Subgroups — C₃×#60471 #10679078

Order 768.

2630 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3585	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3573	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3068	C₂	1	12	yes	maximal, complemented
5	C₃×#3067	C₂	1	6	yes	maximal, complemented
6	C₂×C₃×#472	C₂	1	6	yes	maximal, complemented
7	C₃×#2916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2888	C₂	1	2	yes	maximal, complemented
9	#60471	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃×#585	C₂²	1	1	yes	characteristic
11	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	—
12	C₃×#577	—	2	8	no	—
13	C₃×#576	—	2	8	no	—
14	C₃×#576	—	2	4	no	—
15	C₃×#576	—	2	4	no	—
16	C₃×#575	C₂²	1	12	yes	complemented
17	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	12	yes	complemented
18	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
19	C₂×C₃×#135	C₂²	1	3	yes	complemented
20	C₂²×C₃×D₈	C₂²	1	3	yes	complemented
21	C₃×#568	—	2	4	no	—
22	C₃×#568	C₂²	1	1	yes	characteristic
23	C₃×#568	C₂²	1	2	yes	—
24	C₃×#568	C₂²	1	6	yes	complemented
25	C₂×C₃×#131	—	2	4	no	—
26	C₂×C₃×#131	C₂²	1	1	yes	characteristic
27	C₂×C₃×#131	C₂²	1	6	yes	complemented
28	C₃×#473	C₂²	1	4	yes	complemented
29	C₃×#472	C₂²	1	12	yes	complemented
30	C₃×#472	C₂²	1	24	yes	complemented
31	C₃×#471	C₂²	1	24	yes	complemented
32	C₃×#430	C₂²	1	6	yes	complemented
33	C₂×C₃×#108	C₂²	1	6	yes	complemented
34	C₃×#413	C₂²	1	12	yes	complemented
35	C₂×C₃×#100	C₂²	1	12	yes	complemented
36	#3585	C₂×C₃	1	2	yes	complemented
37	C₂×#576	C₂×C₃	1	1	yes	characteristic, complemented
38	#3573	C₂×C₃	1	1	yes	characteristic, complemented
39	#3068	C₂×C₃	1	12	yes	complemented
40	#3067	C₂×C₃	1	6	yes	complemented
41	C₂×#472	C₂×C₃	1	6	yes	complemented
42	#2916	C₂×C₃	1	1	yes	characteristic, complemented
43	#2888	C₂×C₃	1	2	yes	complemented
44	C₃×2₋¹⁺⁴	—	2	1	no	—
45	C₃×2₋¹⁺⁴	D₄	1	4	yes	—
46	C₃×H(5,𝔽₂)	—	2	3	no	—
47	C₃×H(5,𝔽₂)	—	2	8	no	—
48	C₃×H(5,𝔽₂)	—	2	8	no	—
49	C₃×H(5,𝔽₂)	D₄	1	4	yes	—
50	C₂×C₃×#41	—	2	4	no	—
51	C₂×C₃×#41	—	2	2	no	—
52	C₂×C₃×#41	C₂³	1	6	yes	—
53	C₂×C₃×#41	C₂³	1	6	yes	—
54	C₂×C₃×#41	C₂³	1	1	yes	characteristic
55	C₂²×C₃×D₄	—	2	6	no	—
56	C₂²×C₃×D₄	C₂³	1	6	yes	—
57	C₃×#137	—	2	12	no	—
58	C₃×#137	C₂³	1	8	yes	—
59	C₃×AGL(1,ℤ/8)	—	2	24	no	—
60	C₃×AGL(1,ℤ/8)	—	2	12	no	—
61	C₃×AGL(1,ℤ/8)	—	2	24	no	—
62	C₃×AGL(1,ℤ/8)	C₂³	1	24	yes	—
63	C₃×#135	—	2	24	no	—
64	C₃×#135	—	2	6	no	—
65	C₃×#135	—	2	6	no	—
66	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₃×SD₁₆	—	2	12	no	—
68	C₂×C₃×SD₁₆	C₂³	1	6	yes	—
69	C₂×C₃×D₈	—	2	12	no	—
70	C₂×C₃×D₈	—	2	6	no	—
71	C₂×C₃×D₈	—	2	6	no	—
72	C₂×C₃×D₈	C₂³	1	3	yes	—
73	C₂×C₃×D₈	C₂³	1	6	yes	—
74	C₃×#131	—	2	4	no	—
75	C₃×#131	—	2	8	no	—
76	C₃×#131	—	2	12	no	—
77	C₃×#131	—	2	6	no	—
78	C₃×#131	—	2	6	no	—
79	C₃×#131	D₄	1	4	yes	—
80	C₃×#131	D₄	1	4	yes	—
81	C₃×#131	C₂³	1	4	yes	—
82	C₃×#131	C₂³	1	12	yes	—
83	C₂×C₃×M₁₆	—	2	12	no	—
84	C₂×C₃×M₁₆	—	2	6	no	—
85	C₂×C₃×M₁₆	C₂³	1	6	yes	—
86	C₂×C₃×M₁₆	C₂³	1	12	yes	—
87	C₂×C₃×M₁₆	C₂³	1	3	yes	—
88	C₂²×C₃×C₈	—	2	6	no	—
89	C₂²×C₃×C₈	C₂³	1	3	yes	—
90	C₃×#108	C₂³	1	4	yes	—
91	C₃×#108	C₂³	1	12	yes	—
92	C₃×#101	C₂³	1	8	yes	—
93	C₃×#100	C₂³	1	24	yes	—
94	#585	C₂²×C₃	1	1	yes	characteristic
95	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	—
96	#577	—	2	8	no	—
97	#576	—	2	8	no	—
98	#576	—	2	4	no	—
99	#576	—	2	4	no	—
100	#575	C₂²×C₃	1	12	yes	complemented
101	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	12	yes	complemented
102	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	6	yes	complemented
103	C₂×#135	C₂²×C₃	1	3	yes	complemented
104	C₂²×D₈	C₂²×C₃	1	3	yes	complemented
105	#568	—	2	4	no	—
106	#568	C₂²×C₃	1	2	yes	—
107	#568	C₂²×C₃	1	1	yes	characteristic
108	#568	C₂²×C₃	1	6	yes	complemented
109	C₂×#131	—	2	4	no	—
110	C₂×#131	C₂²×C₃	1	1	yes	characteristic
111	C₂×#131	C₂²×C₃	1	6	yes	complemented
112	#473	C₂²×C₃	1	4	yes	complemented
113	#472	C₂²×C₃	1	12	yes	complemented
114	#472	C₂²×C₃	1	24	yes	complemented
115	#471	C₂²×C₃	1	24	yes	complemented
116	#430	C₂²×C₃	1	6	yes	complemented
117	C₂×#108	C₂²×C₃	1	6	yes	complemented
118	#413	C₂²×C₃	1	12	yes	complemented
119	C₂×#100	C₂²×C₃	1	12	yes	complemented
120	C₂⁴×C₃	—	2	6	no	—
121	C₃×#41	—	2	4	no	—
122	C₃×#41	—	2	12	no	—
123	C₃×#41	—	2	6	no	—
124	C₃×#41	—	2	6	no	—
125	C₃×#41	—	2	12	no	—
126	C₃×#41	—	2	12	no	—
127	C₃×#41	—	4	8	no	—
128	C₃×#41	C₂×D₄	1	12	yes	—
129	C₃×#41	C₂×D₄	1	4	yes	—
130	C₃×#41	C₂×D₄	1	4	yes	—
131	C₃×#41	C₂⁴	1	4	yes	—
132	C₂×C₃×Q₈	—	2	4	no	—
133	C₂×C₃×Q₈	C₂×D₄	1	6	yes	—
134	C₂×C₃×Q₈	#41	1	1	yes	characteristic
135	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
136	C₂×C₃×D₄	—	2	6	no	—
137	C₂×C₃×D₄	—	2	12	no	—
138	C₂×C₃×D₄	—	2	6	no	—
139	C₂×C₃×D₄	—	2	12	no	—
140	C₂×C₃×D₄	—	2	12	no	—
141	C₂×C₃×D₄	—	2	6	no	—
142	C₂×C₃×D₄	—	4	24	no	—
143	C₂×C₃×D₄	C₂×D₄	1	6	yes	—
144	C₂×C₃×D₄	#41	1	3	yes	—
145	C₂×C₃×D₄	C₂⁴	1	6	yes	—
146	C₂²×C₃×C₄	—	2	6	no	—
147	C₂²×C₃×C₄	—	2	6	no	—
148	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
149	C₃×Q₁₆	—	2	8	no	—
150	C₃×Q₁₆	—	2	1	no	—
151	C₃×Q₁₆	—	2	1	no	—
152	C₃×SD₁₆	—	2	24	no	—
153	C₃×SD₁₆	—	2	8	no	—
154	C₃×SD₁₆	—	2	12	no	—
155	C₃×D₈	—	2	24	no	—
156	C₃×D₈	—	2	3	no	—
157	C₃×D₈	—	2	3	no	—
158	C₃×D₈	—	2	12	no	—
159	C₃×M₁₆	—	2	6	no	—
160	C₃×M₁₆	—	2	12	no	—
161	C₃×M₁₆	—	2	12	no	—
162	C₃×M₁₆	—	2	4	no	—
163	C₃×M₁₆	C₂×D₄	1	12	yes	—
164	C₃×M₁₆	C₂⁴	1	4	yes	—
165	C₃×M₁₆	C₂⁴	1	8	yes	—
166	C₂×C₃×C₈	—	2	6	no	—
167	C₂×C₃×C₈	—	2	12	no	—
168	C₂×C₃×C₈	—	2	4	no	—
169	C₂×C₃×C₈	—	2	12	no	—
170	C₂×C₃×C₈	C₂×D₄	1	6	yes	—
171	C₂×C₃×C₈	C₂×D₄	1	6	yes	—
172	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
173	C₂×C₃×C₈	C₂⁴	1	3	yes	—
174	2₋¹⁺⁴	—	2	1	no	—
175	2₋¹⁺⁴	C₃×D₄	1	4	yes	—
176	H(5,𝔽₂)	—	2	3	no	—
177	H(5,𝔽₂)	—	2	8	no	—
178	H(5,𝔽₂)	—	2	8	no	—
179	H(5,𝔽₂)	C₃×D₄	1	4	yes	—
180	C₂×#41	—	2	4	no	—
181	C₂×#41	—	2	2	no	—
182	C₂×#41	C₂³×C₃	1	6	yes	—
183	C₂×#41	C₂³×C₃	1	6	yes	—
184	C₂×#41	C₂³×C₃	1	1	yes	characteristic
185	C₂²×D₄	—	2	6	no	—
186	C₂²×D₄	C₂³×C₃	1	6	yes	—
187	#137	—	2	12	no	—
188	#137	C₂³×C₃	1	8	yes	—
189	AGL(1,ℤ/8)	—	2	24	no	—
190	AGL(1,ℤ/8)	—	2	12	no	—
191	AGL(1,ℤ/8)	—	2	24	no	—
192	AGL(1,ℤ/8)	C₂³×C₃	1	24	yes	—
193	#135	—	2	24	no	—
194	#135	—	2	6	no	—
195	#135	—	2	6	no	—
196	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
197	C₂×SD₁₆	—	2	12	no	—
198	C₂×SD₁₆	C₂³×C₃	1	6	yes	—
199	C₂×D₈	—	2	12	no	—
200	C₂×D₈	—	2	6	no	—
201	C₂×D₈	—	2	6	no	—
202	C₂×D₈	C₂³×C₃	1	3	yes	—
203	C₂×D₈	C₂³×C₃	1	6	yes	—
204	#131	—	2	4	no	—
205	#131	—	2	8	no	—
206	#131	—	2	12	no	—
207	#131	—	2	6	no	—
208	#131	—	2	6	no	—
209	#131	C₃×D₄	1	4	yes	—
210	#131	C₃×D₄	1	4	yes	—
211	#131	C₂³×C₃	1	4	yes	—
212	#131	C₂³×C₃	1	12	yes	—
213	C₂×M₁₆	—	2	12	no	—
214	C₂×M₁₆	—	2	6	no	—
215	C₂×M₁₆	C₂³×C₃	1	6	yes	—
216	C₂×M₁₆	C₂³×C₃	1	12	yes	—
217	C₂×M₁₆	C₂³×C₃	1	3	yes	—
218	C₂²×C₈	—	2	6	no	—
219	C₂²×C₈	C₂³×C₃	1	3	yes	—
220	#108	C₂³×C₃	1	4	yes	—
221	#108	C₂³×C₃	1	12	yes	—
222	#101	C₂³×C₃	1	8	yes	—
223	#100	C₂³×C₃	1	24	yes	—
224	C₂³×C₃	—	2	6	no	—
225	C₂³×C₃	—	2	6	no	—
226	C₂³×C₃	—	4	12	no	—
227	C₂³×C₃	—	16	6	no	—
228	C₂³×C₃	C₂×#41	1	3	yes	—
229	C₃×Q₈	—	2	6	no	—
230	C₃×Q₈	—	2	2	no	—
231	C₃×Q₈	—	2	2	no	—
232	C₃×Q₈	#121	1	4	yes	—
233	C₃×Q₈	C₂²×D₄	1	4	yes	—
234	C₃×D₄	—	2	12	no	—
235	C₃×D₄	—	2	4	no	—
236	C₃×D₄	—	2	6	no	—
237	C₃×D₄	—	2	6	no	—
238	C₃×D₄	—	2	6	no	—
239	C₃×D₄	—	4	12	no	—
240	C₃×D₄	—	4	12	no	—
241	C₃×D₄	#121	1	12	yes	—
242	C₃×D₄	C₂²×D₄	1	4	yes	—
243	C₂×C₃×C₄	—	2	6	no	—
244	C₂×C₃×C₄	—	2	12	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	4	12	no	—
248	C₂×C₃×C₄	C₂²×D₄	1	6	yes	—
249	C₂×C₃×C₄	C₂²×D₄	1	6	yes	—
250	C₂×C₃×C₄	C₂×#41	1	3	yes	—
251	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
252	C₃×C₈	—	2	4	no	—
253	C₃×C₈	—	2	8	no	—
254	C₃×C₈	C₂²×D₄	1	1	yes	characteristic
255	C₃×C₈	C₂²×D₄	1	6	yes	—
256	C₃×C₈	C₂²×D₄	1	1	yes	characteristic
257	C₂⁴	—	2	6	no	—
258	#41	—	2	4	no	—
259	#41	—	2	12	no	—
260	#41	—	2	6	no	—
261	#41	—	2	6	no	—
262	#41	—	2	12	no	—
263	#41	—	2	12	no	—
264	#41	—	4	8	no	—
265	#41	C₂×C₃×D₄	1	12	yes	—
266	#41	C₂×C₃×D₄	1	4	yes	—
267	#41	C₂×C₃×D₄	1	4	yes	—
268	#41	C₂⁴×C₃	1	4	yes	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	C₂×C₃×D₄	1	6	yes	—
271	C₂×Q₈	C₃×#41	1	1	yes	characteristic
272	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
273	C₂×D₄	—	2	6	no	—
274	C₂×D₄	—	2	12	no	—
275	C₂×D₄	—	2	6	no	—
276	C₂×D₄	—	2	12	no	—
277	C₂×D₄	—	2	12	no	—
278	C₂×D₄	—	2	6	no	—
279	C₂×D₄	—	4	24	no	—
280	C₂×D₄	C₂×C₃×D₄	1	6	yes	—
281	C₂×D₄	C₃×#41	1	3	yes	—
282	C₂×D₄	C₂⁴×C₃	1	6	yes	—
283	C₂²×C₄	—	2	6	no	—
284	C₂²×C₄	—	2	6	no	—
285	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
286	Q₁₆	—	2	8	no	—
287	Q₁₆	—	2	1	no	—
288	Q₁₆	—	2	1	no	—
289	SD₁₆	—	2	24	no	—
290	SD₁₆	—	2	8	no	—
291	SD₁₆	—	2	12	no	—
292	D₈	—	2	24	no	—
293	D₈	—	2	3	no	—
294	D₈	—	2	3	no	—
295	D₈	—	2	12	no	—
296	M₁₆	—	2	6	no	—
297	M₁₆	—	2	12	no	—
298	M₁₆	—	2	12	no	—
299	M₁₆	—	2	4	no	—
300	M₁₆	C₂×C₃×D₄	1	12	yes	—
301	M₁₆	C₂⁴×C₃	1	4	yes	—
302	M₁₆	C₂⁴×C₃	1	8	yes	—
303	C₂×C₈	—	2	6	no	—
304	C₂×C₈	—	2	12	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	12	no	—
307	C₂×C₈	C₂×C₃×D₄	1	6	yes	—
308	C₂×C₈	C₂×C₃×D₄	1	6	yes	—
309	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
310	C₂×C₈	C₂⁴×C₃	1	3	yes	—
311	C₂²×C₃	—	2	4	no	—
312	C₂²×C₃	—	4	3	no	—
313	C₂²×C₃	—	4	6	no	—
314	C₂²×C₃	—	8	6	no	—
315	C₂²×C₃	—	8	6	no	—
316	C₂²×C₃	—	16	12	no	—
317	C₂²×C₃	C₂×#121	1	6	yes	—
318	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
319	C₃×C₄	—	2	4	no	—
320	C₃×C₄	—	4	2	no	—
321	C₃×C₄	C₂×#121	1	6	yes	—
322	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
323	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
324	C₂³	—	2	6	no	—
325	C₂³	—	2	6	no	—
326	C₂³	—	4	12	no	—
327	C₂³	—	16	6	no	—
328	C₂³	C₂×C₃×#41	1	3	yes	—
329	Q₈	—	2	6	no	—
330	Q₈	—	2	2	no	—
331	Q₈	—	2	2	no	—
332	Q₈	C₃×#121	1	4	yes	—
333	Q₈	C₂²×C₃×D₄	1	4	yes	—
334	D₄	—	2	4	no	—
335	D₄	—	2	12	no	—
336	D₄	—	2	6	no	—
337	D₄	—	2	6	no	—
338	D₄	—	2	6	no	—
339	D₄	—	4	12	no	—
340	D₄	—	4	12	no	—
341	D₄	C₃×#121	1	12	yes	—
342	D₄	C₂²×C₃×D₄	1	4	yes	—
343	C₂×C₄	—	2	6	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	12	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	12	no	—
348	C₂×C₄	C₂²×C₃×D₄	1	6	yes	—
349	C₂×C₄	C₂²×C₃×D₄	1	6	yes	—
350	C₂×C₄	C₂×C₃×#41	1	3	yes	—
351	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
352	C₈	—	2	4	no	—
353	C₈	—	2	8	no	—
354	C₈	C₂²×C₃×D₄	1	1	yes	characteristic
355	C₈	C₂²×C₃×D₄	1	6	yes	—
356	C₈	C₂²×C₃×D₄	1	1	yes	characteristic
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	2	6	no	—
359	C₂×C₃	—	4	4	no	—
360	C₂×C₃	—	8	6	no	—
361	C₂×C₃	C₂²×#121	1	1	yes	characteristic
362	C₂²	—	2	4	no	—
363	C₂²	—	4	3	no	—
364	C₂²	—	4	6	no	—
365	C₂²	—	8	6	no	—
366	C₂²	—	8	6	no	—
367	C₂²	—	16	12	no	—
368	C₂²	C₂×C₃×#121	1	6	yes	—
369	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
370	C₄	—	2	4	no	—
371	C₄	—	4	2	no	—
372	C₄	C₂×C₃×#121	1	6	yes	—
373	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
374	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
375	C₃	#60471	1	1	yes	characteristic, direct product factor, Sylow
376	C₂	—	2	1	no	—
377	C₂	—	2	6	no	—
378	C₂	—	4	4	no	—
379	C₂	—	8	6	no	—
380	C₂	C₂²×C₃×#121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂²×#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3585	C₂	semidirect
2. C₂×C₃×#576	C₂	semidirect
3. C₃×#3573	C₂	semidirect
4. C₃×#3068	C₂	semidirect
5. C₃×#3067	C₂	semidirect
6. C₂×C₃×#472	C₂	semidirect
7. C₃×#2916	C₂	semidirect
8. C₃×#2888	C₂	semidirect
9. #60471	C₃	direct (N × H)
16. C₃×#575	C₂²	semidirect
17. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₃×#135	C₂²	semidirect
20. C₂²×C₃×D₈	C₂²	semidirect
24. C₃×#568	C₂²	semidirect
27. C₂×C₃×#131	C₂²	semidirect
28. C₃×#473	C₂²	semidirect
29. C₃×#472	C₂²	semidirect
30. C₃×#472	C₂²	semidirect
31. C₃×#471	C₂²	semidirect
32. C₃×#430	C₂²	semidirect
33. C₂×C₃×#108	C₂²	semidirect
34. C₃×#413	C₂²	semidirect
35. C₂×C₃×#100	C₂²	semidirect
36. #3585	C₂×C₃	semidirect
37. C₂×#576	C₂×C₃	semidirect
38. #3573	C₂×C₃	semidirect
39. #3068	C₂×C₃	semidirect
40. #3067	C₂×C₃	semidirect
41. C₂×#472	C₂×C₃	semidirect
42. #2916	C₂×C₃	semidirect
43. #2888	C₂×C₃	semidirect
100. #575	C₂²×C₃	semidirect
101. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
102. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
103. C₂×#135	C₂²×C₃	semidirect
104. C₂²×D₈	C₂²×C₃	semidirect
108. #568	C₂²×C₃	semidirect
111. C₂×#131	C₂²×C₃	semidirect
112. #473	C₂²×C₃	semidirect
113. #472	C₂²×C₃	semidirect
114. #472	C₂²×C₃	semidirect
115. #471	C₂²×C₃	semidirect
116. #430	C₂²×C₃	semidirect
117. C₂×#108	C₂²×C₃	semidirect
118. #413	C₂²×C₃	semidirect
119. C₂×#100	C₂²×C₃	semidirect
375. C₃	#60471	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×#3585	2
C₂×C₃×#576	2
C₃×#3573	2
C₃×#3068	2
C₃×#3067	2
C₂×C₃×#472	2
C₃×#2916	2
C₃×#2888	2
#60471	3

Subgroups — C3×#60471 #10679078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60471 #10679078