Subgroups — C₃×#33580 #10652187

Order 768.

770 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#509	C₂	1	2	yes	maximal, complemented
2	C₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2210	C₂	1	4	yes	maximal, complemented
5	C₃×#2208	C₂	1	2	yes	maximal, complemented
6	C₃×#2206	C₂	1	2	yes	maximal, complemented
7	C₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2139	C₂	1	2	yes	maximal, complemented
9	#33580	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₃×#135	—	2	1	no	—
11	C₂×C₃×#135	C₂²	1	2	yes	—
12	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic
13	C₃×#532	—	2	1	no	—
14	C₂×C₃×C₄×D₄	—	2	1	no	—
15	C₃×#509	—	2	8	no	—
16	C₂×C₃×SD₃₂	C₂²	1	4	yes	—
17	C₂×C₃×D₁₆	C₂²	1	4	yes	—
18	C₂×C₃×M₃₂	C₂²	1	2	yes	—
19	C₃×#495	—	2	1	no	—
20	C₃×#495	C₂²	1	2	yes	complemented
21	C₃×#494	C₂²	1	1	yes	characteristic, complemented
22	C₃×#493	C₂²	1	1	yes	characteristic, complemented
23	C₃×#492	—	2	1	no	—
24	C₃×C₄×D₈	—	2	1	no	—
25	C₃×C₄×D₈	—	2	1	no	—
26	C₃×C₄×D₈	C₂²	1	2	yes	—
27	C₃×C₄×D₈	C₂²	1	2	yes	—
28	C₂×C₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₃×#102	—	2	1	no	—
30	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
32	C₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
33	C₃×#358	C₂²	1	4	yes	complemented
34	C₃×#357	C₂²	1	4	yes	complemented
35	C₂×#509	C₂×C₃	1	2	yes	complemented
36	#3147	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×C₄×D₈	C₂×C₃	1	1	yes	characteristic, complemented
38	#2210	C₂×C₃	1	4	yes	complemented
39	#2208	C₂×C₃	1	2	yes	complemented
40	#2206	C₂×C₃	1	2	yes	complemented
41	#2150	C₂×C₃	1	1	yes	characteristic, complemented
42	#2139	C₂×C₃	1	2	yes	complemented
43	C₂×C₃×#41	—	2	2	no	—
44	C₂²×C₃×D₄	—	2	1	no	—
45	C₂³×C₃×C₄	—	4	1	no	—
46	C₃×#135	—	2	4	no	—
47	C₃×#135	—	2	4	no	—
48	C₃×#135	—	4	4	no	—
49	C₂×C₃×Q₁₆	—	2	1	no	—
50	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
51	C₂×C₃×SD₁₆	—	2	2	no	—
52	C₂×C₃×SD₁₆	—	2	2	no	—
53	C₂×C₃×D₈	—	2	1	no	—
54	C₂×C₃×D₈	—	2	1	no	—
55	C₂×C₃×D₈	—	2	2	no	—
56	C₂×C₃×D₈	D₄	1	4	yes	complemented
57	C₂×C₃×D₈	C₂³	1	2	yes	—
58	C₂×C₃×D₈	C₂³	1	2	yes	—
59	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
60	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
61	C₃×C₄⋊Q₈	—	2	1	no	—
62	C₃×#127	—	2	1	no	—
63	C₃×#124	—	2	2	no	—
64	C₃×#121	—	4	1	no	—
65	C₃×#121	—	4	1	no	—
66	C₃×C₄×D₄	—	2	2	no	—
67	C₃×C₄×D₄	—	2	2	no	—
68	C₃×C₄×D₄	—	4	1	no	—
69	C₃×C₄×D₄	—	4	1	no	—
70	C₃×C₄×D₄	—	4	1	no	—
71	C₃×C₄×D₄	—	4	1	no	—
72	C₂×C₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₃×C₂²⋊C₄	—	4	1	no	—
74	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
75	C₃×SD₃₂	—	2	8	no	—
76	C₃×D₁₆	—	2	8	no	—
77	C₃×M₃₂	—	2	4	no	—
78	C₂×C₃×C₁₆	C₂³	1	4	yes	—
79	C₃×#107	—	2	1	no	—
80	C₃×#107	C₂³	1	2	yes	—
81	C₃×#102	—	2	2	no	—
82	C₃×#102	—	2	2	no	—
83	C₃×C₄×C₈	D₄	1	1	yes	characteristic
84	C₃×C₄×C₈	D₄	1	1	yes	characteristic
85	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
86	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
87	C₂×#135	—	2	1	no	—
88	C₂×#135	C₂²×C₃	1	2	yes	—
89	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic
90	#532	—	2	1	no	—
91	C₂×C₄×D₄	—	2	1	no	—
92	#509	—	2	8	no	—
93	C₂×SD₃₂	C₂²×C₃	1	4	yes	—
94	C₂×D₁₆	C₂²×C₃	1	4	yes	—
95	C₂×M₃₂	C₂²×C₃	1	2	yes	—
96	#495	—	2	1	no	—
97	#495	C₂²×C₃	1	2	yes	complemented
98	#494	C₂²×C₃	1	1	yes	characteristic, complemented
99	#493	C₂²×C₃	1	1	yes	characteristic, complemented
100	#492	—	2	1	no	—
101	C₄×D₈	—	2	1	no	—
102	C₄×D₈	—	2	1	no	—
103	C₄×D₈	C₂²×C₃	1	2	yes	—
104	C₄×D₈	C₂²×C₃	1	2	yes	—
105	C₂×#107	C₂²×C₃	1	1	yes	characteristic
106	C₂×#102	—	2	1	no	—
107	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
108	C₄⋊C₁₆	C₂²×C₃	1	2	yes	complemented
109	C₄⋊C₁₆	C₂²×C₃	1	2	yes	complemented
110	#358	C₂²×C₃	1	4	yes	complemented
111	#357	C₂²×C₃	1	4	yes	complemented
112	C₂⁴×C₃	—	4	1	no	—
113	C₃×#41	—	4	4	no	—
114	C₃×#41	—	4	4	no	—
115	C₂×C₃×Q₈	—	2	2	no	—
116	C₂×C₃×D₄	—	2	4	no	—
117	C₂×C₃×D₄	—	2	2	no	—
118	C₂×C₃×D₄	—	2	2	no	—
119	C₂×C₃×D₄	—	4	2	no	—
120	C₂×C₃×D₄	—	4	1	no	—
121	C₂×C₃×D₄	—	4	1	no	—
122	C₂×C₃×D₄	—	4	1	no	—
123	C₂×C₃×D₄	—	4	2	no	—
124	C₂²×C₃×C₄	—	4	1	no	—
125	C₂²×C₃×C₄	—	4	2	no	—
126	C₂²×C₃×C₄	—	4	2	no	—
127	C₂²×C₃×C₄	—	4	2	no	—
128	C₂²×C₃×C₄	—	8	4	no	—
129	C₂²×C₃×C₄	D₈	1	1	yes	characteristic
130	C₂²×C₃×C₄	D₈	1	1	yes	characteristic
131	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
132	C₃×Q₁₆	—	2	2	no	—
133	C₃×Q₁₆	—	2	2	no	—
134	C₃×Q₁₆	—	4	2	no	—
135	C₃×SD₁₆	—	4	4	no	—
136	C₃×SD₁₆	—	4	4	no	—
137	C₃×D₈	—	2	4	no	—
138	C₃×D₈	—	2	2	no	—
139	C₃×D₈	—	2	2	no	—
140	C₃×D₈	—	2	2	no	—
141	C₃×D₈	—	4	2	no	—
142	C₃×D₈	C₂×D₄	1	4	yes	—
143	C₂×C₃×C₈	—	2	2	no	—
144	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
148	C₂×C₃×C₈	#41	1	2	yes	—
149	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
150	C₃×C₄⋊C₄	—	2	2	no	—
151	C₃×C₄⋊C₄	—	4	1	no	—
152	C₃×C₄⋊C₄	—	4	1	no	—
153	C₃×C₄⋊C₄	—	4	1	no	—
154	C₃×C₂²⋊C₄	—	4	2	no	—
155	C₃×C₂²⋊C₄	—	4	2	no	—
156	C₃×C₂²⋊C₄	—	4	2	no	—
157	C₃×C₂²⋊C₄	—	4	2	no	—
158	C₃×C₄²	D₈	1	1	yes	characteristic
159	C₃×C₄²	D₈	1	1	yes	characteristic
160	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
161	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
162	C₃×C₁₆	—	2	4	no	—
163	C₂×#41	—	2	2	no	—
164	C₂²×D₄	—	2	1	no	—
165	C₂³×C₄	—	4	1	no	—
166	#135	—	2	4	no	—
167	#135	—	2	4	no	—
168	#135	—	4	4	no	—
169	C₂×Q₁₆	—	2	1	no	—
170	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
171	C₂×SD₁₆	—	2	2	no	—
172	C₂×SD₁₆	—	2	2	no	—
173	C₂×D₈	—	2	1	no	—
174	C₂×D₈	—	2	1	no	—
175	C₂×D₈	—	2	2	no	—
176	C₂×D₈	C₃×D₄	1	4	yes	complemented
177	C₂×D₈	C₂³×C₃	1	2	yes	—
178	C₂×D₈	C₂³×C₃	1	2	yes	—
179	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
180	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
181	C₄⋊Q₈	—	2	1	no	—
182	#127	—	2	1	no	—
183	#124	—	2	2	no	—
184	#121	—	4	1	no	—
185	#121	—	4	1	no	—
186	C₄×D₄	—	2	2	no	—
187	C₄×D₄	—	2	2	no	—
188	C₄×D₄	—	4	1	no	—
189	C₄×D₄	—	4	1	no	—
190	C₄×D₄	—	4	1	no	—
191	C₄×D₄	—	4	1	no	—
192	C₂×C₄⋊C₄	—	2	1	no	—
193	C₂×C₂²⋊C₄	—	4	1	no	—
194	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
195	SD₃₂	—	2	8	no	—
196	D₁₆	—	2	8	no	—
197	M₃₂	—	2	4	no	—
198	C₂×C₁₆	C₂³×C₃	1	4	yes	—
199	#107	—	2	1	no	—
200	#107	C₂³×C₃	1	2	yes	—
201	#102	—	2	2	no	—
202	#102	—	2	2	no	—
203	C₄×C₈	C₃×D₄	1	1	yes	characteristic
204	C₄×C₈	C₃×D₄	1	1	yes	characteristic
205	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
206	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
207	C₂³×C₃	—	4	2	no	—
208	C₂³×C₃	—	4	4	no	—
209	C₂³×C₃	—	4	2	no	—
210	C₂³×C₃	—	8	2	no	—
211	C₂³×C₃	—	8	2	no	—
212	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
213	C₃×Q₈	—	4	2	no	—
214	C₃×Q₈	—	4	2	no	—
215	C₃×D₄	—	2	4	no	—
216	C₃×D₄	—	4	2	no	—
217	C₃×D₄	—	4	2	no	—
218	C₃×D₄	—	4	2	no	—
219	C₃×D₄	—	4	4	no	—
220	C₃×D₄	—	8	2	no	—
221	C₃×D₄	—	8	4	no	—
222	C₃×D₄	—	8	2	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	4	1	no	—
225	C₂×C₃×C₄	—	4	2	no	—
226	C₂×C₃×C₄	—	4	2	no	—
227	C₂×C₃×C₄	—	8	4	no	—
228	C₂×C₃×C₄	—	8	2	no	—
229	C₂×C₃×C₄	—	8	4	no	—
230	C₂×C₃×C₄	—	8	4	no	—
231	C₂×C₃×C₄	#121	1	2	yes	—
232	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
237	C₂×C₃×C₄	AGL(1,ℤ/8)	1	2	yes	—
238	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
239	C₃×C₈	—	2	1	no	—
240	C₃×C₈	—	2	1	no	—
241	C₃×C₈	#121	1	2	yes	—
242	C₃×C₈	C₂²×D₄	1	1	yes	characteristic
243	C₃×C₈	C₂×#41	1	1	yes	characteristic
244	C₂⁴	—	4	1	no	—
245	#41	—	4	4	no	—
246	#41	—	4	4	no	—
247	C₂×Q₈	—	2	2	no	—
248	C₂×D₄	—	2	4	no	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	4	2	no	—
252	C₂×D₄	—	4	1	no	—
253	C₂×D₄	—	4	1	no	—
254	C₂×D₄	—	4	1	no	—
255	C₂×D₄	—	4	2	no	—
256	C₂²×C₄	—	4	1	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	8	4	no	—
261	C₂²×C₄	C₃×D₈	1	1	yes	characteristic
262	C₂²×C₄	C₃×D₈	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
264	Q₁₆	—	2	2	no	—
265	Q₁₆	—	2	2	no	—
266	Q₁₆	—	4	2	no	—
267	SD₁₆	—	4	4	no	—
268	SD₁₆	—	4	4	no	—
269	D₈	—	2	4	no	—
270	D₈	—	2	2	no	—
271	D₈	—	2	2	no	—
272	D₈	—	2	2	no	—
273	D₈	—	4	2	no	—
274	D₈	C₂×C₃×D₄	1	4	yes	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
277	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
278	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
279	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
280	C₂×C₈	C₃×#41	1	2	yes	—
281	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	4	1	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₂²⋊C₄	—	4	2	no	—
287	C₂²⋊C₄	—	4	2	no	—
288	C₂²⋊C₄	—	4	2	no	—
289	C₂²⋊C₄	—	4	2	no	—
290	C₄²	C₃×D₈	1	1	yes	characteristic
291	C₄²	C₃×D₈	1	1	yes	characteristic
292	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
293	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
294	C₁₆	—	2	4	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	4	4	no	—
298	C₂²×C₃	—	8	8	no	—
299	C₂²×C₃	—	8	2	no	—
300	C₂²×C₃	—	8	2	no	—
301	C₂²×C₃	—	8	2	no	—
302	C₂²×C₃	—	8	2	no	—
303	C₂²×C₃	—	8	2	no	—
304	C₂²×C₃	#459	1	2	yes	—
305	C₂²×C₃	C₂²×D₈	1	1	yes	characteristic
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	8	2	no	—
310	C₃×C₄	—	8	2	no	—
311	C₃×C₄	#459	1	2	yes	—
312	C₃×C₄	#509	1	2	yes	complemented
313	C₃×C₄	C₂×#121	1	1	yes	characteristic
314	C₃×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
315	C₂³	—	4	2	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	8	2	no	—
319	C₂³	—	8	2	no	—
320	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
321	Q₈	—	4	2	no	—
322	Q₈	—	4	2	no	—
323	D₄	—	2	4	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	4	no	—
330	D₄	—	8	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	8	4	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	—	8	4	no	—
338	C₂×C₄	—	8	4	no	—
339	C₂×C₄	C₃×#121	1	2	yes	—
340	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
341	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
342	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
344	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
345	C₂×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
346	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
347	C₈	—	2	1	no	—
348	C₈	—	2	1	no	—
349	C₈	C₃×#121	1	2	yes	—
350	C₈	C₂²×C₃×D₄	1	1	yes	characteristic
351	C₈	C₂×C₃×#41	1	1	yes	characteristic
352	C₂×C₃	—	2	2	no	—
353	C₂×C₃	—	8	4	no	—
354	C₂×C₃	—	16	2	no	—
355	C₂×C₃	C₂×#459	1	1	yes	characteristic
356	C₂×C₃	C₂×#509	1	1	yes	characteristic
357	C₂×C₃	#3414	1	1	yes	characteristic
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	8	8	no	—
362	C₂²	—	8	2	no	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	C₃×#459	1	2	yes	—
368	C₂²	C₂²×C₃×D₈	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	8	2	no	—
373	C₄	—	8	2	no	—
374	C₄	C₃×#459	1	2	yes	—
375	C₄	C₃×#509	1	2	yes	complemented
376	C₄	C₂×C₃×#121	1	1	yes	characteristic
377	C₄	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₃	#33580	1	1	yes	characteristic, direct product factor, Sylow
379	C₂	—	2	2	no	—
380	C₂	—	8	4	no	—
381	C₂	—	16	2	no	—
382	C₂	C₂×C₃×#459	1	1	yes	characteristic
383	C₂	C₂×C₃×#509	1	1	yes	characteristic
384	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. C₂×C₃×#509	C₂	semidirect
2. C₃×#3147	C₂	semidirect
3. C₂×C₃×C₄×D₈	C₂	semidirect
4. C₃×#2210	C₂	semidirect
5. C₃×#2208	C₂	semidirect
6. C₃×#2206	C₂	semidirect
7. C₃×#2150	C₂	semidirect
8. C₃×#2139	C₂	semidirect
9. #33580	C₃	direct (N × H)
20. C₃×#495	C₂²	semidirect
21. C₃×#494	C₂²	semidirect
22. C₃×#493	C₂²	semidirect
31. C₃×C₄⋊C₁₆	C₂²	semidirect
32. C₃×C₄⋊C₁₆	C₂²	semidirect
33. C₃×#358	C₂²	semidirect
34. C₃×#357	C₂²	semidirect
35. C₂×#509	C₂×C₃	semidirect
36. #3147	C₂×C₃	semidirect
37. C₂×C₄×D₈	C₂×C₃	semidirect
38. #2210	C₂×C₃	semidirect
39. #2208	C₂×C₃	semidirect
40. #2206	C₂×C₃	semidirect
41. #2150	C₂×C₃	semidirect
42. #2139	C₂×C₃	semidirect
56. C₂×C₃×D₈	D₄	semidirect
97. #495	C₂²×C₃	semidirect
98. #494	C₂²×C₃	semidirect
99. #493	C₂²×C₃	semidirect
108. C₄⋊C₁₆	C₂²×C₃	semidirect
109. C₄⋊C₁₆	C₂²×C₃	semidirect
110. #358	C₂²×C₃	semidirect
111. #357	C₂²×C₃	semidirect
176. C₂×D₈	C₃×D₄	semidirect
312. C₃×C₄	#509	semidirect
375. C₄	C₃×#509	semidirect
378. C₃	#33580	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×C₃×#509	2
C₃×#3147	2
C₂×C₃×C₄×D₈	2
C₃×#2210	2
C₃×#2208	2
C₃×#2206	2
C₃×#2150	2
C₃×#2139	2
#33580	3

Subgroups — C3×#33580 #10652187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33580 #10652187