Subgroups — C₂×C₃×#5720 #11910155

Order 1152.

2937 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#939	C₂	1	6	yes	maximal, complemented
3	C₂×C₃×#937	C₂	1	3	yes	maximal, complemented
4	C₂×C₃×#935	C₂	1	3	yes	maximal, complemented
5	C₃×#5720	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×#876	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#560	—	3	1	no	maximal
8	C₂×#5720	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₃²×D₄	C₂²	1	3	yes	—
11	C₂²×C₃²×D₄	C₂²	1	3	yes	complemented
12	C₂²×C₃×#67	C₂²	1	6	yes	—
13	C₂³×C₃×Dic₃	C₂²	1	3	yes	complemented
14	C₃²×#127	C₂²	1	8	yes	complemented
15	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×#217	C₂²	1	3	yes	—
17	C₂×C₃×#217	C₂²	1	3	yes	complemented
18	C₃×#939	C₂²	1	48	yes	complemented
19	C₃×#937	C₂²	1	24	yes	complemented
20	C₃×#935	C₂²	1	24	yes	complemented
21	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	6	yes	—
22	C₂×C₃×Dic₃⋊C₄	C₂²	1	6	yes	complemented
23	C₃×#876	C₂²	1	16	yes	complemented
24	C₃×#560	—	3	16	no	—
25	C₂×C₃×#127	—	2	1	no	—
26	C₂×C₃×#127	D₃	1	1	yes	characteristic, complemented
27	C₂×C₃×#127	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₃×#126	—	3	2	no	—
29	C₂×C₃×#123	—	3	3	no	—
30	C₂×C₃×#121	—	3	6	no	—
31	C₂×C₃×#120	—	3	3	no	—
32	C₂×#939	C₂×C₃	1	6	yes	complemented
33	C₂×#937	C₂×C₃	1	3	yes	complemented
34	C₂×#935	C₂×C₃	1	3	yes	complemented
35	#5720	C₂×C₃	1	16	yes	direct product factor
36	C₂×#876	C₂×C₃	1	2	yes	complemented
37	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
38	C₂⁴×C₃²	C₂³	1	3	yes	—
39	C₂³×C₃×D₃	—	4	6	no	—
40	C₂³×C₃×D₃	C₂³	1	2	yes	—
41	C₂³×C₃×D₃	C₂³	1	4	yes	—
42	C₂×C₃²×D₄	—	4	6	no	—
43	C₂×C₃²×D₄	—	4	6	no	—
44	C₂×C₃²×D₄	C₂³	1	12	yes	—
45	C₂×C₃²×D₄	C₂³	1	12	yes	complemented
46	C₂²×C₃²×C₄	C₂³	1	3	yes	—
47	C₂×C₃×#67	—	4	12	no	—
48	C₂×C₃×#67	C₂³	1	24	yes	—
49	C₂²×C₃×Dic₃	—	4	6	no	—
50	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
51	C₂²×C₃×Dic₃	C₂³	1	12	yes	complemented
52	C₃²×C₄²	C₂³	1	4	yes	complemented
53	C₃×#217	C₂³	1	12	yes	—
54	C₃×#217	C₂³	1	12	yes	complemented
55	C₃×(C₂×D₃)⋊C₄	C₂³	1	24	yes	—
56	C₃×Dic₃⋊C₄	C₂³	1	24	yes	complemented
57	C₂×#560	—	3	1	no	Sylow
58	C₂⁵×C₃	—	3	1	no	—
59	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
60	C₂²×C₃×D₄	—	2	3	no	—
61	C₂²×C₃×D₄	—	2	3	no	—
62	C₂²×C₃×D₄	—	3	6	no	—
63	C₂²×C₃×D₄	C₂×D₃	1	3	yes	—
64	C₂²×C₃×D₄	C₂×D₃	1	3	yes	complemented
65	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	—
66	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	complemented
67	C₂³×C₃×C₄	—	3	3	no	—
68	C₂²×#67	C₂²×C₃	1	6	yes	—
69	C₂³×Dic₃	C₂²×C₃	1	3	yes	complemented
70	C₃×#127	—	2	8	no	—
71	C₃×#127	C₂×D₃	1	8	yes	complemented
72	C₃×#127	C₂²×C₃	1	8	yes	complemented
73	C₃×#126	—	3	16	no	—
74	C₃×#123	—	3	24	no	—
75	C₃×#121	—	3	48	no	—
76	C₃×#120	—	3	24	no	—
77	C₂×C₃×C₄⋊C₄	—	3	6	no	—
78	C₂×C₃×C₂²⋊C₄	—	3	3	no	—
79	C₂×C₃×C₂²⋊C₄	—	3	3	no	—
80	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
81	C₂×C₃×C₄²	—	2	1	no	—
82	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
83	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
84	C₂×#217	C₂²×C₃	1	3	yes	—
85	C₂×#217	C₂²×C₃	1	3	yes	complemented
86	#939	C₂²×C₃	1	48	yes	complemented
87	#937	C₂²×C₃	1	24	yes	complemented
88	#935	C₂²×C₃	1	24	yes	complemented
89	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	6	yes	—
90	C₂×Dic₃⋊C₄	C₂²×C₃	1	6	yes	complemented
91	#876	C₂²×C₃	1	16	yes	complemented
92	C₂³×C₃²	—	2	6	no	—
93	C₂³×C₃²	—	2	6	no	—
94	C₂³×C₃²	—	2	12	no	—
95	C₂³×C₃²	C₂⁴	1	2	yes	—
96	C₂³×C₃²	C₂⁴	1	6	yes	—
97	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
98	C₂²×C₃×D₃	—	2	12	no	—
99	C₂²×C₃×D₃	—	4	12	no	—
100	C₂²×C₃×D₃	—	4	16	no	—
101	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
102	C₃²×D₄	—	4	12	no	—
103	C₃²×D₄	—	4	12	no	—
104	C₂×C₃²×C₄	—	2	6	no	—
105	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
106	C₃×#67	—	4	24	no	—
107	C₂×C₃×Dic₃	—	2	12	no	—
108	C₂×C₃×Dic₃	—	4	12	no	—
109	C₂×C₃×Dic₃	C₂⁴	1	12	yes	—
110	#560	—	3	16	no	—
111	C₂×#127	C₃×D₃	1	1	yes	characteristic, complemented
112	C₂×#126	—	3	2	no	—
113	C₂×#123	—	3	3	no	—
114	C₂×#121	—	3	6	no	—
115	C₂×#120	—	3	3	no	—
116	C₂⁴×C₃	—	2	1	no	—
117	C₂⁴×C₃	—	2	3	no	—
118	C₂⁴×C₃	—	3	2	no	—
119	C₂⁴×C₃	—	3	4	no	—
120	C₂⁴×C₃	—	12	6	no	—
121	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
122	C₂⁴×C₃	C₂²×D₃	1	3	yes	—
123	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
124	C₂⁴×C₃	C₂³×C₃	1	3	yes	—
125	C₂³×D₃	—	4	6	no	—
126	C₂³×D₃	C₂³×C₃	1	2	yes	—
127	C₂³×D₃	C₂³×C₃	1	4	yes	—
128	C₂×C₃×D₄	—	2	12	no	—
129	C₂×C₃×D₄	—	2	12	no	—
130	C₂×C₃×D₄	—	3	24	no	—
131	C₂×C₃×D₄	—	4	6	no	—
132	C₂×C₃×D₄	—	4	6	no	—
133	C₂×C₃×D₄	—	4	6	no	—
134	C₂×C₃×D₄	—	4	6	no	—
135	C₂×C₃×D₄	—	4	12	no	—
136	C₂×C₃×D₄	—	4	12	no	—
137	C₂×C₃×D₄	—	12	12	no	—
138	C₂×C₃×D₄	C₂²×D₃	1	12	yes	—
139	C₂×C₃×D₄	C₂²×D₃	1	12	yes	complemented
140	C₂×C₃×D₄	C₂³×C₃	1	12	yes	—
141	C₂×C₃×D₄	C₂³×C₃	1	12	yes	complemented
142	C₂²×C₃×C₄	—	2	3	no	—
143	C₂²×C₃×C₄	—	3	6	no	—
144	C₂²×C₃×C₄	—	3	12	no	—
145	C₂²×C₃×C₄	—	12	6	no	—
146	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
147	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
148	C₂×#67	—	4	12	no	—
149	C₂×#67	C₂³×C₃	1	24	yes	—
150	C₂²×Dic₃	—	4	6	no	—
151	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
152	C₂²×Dic₃	C₂³×C₃	1	12	yes	complemented
153	C₃×C₄⋊C₄	—	3	24	no	—
154	C₃×C₂²⋊C₄	—	3	12	no	—
155	C₃×C₂²⋊C₄	—	3	12	no	—
156	C₃×C₂²⋊C₄	—	3	24	no	—
157	C₃×C₄²	—	2	4	no	—
158	C₃×C₄²	C₂²×D₃	1	4	yes	complemented
159	C₃×C₄²	C₂³×C₃	1	4	yes	complemented
160	#217	C₂³×C₃	1	12	yes	—
161	#217	C₂³×C₃	1	12	yes	complemented
162	(C₂×D₃)⋊C₄	C₂³×C₃	1	24	yes	—
163	Dic₃⋊C₄	C₂³×C₃	1	24	yes	complemented
164	C₂²×C₃²	—	2	6	no	—
165	C₂²×C₃²	—	2	12	no	—
166	C₂²×C₃²	—	2	6	no	—
167	C₂²×C₃²	—	4	4	no	—
168	C₂²×C₃²	—	4	12	no	—
169	C₂²×C₃²	H(5,𝔽₂)	1	6	yes	—
170	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
171	C₂×C₃×D₃	—	2	12	no	—
172	C₂×C₃×D₃	—	4	16	no	—
173	C₂×C₃×D₃	—	4	8	no	—
174	C₃²×C₄	—	2	6	no	—
175	C₃×Dic₃	—	2	12	no	—
176	C₂⁵	—	3	1	no	—
177	C₂²×D₄	—	3	6	no	—
178	C₂²×D₄	C₂×C₃×D₃	1	3	yes	—
179	C₂²×D₄	C₂×C₃×D₃	1	3	yes	complemented
180	C₂³×C₄	—	3	3	no	—
181	#127	C₂×C₃×D₃	1	8	yes	complemented
182	#126	—	3	16	no	—
183	#123	—	3	24	no	—
184	#121	—	3	48	no	—
185	#120	—	3	24	no	—
186	C₂×C₄⋊C₄	—	3	6	no	—
187	C₂×C₂²⋊C₄	—	3	3	no	—
188	C₂×C₂²⋊C₄	—	3	3	no	—
189	C₂×C₂²⋊C₄	—	3	6	no	—
190	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
191	C₂³×C₃	—	2	6	no	—
192	C₂³×C₃	—	2	12	no	—
193	C₂³×C₃	—	2	6	no	—
194	C₂³×C₃	—	2	6	no	—
195	C₂³×C₃	—	2	12	no	—
196	C₂³×C₃	—	2	6	no	—
197	C₂³×C₃	—	2	1	no	—
198	C₂³×C₃	—	2	2	no	—
199	C₂³×C₃	—	2	6	no	—
200	C₂³×C₃	—	3	4	no	—
201	C₂³×C₃	—	4	6	no	—
202	C₂³×C₃	—	4	12	no	—
203	C₂³×C₃	—	4	6	no	—
204	C₂³×C₃	—	6	12	no	—
205	C₂³×C₃	—	12	12	no	—
206	C₂³×C₃	—	12	16	no	—
207	C₂³×C₃	C₂³×D₃	1	2	yes	—
208	C₂³×C₃	C₂³×D₃	1	6	yes	—
209	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
210	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
211	C₂³×C₃	C₂⁴×C₃	1	6	yes	—
212	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
213	C₂²×D₃	—	2	12	no	—
214	C₂²×D₃	—	4	12	no	—
215	C₂²×D₃	—	4	16	no	—
216	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
217	C₃×D₄	—	4	12	no	—
218	C₃×D₄	—	4	12	no	—
219	C₃×D₄	—	4	12	no	—
220	C₃×D₄	—	4	12	no	—
221	C₃×D₄	—	4	24	no	—
222	C₃×D₄	—	4	24	no	—
223	C₃×D₄	—	12	24	no	—
224	C₂×C₃×C₄	—	2	12	no	—
225	C₂×C₃×C₄	—	2	6	no	—
226	C₂×C₃×C₄	—	2	6	no	—
227	C₂×C₃×C₄	—	2	6	no	—
228	C₂×C₃×C₄	—	3	12	no	—
229	C₂×C₃×C₄	—	6	12	no	—
230	C₂×C₃×C₄	—	12	12	no	—
231	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
232	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
233	#67	—	4	24	no	—
234	C₂×Dic₃	—	2	12	no	—
235	C₂×Dic₃	—	4	12	no	—
236	C₂×Dic₃	C₂⁴×C₃	1	12	yes	—
237	C₂×C₃²	—	4	2	no	—
238	C₂×C₃²	—	4	6	no	—
239	C₂×C₃²	#560	1	4	yes	complemented
240	C₂×C₃²	C₂×H(5,𝔽₂)	1	3	yes	—
241	C₃×D₃	—	4	4	no	—
242	C₂⁴	—	3	2	no	—
243	C₂⁴	—	3	4	no	—
244	C₂⁴	—	12	6	no	—
245	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
246	C₂⁴	C₂²×C₃×D₃	1	3	yes	—
247	C₂×D₄	—	3	24	no	—
248	C₂×D₄	—	4	6	no	—
249	C₂×D₄	—	4	6	no	—
250	C₂×D₄	—	12	12	no	—
251	C₂×D₄	C₂²×C₃×D₃	1	12	yes	—
252	C₂×D₄	C₂²×C₃×D₃	1	12	yes	complemented
253	C₂²×C₄	—	3	6	no	—
254	C₂²×C₄	—	3	12	no	—
255	C₂²×C₄	—	12	6	no	—
256	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
257	C₄⋊C₄	—	3	24	no	—
258	C₂²⋊C₄	—	3	12	no	—
259	C₂²⋊C₄	—	3	12	no	—
260	C₂²⋊C₄	—	3	24	no	—
261	C₄²	C₂²×C₃×D₃	1	4	yes	complemented
262	C₂²×C₃	—	2	6	no	—
263	C₂²×C₃	—	2	12	no	—
264	C₂²×C₃	—	2	6	no	—
265	C₂²×C₃	—	2	6	no	—
266	C₂²×C₃	—	2	12	no	—
267	C₂²×C₃	—	2	6	no	—
268	C₂²×C₃	—	2	6	no	—
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	4	6	no	—
271	C₂²×C₃	—	4	12	no	—
272	C₂²×C₃	—	4	6	no	—
273	C₂²×C₃	—	4	4	no	—
274	C₂²×C₃	—	4	12	no	—
275	C₂²×C₃	—	4	4	no	—
276	C₂²×C₃	—	4	12	no	—
277	C₂²×C₃	—	6	12	no	—
278	C₂²×C₃	—	8	4	no	—
279	C₂²×C₃	—	8	12	no	—
280	C₂²×C₃	—	12	16	no	—
281	C₂²×C₃	—	12	8	no	—
282	C₂²×C₃	#1004	1	6	yes	—
283	C₂²×C₃	C₃×H(5,𝔽₂)	1	6	yes	—
284	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
285	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
286	C₂×D₃	—	2	12	no	—
287	C₂×D₃	—	4	16	no	—
288	C₂×D₃	—	4	8	no	—
289	C₃×C₄	—	2	12	no	—
290	C₃×C₄	—	2	6	no	—
291	C₃×C₄	—	2	6	no	—
292	C₃×C₄	—	6	12	no	—
293	Dic₃	—	2	12	no	—
294	C₃²	C₂×#560	1	1	yes	characteristic, complemented, Sylow
295	C₂³	—	2	6	no	—
296	C₂³	—	2	12	no	—
297	C₂³	—	2	6	no	—
298	C₂³	—	3	4	no	—
299	C₂³	—	6	12	no	—
300	C₂³	—	12	12	no	—
301	C₂³	—	12	16	no	—
302	C₂³	C₂³×C₃×D₃	1	2	yes	—
303	C₂³	C₂³×C₃×D₃	1	6	yes	—
304	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
305	D₄	—	4	12	no	—
306	D₄	—	4	12	no	—
307	D₄	—	12	24	no	—
308	C₂×C₄	—	2	6	no	—
309	C₂×C₄	—	3	12	no	—
310	C₂×C₄	—	6	12	no	—
311	C₂×C₄	—	12	12	no	—
312	C₂×C₄	C₂³×C₃×D₃	1	6	yes	—
313	C₂×C₃	—	2	3	no	—
314	C₂×C₃	—	2	4	no	—
315	C₂×C₃	—	4	2	no	—
316	C₂×C₃	—	4	6	no	—
317	C₂×C₃	—	4	2	no	—
318	C₂×C₃	—	4	6	no	—
319	C₂×C₃	—	8	2	no	—
320	C₂×C₃	—	8	6	no	—
321	C₂×C₃	—	12	4	no	—
322	C₂×C₃	#5720	1	4	yes	direct product factor
323	C₂×C₃	C₃×#560	1	4	yes	complemented
324	C₂×C₃	C₂×#1004	1	3	yes	—
325	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	3	yes	—
326	D₃	—	4	4	no	—
327	C₂²	—	2	6	no	—
328	C₂²	—	2	12	no	—
329	C₂²	—	2	6	no	—
330	C₂²	—	4	4	no	—
331	C₂²	—	4	12	no	—
332	C₂²	—	6	12	no	—
333	C₂²	—	12	16	no	—
334	C₂²	—	12	8	no	—
335	C₂²	C₃×#1004	1	6	yes	—
336	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
337	C₄	—	2	6	no	—
338	C₄	—	6	12	no	—
339	C₃	—	2	1	no	—
340	C₃	C₂×#5720	1	1	yes	characteristic, direct product factor
341	C₃	C₂×C₃×#560	1	1	yes	characteristic, complemented
342	C₂	—	4	2	no	—
343	C₂	—	4	6	no	—
344	C₂	—	12	4	no	—
345	C₂	C₃×#5720	1	4	yes	direct product factor
346	C₂	C₂×C₃×#1004	1	3	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#127	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#127	D₃
hypocenter	C₃	C₂×C₃×#560
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#127

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#127	C₂	semidirect
2. C₂×C₃×#939	C₂	semidirect
3. C₂×C₃×#937	C₂	semidirect
4. C₂×C₃×#935	C₂	semidirect
5. C₃×#5720	C₂	direct (N × H)
6. C₂×C₃×#876	C₂	semidirect
8. C₂×#5720	C₃	direct (N × H)
11. C₂²×C₃²×D₄	C₂²	semidirect
13. C₂³×C₃×Dic₃	C₂²	semidirect
14. C₃²×#127	C₂²	semidirect
15. C₂×C₃²×C₄²	C₂²	semidirect
17. C₂×C₃×#217	C₂²	semidirect
18. C₃×#939	C₂²	semidirect
19. C₃×#937	C₂²	semidirect
20. C₃×#935	C₂²	semidirect
22. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
23. C₃×#876	C₂²	semidirect
26. C₂×C₃×#127	D₃	semidirect
27. C₂×C₃×#127	C₂×C₃	semidirect
32. C₂×#939	C₂×C₃	semidirect
33. C₂×#937	C₂×C₃	semidirect
34. C₂×#935	C₂×C₃	semidirect
35. #5720	C₂×C₃	direct (N × H)
36. C₂×#876	C₂×C₃	semidirect
45. C₂×C₃²×D₄	C₂³	semidirect
51. C₂²×C₃×Dic₃	C₂³	semidirect
52. C₃²×C₄²	C₂³	semidirect
54. C₃×#217	C₂³	semidirect
56. C₃×Dic₃⋊C₄	C₂³	semidirect
64. C₂²×C₃×D₄	C₂×D₃	semidirect
66. C₂²×C₃×D₄	C₂²×C₃	semidirect
69. C₂³×Dic₃	C₂²×C₃	semidirect
71. C₃×#127	C₂×D₃	semidirect
72. C₃×#127	C₂²×C₃	semidirect
82. C₂×C₃×C₄²	C₂×D₃	semidirect
83. C₂×C₃×C₄²	C₂²×C₃	semidirect
85. C₂×#217	C₂²×C₃	semidirect
86. #939	C₂²×C₃	semidirect
87. #937	C₂²×C₃	semidirect
88. #935	C₂²×C₃	semidirect
90. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
91. #876	C₂²×C₃	semidirect
111. C₂×#127	C₃×D₃	semidirect
139. C₂×C₃×D₄	C₂²×D₃	semidirect
141. C₂×C₃×D₄	C₂³×C₃	semidirect
152. C₂²×Dic₃	C₂³×C₃	semidirect
158. C₃×C₄²	C₂²×D₃	semidirect
159. C₃×C₄²	C₂³×C₃	semidirect
161. #217	C₂³×C₃	semidirect
163. Dic₃⋊C₄	C₂³×C₃	semidirect
179. C₂²×D₄	C₂×C₃×D₃	semidirect
181. #127	C₂×C₃×D₃	semidirect
190. C₂×C₄²	C₂×C₃×D₃	semidirect
239. C₂×C₃²	#560	semidirect
252. C₂×D₄	C₂²×C₃×D₃	semidirect
261. C₄²	C₂²×C₃×D₃	semidirect
294. C₃²	C₂×#560	semidirect
322. C₂×C₃	#5720	direct (N × H)
323. C₂×C₃	C₃×#560	semidirect
340. C₃	C₂×#5720	direct (N × H)
341. C₃	C₂×C₃×#560	semidirect
345. C₂	C₃×#5720	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×C₃²×#127	2
C₂×C₃×#939	2
C₂×C₃×#937	2
C₂×C₃×#935	2
C₃×#5720	2
C₂×C₃×#876	2
C₂×C₃×#560	3
C₂×#5720	3

Subgroups — C2×C3×#5720 #11910155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5720 #11910155