Subgroups — C₂×C₃×#1678 #10637726

Order 768.

722 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#486	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#460	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1678	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#331	C₂	1	1	yes	maximal, characteristic
9	C₂×#1678	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₃×SD₁₆	—	2	1	no	—
11	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
14	C₃×#486	—	2	2	no	—
15	C₃×#486	C₂²	1	4	yes	—
16	C₃×#477	—	2	2	no	—
17	C₃×#477	C₂²	1	4	yes	complemented
18	C₃×#460	—	2	2	no	—
19	C₃×#460	C₂²	1	4	yes	—
20	C₃×C₈×Q₈	—	2	2	no	—
21	C₃×C₈×Q₈	C₂²	1	4	yes	complemented
22	C₂×C₃×#107	—	2	1	no	—
23	C₂×C₃×C₄⋊C₈	—	2	1	no	—
24	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×#103	—	2	1	no	—
28	C₂×C₃×#102	—	2	1	no	—
29	C₂×C₃×#102	—	2	1	no	—
30	C₂×C₃×#102	—	2	1	no	—
31	C₂×C₃×C₄×C₈	—	2	1	no	—
32	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
33	C₃×#334	C₂²	1	4	yes	complemented
34	C₃×#333	C₂²	1	4	yes	complemented
35	C₃×#331	C₂²	1	4	yes	—
36	C₂×#486	C₂×C₃	1	1	yes	characteristic
37	C₂×#477	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#460	C₂×C₃	1	1	yes	characteristic
39	C₂×C₈×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
40	#1678	C₂×C₃	1	8	yes	direct product factor
41	C₂×#334	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×#333	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#331	C₂×C₃	1	1	yes	characteristic
44	C₂²×C₃×Q₈	—	2	1	no	—
45	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
46	C₂²×C₃×D₄	—	2	1	no	—
47	C₂²×C₃×D₄	—	2	1	no	—
48	C₂²×C₃×D₄	—	2	1	no	—
49	C₂×C₃×SD₁₆	—	2	4	no	—
50	C₂×C₃×SD₁₆	—	4	4	no	—
51	C₂²×C₃×C₈	—	2	1	no	—
52	C₂²×C₃×C₈	—	2	1	no	—
53	C₂²×C₃×C₈	—	2	1	no	—
54	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
55	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
56	C₃×C₄⋊Q₈	—	2	1	no	—
57	C₃×C₄⋊Q₈	—	2	1	no	—
58	C₃×C₄⋊Q₈	—	2	1	no	—
59	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₃×#127	—	2	1	no	—
61	C₃×#127	—	2	1	no	—
62	C₃×#127	—	2	1	no	—
63	C₃×#127	C₂³	1	2	yes	—
64	C₃×C₄×Q₈	—	2	1	no	—
65	C₃×C₄×Q₈	—	2	1	no	—
66	C₃×C₄×Q₈	D₄	1	2	yes	—
67	C₃×C₄×Q₈	C₂³	1	2	yes	—
68	C₂×C₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₃×C₄²	—	2	1	no	—
73	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
74	C₃×#107	—	2	4	no	—
75	C₃×C₄⋊C₈	—	2	4	no	—
76	C₃×C₄⋊C₈	—	2	1	no	—
77	C₃×C₄⋊C₈	—	2	1	no	—
78	C₃×C₄⋊C₈	—	2	1	no	—
79	C₃×C₄⋊C₈	C₂³	1	2	yes	—
80	C₃×C₄⋊C₈	C₂³	1	2	yes	—
81	C₃×C₄⋊C₈	C₂³	1	2	yes	—
82	C₃×#103	—	2	4	no	—
83	C₃×#102	—	2	4	no	—
84	C₃×#102	—	2	4	no	—
85	C₃×#102	—	2	4	no	—
86	C₃×C₄×C₈	—	2	4	no	—
87	C₃×C₄×C₈	D₄	1	2	yes	—
88	C₃×C₄×C₈	C₂³	1	2	yes	—
89	C₂²×SD₁₆	—	2	1	no	—
90	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
91	C₂×#127	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
93	#486	—	2	2	no	—
94	#486	C₂²×C₃	1	4	yes	—
95	#477	—	2	2	no	—
96	#477	C₂²×C₃	1	4	yes	complemented
97	#460	—	2	2	no	—
98	#460	C₂²×C₃	1	4	yes	—
99	C₈×Q₈	—	2	2	no	—
100	C₈×Q₈	C₂²×C₃	1	4	yes	complemented
101	C₂×#107	—	2	1	no	—
102	C₂×C₄⋊C₈	—	2	1	no	—
103	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
106	C₂×#103	—	2	1	no	—
107	C₂×#102	—	2	1	no	—
108	C₂×#102	—	2	1	no	—
109	C₂×#102	—	2	1	no	—
110	C₂×C₄×C₈	—	2	1	no	—
111	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
112	#334	C₂²×C₃	1	4	yes	complemented
113	#333	C₂²×C₃	1	4	yes	complemented
114	#331	C₂²×C₃	1	4	yes	—
115	C₂⁴×C₃	—	4	1	no	—
116	C₂×C₃×Q₈	—	2	1	no	—
117	C₂×C₃×Q₈	—	2	2	no	—
118	C₂×C₃×Q₈	—	2	2	no	—
119	C₂×C₃×Q₈	—	4	1	no	—
120	C₂×C₃×Q₈	—	8	2	no	—
121	C₂×C₃×Q₈	SD₁₆	1	4	yes	—
122	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
123	C₂×C₃×D₄	—	2	2	no	—
124	C₂×C₃×D₄	—	2	2	no	—
125	C₂×C₃×D₄	—	2	2	no	—
126	C₂×C₃×D₄	—	4	1	no	—
127	C₂×C₃×D₄	—	4	1	no	—
128	C₂×C₃×D₄	—	4	1	no	—
129	C₂×C₃×D₄	—	4	2	no	—
130	C₂×C₃×D₄	—	4	2	no	—
131	C₂×C₃×D₄	—	4	2	no	—
132	C₂×C₃×D₄	—	4	2	no	—
133	C₂×C₃×D₄	—	8	2	no	—
134	C₂²×C₃×C₄	—	2	1	no	—
135	C₂²×C₃×C₄	—	2	1	no	—
136	C₂²×C₃×C₄	—	4	1	no	—
137	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₃×C₄	#41	1	1	yes	characteristic
140	C₃×SD₁₆	—	4	8	no	—
141	C₂×C₃×C₈	—	2	2	no	—
142	C₂×C₃×C₈	—	2	2	no	—
143	C₂×C₃×C₈	—	2	2	no	—
144	C₂×C₃×C₈	—	2	2	no	—
145	C₂×C₃×C₈	—	2	2	no	—
146	C₂×C₃×C₈	—	4	2	no	—
147	C₂×C₃×C₈	—	4	2	no	—
148	C₂×C₃×C₈	—	4	2	no	—
149	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
150	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
151	C₃×C₄⋊C₄	—	2	2	no	—
152	C₃×C₄⋊C₄	—	2	1	no	—
153	C₃×C₄⋊C₄	—	2	2	no	—
154	C₃×C₄⋊C₄	—	2	2	no	—
155	C₃×C₄⋊C₄	—	2	2	no	—
156	C₃×C₄⋊C₄	—	4	1	no	—
157	C₃×C₄⋊C₄	—	4	1	no	—
158	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
159	C₃×C₄²	—	2	2	no	—
160	C₃×C₄²	—	2	2	no	—
161	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
162	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
163	C₃×C₄²	#41	1	1	yes	characteristic
164	C₃×C₄²	C₂⁴	1	1	yes	characteristic
165	C₂²×Q₈	—	2	1	no	—
166	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
167	C₂²×D₄	—	2	1	no	—
168	C₂²×D₄	—	2	1	no	—
169	C₂²×D₄	—	2	1	no	—
170	C₂×SD₁₆	—	2	4	no	—
171	C₂×SD₁₆	—	4	4	no	—
172	C₂²×C₈	—	2	1	no	—
173	C₂²×C₈	—	2	1	no	—
174	C₂²×C₈	—	2	1	no	—
175	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
176	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
177	C₄⋊Q₈	—	2	1	no	—
178	C₄⋊Q₈	—	2	1	no	—
179	C₄⋊Q₈	—	2	1	no	—
180	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
181	#127	—	2	1	no	—
182	#127	—	2	1	no	—
183	#127	—	2	1	no	—
184	#127	C₂³×C₃	1	2	yes	—
185	C₄×Q₈	—	2	1	no	—
186	C₄×Q₈	—	2	1	no	—
187	C₄×Q₈	C₃×D₄	1	2	yes	—
188	C₄×Q₈	C₂³×C₃	1	2	yes	—
189	C₂×C₄⋊C₄	—	2	1	no	—
190	C₂×C₄⋊C₄	—	2	1	no	—
191	C₂×C₄⋊C₄	—	2	1	no	—
192	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
193	C₂×C₄²	—	2	1	no	—
194	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
195	#107	—	2	4	no	—
196	C₄⋊C₈	—	2	4	no	—
197	C₄⋊C₈	—	2	1	no	—
198	C₄⋊C₈	—	2	1	no	—
199	C₄⋊C₈	—	2	1	no	—
200	C₄⋊C₈	C₂³×C₃	1	2	yes	—
201	C₄⋊C₈	C₂³×C₃	1	2	yes	—
202	C₄⋊C₈	C₂³×C₃	1	2	yes	—
203	#103	—	2	4	no	—
204	#102	—	2	4	no	—
205	#102	—	2	4	no	—
206	#102	—	2	4	no	—
207	C₄×C₈	—	2	4	no	—
208	C₄×C₈	C₃×D₄	1	2	yes	—
209	C₄×C₈	C₂³×C₃	1	2	yes	—
210	C₂³×C₃	—	4	2	no	—
211	C₂³×C₃	—	8	2	no	—
212	C₂³×C₃	—	8	2	no	—
213	C₂³×C₃	—	8	2	no	—
214	C₂³×C₃	#121	1	1	yes	characteristic
215	C₃×Q₈	—	2	2	no	—
216	C₃×Q₈	—	2	4	no	—
217	C₃×Q₈	—	8	2	no	—
218	C₃×Q₈	—	8	2	no	—
219	C₃×Q₈	C₂×SD₁₆	1	4	yes	—
220	C₃×D₄	—	4	2	no	—
221	C₃×D₄	—	4	2	no	—
222	C₃×D₄	—	4	2	no	—
223	C₃×D₄	—	4	2	no	—
224	C₃×D₄	—	8	2	no	—
225	C₃×D₄	—	8	2	no	—
226	C₃×D₄	—	8	2	no	—
227	C₃×D₄	—	8	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	4	2	no	—
233	C₂×C₃×C₄	—	4	2	no	—
234	C₂×C₃×C₄	—	8	2	no	—
235	C₂×C₃×C₄	#121	1	1	yes	characteristic
236	C₂×C₃×C₄	#121	1	1	yes	characteristic
237	C₂×C₃×C₄	#121	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂×SD₁₆	1	2	yes	—
239	C₂×C₃×C₄	#135	1	2	yes	—
240	C₂×C₃×C₄	#135	1	2	yes	—
241	C₂×C₃×C₄	#137	1	2	yes	—
242	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
245	C₃×C₈	—	2	2	no	—
246	C₃×C₈	—	2	2	no	—
247	C₃×C₈	—	4	2	no	—
248	C₃×C₈	—	4	2	no	—
249	C₃×C₈	—	4	2	no	—
250	C₂⁴	—	4	1	no	—
251	C₂×Q₈	—	2	1	no	—
252	C₂×Q₈	—	2	2	no	—
253	C₂×Q₈	—	2	2	no	—
254	C₂×Q₈	—	4	1	no	—
255	C₂×Q₈	—	8	2	no	—
256	C₂×Q₈	C₃×SD₁₆	1	4	yes	—
257	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	4	1	no	—
262	C₂×D₄	—	4	1	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂×D₄	—	4	2	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	8	2	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
274	C₂²×C₄	C₃×#41	1	1	yes	characteristic
275	SD₁₆	—	4	8	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	4	2	no	—
282	C₂×C₈	—	4	2	no	—
283	C₂×C₈	—	4	2	no	—
284	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
285	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	—	4	1	no	—
293	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
297	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
298	C₄²	C₃×#41	1	1	yes	characteristic
299	C₄²	C₂⁴×C₃	1	1	yes	characteristic
300	C₂²×C₃	—	8	2	no	—
301	C₂²×C₃	—	8	2	no	—
302	C₂²×C₃	—	8	2	no	—
303	C₂²×C₃	—	16	4	no	—
304	C₂²×C₃	#464	1	2	yes	—
305	C₂²×C₃	#465	1	2	yes	—
306	C₂²×C₃	#472	1	2	yes	—
307	C₂²×C₃	C₂×#121	1	1	yes	characteristic
308	C₃×C₄	—	2	4	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	4	2	no	—
312	C₃×C₄	—	8	2	no	—
313	C₃×C₄	#464	1	2	yes	—
314	C₃×C₄	#465	1	2	yes	—
315	C₃×C₄	C₂²×SD₁₆	1	1	yes	characteristic
316	C₃×C₄	C₂×#135	1	1	yes	characteristic
317	C₃×C₄	C₂×#135	1	1	yes	characteristic
318	C₃×C₄	C₂×#137	1	1	yes	characteristic
319	C₂³	—	4	2	no	—
320	C₂³	—	8	2	no	—
321	C₂³	—	8	2	no	—
322	C₂³	—	8	2	no	—
323	C₂³	C₃×#121	1	1	yes	characteristic
324	Q₈	—	2	2	no	—
325	Q₈	—	2	4	no	—
326	Q₈	—	8	2	no	—
327	Q₈	—	8	2	no	—
328	Q₈	C₂×C₃×SD₁₆	1	4	yes	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	8	2	no	—
334	D₄	—	8	2	no	—
335	D₄	—	8	2	no	—
336	D₄	—	8	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	C₃×#121	1	1	yes	characteristic
345	C₂×C₄	C₃×#121	1	1	yes	characteristic
346	C₂×C₄	C₃×#121	1	1	yes	characteristic
347	C₂×C₄	C₂×C₃×SD₁₆	1	2	yes	—
348	C₂×C₄	C₃×#135	1	2	yes	—
349	C₂×C₄	C₃×#135	1	2	yes	—
350	C₂×C₄	C₃×#137	1	2	yes	—
351	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
352	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
353	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	—	2	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	2	no	—
359	C₂×C₃	—	16	2	no	—
360	C₂×C₃	#1678	1	4	yes	direct product factor
361	C₂×C₃	C₂×#464	1	1	yes	characteristic
362	C₂×C₃	C₂×#465	1	1	yes	characteristic
363	C₂×C₃	C₂×#472	1	1	yes	characteristic
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	16	4	no	—
368	C₂²	C₃×#464	1	2	yes	—
369	C₂²	C₃×#465	1	2	yes	—
370	C₂²	C₃×#472	1	2	yes	—
371	C₂²	C₂×C₃×#121	1	1	yes	characteristic
372	C₄	—	2	4	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	8	2	no	—
377	C₄	C₃×#464	1	2	yes	—
378	C₄	C₃×#465	1	2	yes	—
379	C₄	C₂²×C₃×SD₁₆	1	1	yes	characteristic
380	C₄	C₂×C₃×#135	1	1	yes	characteristic
381	C₄	C₂×C₃×#135	1	1	yes	characteristic
382	C₄	C₂×C₃×#137	1	1	yes	characteristic
383	C₃	C₂×#1678	1	1	yes	characteristic, direct product factor, Sylow
384	C₂	—	16	2	no	—
385	C₂	C₃×#1678	1	4	yes	direct product factor
386	C₂	C₂×C₃×#464	1	1	yes	characteristic
387	C₂	C₂×C₃×#465	1	1	yes	characteristic
388	C₂	C₂×C₃×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃
prime radical	C₂×C₃×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#477	C₂	semidirect
4. C₂×C₃×C₈×Q₈	C₂	semidirect
5. C₃×#1678	C₂	direct (N × H)
6. C₂×C₃×#334	C₂	semidirect
7. C₂×C₃×#333	C₂	semidirect
9. C₂×#1678	C₃	direct (N × H)
17. C₃×#477	C₂²	semidirect
21. C₃×C₈×Q₈	C₂²	semidirect
33. C₃×#334	C₂²	semidirect
34. C₃×#333	C₂²	semidirect
37. C₂×#477	C₂×C₃	semidirect
39. C₂×C₈×Q₈	C₂×C₃	semidirect
40. #1678	C₂×C₃	direct (N × H)
41. C₂×#334	C₂×C₃	semidirect
42. C₂×#333	C₂×C₃	semidirect
96. #477	C₂²×C₃	semidirect
100. C₈×Q₈	C₂²×C₃	semidirect
112. #334	C₂²×C₃	semidirect
113. #333	C₂²×C₃	semidirect
360. C₂×C₃	#1678	direct (N × H)
383. C₃	C₂×#1678	direct (N × H)
385. C₂	C₃×#1678	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×#486	2
C₂×C₃×#477	2
C₂×C₃×#460	2
C₂×C₃×C₈×Q₈	2
C₃×#1678	2
C₂×C₃×#334	2
C₂×C₃×#333	2
C₂×C₃×#331	2
C₂×#1678	3

Subgroups — C2×C3×#1678 #10637726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#1678 #10637726