Subgroups — C₃×#33785 #10652392

Order 768.

594 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2250	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2245	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2244	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2211	C₂	1	2	yes	maximal, complemented
8	C₃×#2210	C₂	1	2	yes	maximal, complemented
9	C₃×#2189	C₂	1	2	yes	maximal, complemented
10	C₃×#2186	C₂	1	2	yes	maximal, complemented
11	C₃×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	#33785	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×#135	—	2	1	no	—
14	C₂×C₃×#135	C₂²	1	2	yes	—
15	C₃×#532	—	2	1	no	—
16	C₃×#529	—	2	1	no	—
17	C₂×C₃×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₃×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₃×D₁₆	C₂²	1	2	yes	—
21	C₃×#499	C₂²	1	1	yes	characteristic
22	C₃×#495	—	2	1	no	—
23	C₃×#495	C₂²	1	1	yes	characteristic
24	C₃×#495	C₂²	1	2	yes	—
25	C₃×#494	C₂²	1	1	yes	characteristic
26	C₃×#493	C₂²	1	1	yes	characteristic
27	C₃×#492	—	2	1	no	—
28	C₃×#488	—	2	1	no	—
29	C₃×#467	C₂²	1	1	yes	characteristic
30	C₃×#466	C₂²	1	1	yes	characteristic
31	C₃×#465	—	2	1	no	—
32	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
33	C₃×C₄×SD₁₆	—	2	1	no	—
34	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊C₁₆	C₂²	1	2	yes	—
37	C₃×#358	C₂²	1	2	yes	—
38	C₃×#358	C₂²	1	2	yes	—
39	C₃×#357	C₂²	1	2	yes	—
40	C₃×#357	C₂²	1	2	yes	—
41	C₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
42	C₃×#346	C₂²	1	1	yes	characteristic
43	C₃×#346	C₂²	1	1	yes	characteristic
44	#3168	C₂×C₃	1	1	yes	characteristic, complemented
45	#3147	C₂×C₃	1	1	yes	characteristic, complemented
46	#2251	C₂×C₃	1	1	yes	characteristic, complemented
47	#2250	C₂×C₃	1	1	yes	characteristic, complemented
48	#2245	C₂×C₃	1	1	yes	characteristic, complemented
49	#2244	C₂×C₃	1	1	yes	characteristic, complemented
50	#2211	C₂×C₃	1	2	yes	complemented
51	#2210	C₂×C₃	1	2	yes	complemented
52	#2189	C₂×C₃	1	2	yes	complemented
53	#2186	C₂×C₃	1	2	yes	complemented
54	#2163	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₃×#41	—	2	2	no	—
56	C₃×#135	—	4	2	no	—
57	C₃×#135	—	4	2	no	—
58	C₃×#135	—	4	4	no	—
59	C₂×C₃×Q₁₆	—	2	1	no	—
60	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
62	C₂×C₃×SD₁₆	—	2	2	no	—
63	C₂×C₃×SD₁₆	—	2	2	no	—
64	C₂×C₃×SD₁₆	—	2	1	no	—
65	C₂×C₃×D₈	—	2	1	no	—
66	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×D₈	C₂³	1	2	yes	—
68	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
69	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
70	C₃×C₄⋊Q₈	—	2	1	no	—
71	C₃×#127	—	2	1	no	—
72	C₃×#126	—	4	1	no	—
73	C₃×#125	—	2	1	no	—
74	C₃×#124	—	2	1	no	—
75	C₃×#124	—	2	2	no	—
76	C₃×#123	—	4	1	no	—
77	C₃×C₂²⋊Q₈	—	2	1	no	—
78	C₃×#121	—	2	1	no	—
79	C₃×#121	—	4	1	no	—
80	C₃×#121	—	4	1	no	—
81	C₃×C₄×Q₈	—	2	1	no	—
82	C₃×C₄×D₄	—	2	1	no	—
83	C₃×C₄×D₄	—	4	1	no	—
84	C₃×C₄×D₄	—	4	1	no	—
85	C₃×C₄×D₄	—	4	1	no	—
86	C₃×#117	—	4	1	no	—
87	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
88	C₃×Q₃₂	—	4	2	no	—
89	C₃×SD₃₂	—	4	2	no	—
90	C₃×SD₃₂	—	4	2	no	—
91	C₃×D₁₆	—	4	2	no	—
92	C₂×C₃×C₁₆	C₂³	1	2	yes	—
93	C₂×C₃×C₁₆	C₂³	1	2	yes	—
94	C₃×#107	C₂³	1	1	yes	characteristic
95	C₃×#107	C₂³	1	1	yes	characteristic
96	C₃×#106	—	2	1	no	—
97	C₃×#103	—	2	1	no	—
98	C₃×#103	—	2	1	no	—
99	C₃×#102	—	2	1	no	—
100	C₃×#102	—	2	1	no	—
101	C₃×C₄×C₈	D₄	1	1	yes	characteristic
102	C₃×C₄×C₈	D₄	1	1	yes	characteristic
103	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
104	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
105	C₂×#135	—	2	1	no	—
106	C₂×#135	C₂²×C₃	1	2	yes	—
107	#532	—	2	1	no	—
108	#529	—	2	1	no	—
109	C₂×Q₃₂	C₂²×C₃	1	2	yes	—
110	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
111	C₂×SD₃₂	C₂²×C₃	1	2	yes	—
112	C₂×D₁₆	C₂²×C₃	1	2	yes	—
113	#499	C₂²×C₃	1	1	yes	characteristic
114	#495	—	2	1	no	—
115	#495	C₂²×C₃	1	2	yes	—
116	#495	C₂²×C₃	1	1	yes	characteristic
117	#494	C₂²×C₃	1	1	yes	characteristic
118	#493	C₂²×C₃	1	1	yes	characteristic
119	#492	—	2	1	no	—
120	#488	—	2	1	no	—
121	#467	C₂²×C₃	1	1	yes	characteristic
122	#466	C₂²×C₃	1	1	yes	characteristic
123	#465	—	2	1	no	—
124	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
125	C₄×SD₁₆	—	2	1	no	—
126	C₄×D₈	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
128	C₄⋊C₁₆	C₂²×C₃	1	2	yes	—
129	#358	C₂²×C₃	1	2	yes	—
130	#358	C₂²×C₃	1	2	yes	—
131	#357	C₂²×C₃	1	2	yes	—
132	#357	C₂²×C₃	1	2	yes	—
133	C₂²⋊C₁₆	C₂²×C₃	1	2	yes	—
134	#346	C₂²×C₃	1	1	yes	characteristic
135	#346	C₂²×C₃	1	1	yes	characteristic
136	C₃×#41	—	4	4	no	—
137	C₃×#41	—	4	4	no	—
138	C₂×C₃×Q₈	—	2	1	no	—
139	C₂×C₃×Q₈	—	2	2	no	—
140	C₂×C₃×D₄	—	2	1	no	—
141	C₂×C₃×D₄	—	2	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	1	no	—
146	C₂²×C₃×C₄	—	4	1	no	—
147	C₂²×C₃×C₄	—	4	2	no	—
148	C₂²×C₃×C₄	D₈	1	1	yes	characteristic
149	C₂²×C₃×C₄	D₈	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
151	C₃×Q₁₆	—	2	2	no	—
152	C₃×Q₁₆	—	2	2	no	—
153	C₃×Q₁₆	—	2	2	no	—
154	C₃×Q₁₆	—	4	2	no	—
155	C₃×SD₁₆	—	4	4	no	—
156	C₃×SD₁₆	—	4	4	no	—
157	C₃×SD₁₆	—	4	2	no	—
158	C₃×D₈	—	2	2	no	—
159	C₃×D₈	—	2	2	no	—
160	C₃×D₈	—	2	2	no	—
161	C₃×D₈	—	4	2	no	—
162	C₂×C₃×C₈	—	2	2	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
168	C₃×C₄⋊C₄	—	2	1	no	—
169	C₃×C₄⋊C₄	—	2	1	no	—
170	C₃×C₄⋊C₄	—	4	1	no	—
171	C₃×C₄⋊C₄	—	4	1	no	—
172	C₃×C₄⋊C₄	—	4	1	no	—
173	C₃×C₄⋊C₄	—	4	1	no	—
174	C₃×C₄⋊C₄	—	4	1	no	—
175	C₃×C₄⋊C₄	—	4	1	no	—
176	C₃×C₂²⋊C₄	—	4	1	no	—
177	C₃×C₂²⋊C₄	—	4	1	no	—
178	C₃×C₂²⋊C₄	—	4	1	no	—
179	C₃×C₂²⋊C₄	—	4	1	no	—
180	C₃×C₂²⋊C₄	—	4	2	no	—
181	C₃×C₂²⋊C₄	—	4	2	no	—
182	C₃×C₂²⋊C₄	—	4	1	no	—
183	C₃×C₄²	—	4	1	no	—
184	C₃×C₄²	D₈	1	1	yes	characteristic
185	C₃×C₄²	D₈	1	1	yes	characteristic
186	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
187	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
188	C₃×C₁₆	—	2	2	no	—
189	C₃×C₁₆	—	2	2	no	—
190	C₂×#41	—	2	2	no	—
191	#135	—	4	2	no	—
192	#135	—	4	2	no	—
193	#135	—	4	4	no	—
194	C₂×Q₁₆	—	2	1	no	—
195	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
196	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
197	C₂×SD₁₆	—	2	2	no	—
198	C₂×SD₁₆	—	2	2	no	—
199	C₂×SD₁₆	—	2	1	no	—
200	C₂×D₈	—	2	1	no	—
201	C₂×D₈	C₂³×C₃	1	2	yes	—
202	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
203	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
204	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
205	C₄⋊Q₈	—	2	1	no	—
206	#127	—	2	1	no	—
207	#126	—	4	1	no	—
208	#125	—	2	1	no	—
209	#124	—	2	1	no	—
210	#124	—	2	2	no	—
211	#123	—	4	1	no	—
212	C₂²⋊Q₈	—	2	1	no	—
213	#121	—	2	1	no	—
214	#121	—	4	1	no	—
215	#121	—	4	1	no	—
216	C₄×Q₈	—	2	1	no	—
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	—	4	1	no	—
219	C₄×D₄	—	4	1	no	—
220	C₄×D₄	—	4	1	no	—
221	#117	—	4	1	no	—
222	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
223	Q₃₂	—	4	2	no	—
224	SD₃₂	—	4	2	no	—
225	SD₃₂	—	4	2	no	—
226	D₁₆	—	4	2	no	—
227	C₂×C₁₆	C₂³×C₃	1	2	yes	—
228	C₂×C₁₆	C₂³×C₃	1	2	yes	—
229	#107	C₂³×C₃	1	1	yes	characteristic
230	#107	C₂³×C₃	1	1	yes	characteristic
231	#106	—	2	1	no	—
232	#103	—	2	1	no	—
233	#103	—	2	1	no	—
234	#102	—	2	1	no	—
235	#102	—	2	1	no	—
236	C₄×C₈	C₃×D₄	1	1	yes	characteristic
237	C₄×C₈	C₃×D₄	1	1	yes	characteristic
238	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
239	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
240	C₂³×C₃	—	4	1	no	—
241	C₂³×C₃	—	4	2	no	—
242	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
243	C₃×Q₈	—	4	2	no	—
244	C₃×Q₈	—	4	1	no	—
245	C₃×Q₈	—	4	2	no	—
246	C₃×Q₈	—	4	1	no	—
247	C₃×D₄	—	4	2	no	—
248	C₃×D₄	—	4	1	no	—
249	C₃×D₄	—	4	2	no	—
250	C₃×D₄	—	4	1	no	—
251	C₃×D₄	—	8	2	no	—
252	C₃×D₄	—	8	2	no	—
253	C₃×D₄	—	8	2	no	—
254	C₃×D₄	—	8	4	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	—	4	1	no	—
259	C₂×C₃×C₄	—	4	1	no	—
260	C₂×C₃×C₄	—	4	1	no	—
261	C₂×C₃×C₄	—	4	1	no	—
262	C₂×C₃×C₄	—	4	2	no	—
263	C₂×C₃×C₄	—	8	2	no	—
264	C₂×C₃×C₄	—	8	4	no	—
265	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
271	C₃×C₈	—	2	1	no	—
272	C₃×C₈	—	2	1	no	—
273	C₃×C₈	AGL(1,ℤ/8)	1	2	yes	—
274	C₃×C₈	H(5,𝔽₂)	1	2	yes	—
275	#41	—	4	4	no	—
276	#41	—	4	4	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	C₃×D₈	1	1	yes	characteristic
288	C₂²×C₄	C₃×D₈	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
290	Q₁₆	—	2	2	no	—
291	Q₁₆	—	2	2	no	—
292	Q₁₆	—	2	2	no	—
293	Q₁₆	—	4	2	no	—
294	SD₁₆	—	4	4	no	—
295	SD₁₆	—	4	4	no	—
296	SD₁₆	—	4	2	no	—
297	D₈	—	2	2	no	—
298	D₈	—	2	2	no	—
299	D₈	—	2	2	no	—
300	D₈	—	4	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
304	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
305	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
306	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₄²	—	4	1	no	—
323	C₄²	C₃×D₈	1	1	yes	characteristic
324	C₄²	C₃×D₈	1	1	yes	characteristic
325	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
326	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
327	C₁₆	—	2	2	no	—
328	C₁₆	—	2	2	no	—
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	8	1	no	—
333	C₂²×C₃	—	8	2	no	—
334	C₂²×C₃	—	8	2	no	—
335	C₂²×C₃	—	8	1	no	—
336	C₂²×C₃	—	8	2	no	—
337	C₂²×C₃	—	8	1	no	—
338	C₂²×C₃	C₂²×D₈	1	1	yes	characteristic
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	2	1	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	8	1	no	—
345	C₃×C₄	—	8	1	no	—
346	C₃×C₄	—	8	2	no	—
347	C₃×C₄	—	8	1	no	—
348	C₃×C₄	#535	1	1	yes	characteristic
349	C₃×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
350	C₂³	—	4	1	no	—
351	C₂³	—	4	2	no	—
352	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
353	Q₈	—	4	2	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	1	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	1	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	2	no	—
363	D₄	—	8	4	no	—
364	D₄	—	8	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	4	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
376	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
377	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
378	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
379	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
381	C₈	—	2	1	no	—
382	C₈	—	2	1	no	—
383	C₈	C₃×AGL(1,ℤ/8)	1	2	yes	—
384	C₈	C₃×H(5,𝔽₂)	1	2	yes	—
385	C₂×C₃	—	4	1	no	—
386	C₂×C₃	—	16	1	no	—
387	C₂×C₃	—	16	2	no	—
388	C₂×C₃	#3205	1	1	yes	characteristic
389	C₂×C₃	#3414	1	1	yes	characteristic
390	C₂×C₃	#3414	1	1	yes	characteristic
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	C₂²×C₃×D₈	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	8	1	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	1	no	—
410	C₄	C₃×#535	1	1	yes	characteristic
411	C₄	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
412	C₃	#33785	1	1	yes	characteristic, direct product factor, Sylow
413	C₂	—	4	1	no	—
414	C₂	—	16	1	no	—
415	C₂	—	16	2	no	—
416	C₂	C₃×#3205	1	1	yes	characteristic
417	C₂	C₃×#3414	1	1	yes	characteristic
418	C₂	C₃×#3414	1	1	yes	characteristic

	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 ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3168	C₂	semidirect
2. C₃×#3147	C₂	semidirect
3. C₃×#2251	C₂	semidirect
4. C₃×#2250	C₂	semidirect
5. C₃×#2245	C₂	semidirect
6. C₃×#2244	C₂	semidirect
7. C₃×#2211	C₂	semidirect
8. C₃×#2210	C₂	semidirect
9. C₃×#2189	C₂	semidirect
10. C₃×#2186	C₂	semidirect
11. C₃×#2163	C₂	semidirect
12. #33785	C₃	direct (N × H)
44. #3168	C₂×C₃	semidirect
45. #3147	C₂×C₃	semidirect
46. #2251	C₂×C₃	semidirect
47. #2250	C₂×C₃	semidirect
48. #2245	C₂×C₃	semidirect
49. #2244	C₂×C₃	semidirect
50. #2211	C₂×C₃	semidirect
51. #2210	C₂×C₃	semidirect
52. #2189	C₂×C₃	semidirect
53. #2186	C₂×C₃	semidirect
54. #2163	C₂×C₃	semidirect
412. C₃	#33785	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×#3168	2
C₃×#3147	2
C₃×#2251	2
C₃×#2250	2
C₃×#2245	2
C₃×#2244	2
C₃×#2211	2
C₃×#2210	2
C₃×#2189	2
C₃×#2186	2
C₃×#2163	2
#33785	3

Subgroups — C3×#33785 #10652392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33785 #10652392