂×C₁₆	C₂³×C₃	1	2	yes	—
220	#107	C₂³×C₃	1	2	yes	—
221	#106	—	2	1	no	—
222	#102	—	2	2	no	—
223	#102	—	2	2	no	—
224	#97	C₃×D₄	1	1	yes	characteristic
225	#97	C₃×D₄	1	1	yes	characteristic
226	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
227	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
228	C₂³×C₃	—	4	2	no	—
229	C₂³×C₃	—	4	1	no	—
230	C₂³×C₃	—	4	1	no	—
231	C₂³×C₃	—	4	1	no	—
232	C₂³×C₃	—	8	2	no	—
233	C₂³×C₃	—	16	2	no	—
234	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
235	C₃×Q₈	—	4	1	no	—
236	C₃×Q₈	—	4	1	no	—
237	C₃×D₄	—	4	1	no	—
238	C₃×D₄	—	4	1	no	—
239	C₃×D₄	—	4	1	no	—
240	C₃×D₄	—	4	2	no	—
241	C₃×D₄	—	4	1	no	—
242	C₃×D₄	—	4	1	no	—
243	C₃×D₄	—	4	1	no	—
244	C₃×D₄	—	4	2	no	—
245	C₃×D₄	—	8	2	no	—
246	C₃×D₄	—	8	2	no	—
247	C₃×D₄	—	16	2	no	—
248	C₃×D₄	—	16	2	no	—
249	C₃×D₄	—	16	2	no	—
250	C₃×D₄	—	16	2	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	4	1	no	—
254	C₂×C₃×C₄	—	4	2	no	—
255	C₂×C₃×C₄	—	8	2	no	—
256	C₂×C₃×C₄	—	16	2	no	—
257	C₂×C₃×C₄	C₂×D₈	1	2	yes	—
258	C₂×C₃×C₄	C₂×D₈	1	2	yes	—
259	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
261	C₃×C₈	—	2	1	no	—
262	C₃×C₈	—	2	1	no	—
263	C₃×C₈	AGL(1,ℤ/8)	1	2	yes	—
264	C₃×C₈	H(5,𝔽₂)	1	2	yes	—
265	C₂⁴	—	4	1	no	—
266	#41	—	4	2	no	—
267	#41	—	4	2	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
284	Q₁₆	—	2	2	no	—
285	SD₁₆	—	4	2	no	—
286	SD₁₆	—	4	2	no	—
287	SD₁₆	—	4	2	no	—
288	D₈	—	2	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	2	no	—
291	D₈	—	2	2	no	—
292	D₈	—	2	2	no	—
293	D₈	—	4	2	no	—
294	D₈	—	4	2	no	—
295	D₈	—	4	2	no	—
296	D₈	—	4	2	no	—
297	M₁₆	—	2	2	no	—
298	C₂×C₈	—	2	2	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	—	4	2	no	—
305	C₄⋊C₄	C₃×D₈	1	2	yes	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	C₃×D₈	1	2	yes	—
311	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
312	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
313	C₁₆	—	2	2	no	—
314	C₁₆	—	2	2	no	—
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	8	2	no	—
318	C₂²×C₃	—	8	2	no	—
319	C₂²×C₃	—	8	2	no	—
320	C₂²×C₃	—	8	2	no	—
321	C₂²×C₃	—	8	2	no	—
322	C₂²×C₃	—	8	1	no	—
323	C₂²×C₃	—	8	1	no	—
324	C₂²×C₃	—	8	1	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	2	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	1	no	—
331	C₃×C₄	—	8	2	no	—
332	C₃×C₄	—	8	1	no	—
333	C₃×C₄	#535	1	1	yes	characteristic
334	C₃×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
335	C₂³	—	4	2	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	8	2	no	—
340	C₂³	—	16	2	no	—
341	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
342	Q₈	—	4	1	no	—
343	Q₈	—	4	1	no	—
344	D₄	—	4	1	no	—
345	D₄	—	4	1	no	—
346	D₄	—	4	1	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	16	2	no	—
355	D₄	—	16	2	no	—
356	D₄	—	16	2	no	—
357	D₄	—	16	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	16	2	no	—
364	C₂×C₄	C₂×C₃×D₈	1	2	yes	—
365	C₂×C₄	C₂×C₃×D₈	1	2	yes	—
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	C₃×AGL(1,ℤ/8)	1	2	yes	—
371	C₈	C₃×H(5,𝔽₂)	1	2	yes	—
372	C₂×C₃	—	4	1	no	—
373	C₂×C₃	—	16	2	no	—
374	C₂×C₃	—	16	1	no	—
375	C₂×C₃	—	16	1	no	—
376	C₂×C₃	—	16	1	no	—
377	C₂×C₃	#3205	1	1	yes	characteristic
378	C₂×C₃	#3415	1	2	yes	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	16	4	no	—
391	C₂²	C₂²×C₃×D₈	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	1	no	—
397	C₄	C₃×#535	1	1	yes	characteristic
398	C₄	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
399	C₃	#33786	1	1	yes	characteristic, direct product factor, Sylow
400	C₂	—	4	1	no	—
401	C₂	—	16	1	no	—
402	C₂	—	16	1	no	—
403	C₂	—	16	2	no	—
404	C₂	—	16	1	no	—
405	C₂	C₃×#3205	1	1	yes	characteristic
406	C₂	C₃×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3176	C₂	semidirect
2. C₃×#3155	C₂	semidirect
3. C₃×#2250	C₂	semidirect
4. C₃×#2246	C₂	semidirect
5. C₃×#2244	C₂	semidirect
6. C₃×#2242	C₂	semidirect
7. C₃×#2210	C₂	semidirect
8. C₃×#2206	C₂	semidirect
9. C₃×#2186	C₂	semidirect
10. C₃×#2184	C₂	semidirect
11. C₃×#2164	C₂	semidirect
12. #33786	C₃	direct (N × H)
18. C₂×C₃×SD₃₂	C₂²	semidirect
21. C₂×C₃×D₁₆	C₂²	semidirect
22. C₃×#499	C₂²	semidirect
29. C₃×#493	C₂²	semidirect
34. C₃×C₄×D₈	C₂²	semidirect
36. C₃×C₄⋊C₁₆	C₂²	semidirect
37. C₃×#358	C₂²	semidirect
40. C₃×#357	C₂²	semidirect
42. C₃×#346	C₂²	semidirect
43. C₃×C₄×C₁₆	C₂²	semidirect
44. #3176	C₂×C₃	semidirect
45. #3155	C₂×C₃	semidirect
46. #2250	C₂×C₃	semidirect
47. #2246	C₂×C₃	semidirect
48. #2244	C₂×C₃	semidirect
49. #2242	C₂×C₃	semidirect
50. #2210	C₂×C₃	semidirect
51. #2206	C₂×C₃	semidirect
52. #2186	C₂×C₃	semidirect
53. #2184	C₂×C₃	semidirect
54. #2164	C₂×C₃	semidirect
106. C₂×SD₃₂	C₂²×C₃	semidirect
109. C₂×D₁₆	C₂²×C₃	semidirect
110. #499	C₂²×C₃	semidirect
117. #493	C₂²×C₃	semidirect
122. C₄×D₈	C₂²×C₃	semidirect
124. C₄⋊C₁₆	C₂²×C₃	semidirect
125. #358	C₂²×C₃	semidirect
128. #357	C₂²×C₃	semidirect
130. #346	C₂²×C₃	semidirect
131. C₄×C₁₆	C₂²×C₃	semidirect
399. C₃	#33786	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×#3176	2
C₃×#3155	2
C₃×#2250	2
C₃×#2246	2
C₃×#2244	2
C₃×#2242	2
C₃×#2210	2
C₃×#2206	2
C₃×#2186	2
C₃×#2184	2
C₃×#2164	2
#33786	3

Subgroups — C3×#33786 #10652393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33786 #10652393