Subgroups — C₂×C₃×#64110 #13179489

Order 1728.

1900 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3748	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64110	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3743	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₈×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
7	C₂×#64110	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#901	—	3	4	no	maximal
9	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×#638	C₄	1	2	yes	—
11	C₃×#3828	C₄	1	4	yes	—
12	C₃×#3828	C₂²	1	4	yes	—
13	C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
15	C₂×C₃×#634	C₄	1	1	yes	characteristic
16	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃³×C₈	C₂²	1	4	yes	complemented
19	C₃×#3748	C₂²	1	4	yes	complemented
20	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
21	C₃×#3743	C₂²	1	8	yes	complemented
22	C₃×C₈×C₃⋊D₃	C₂²	1	8	yes	complemented
23	C₂×#3828	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×#235	—	3	4	no	—
25	C₂²×C₃²×C₈	—	2	4	no	—
26	C₂²×C₃²×C₈	D₃	1	4	yes	complemented
27	C₂²×C₃²×C₈	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#3748	C₂×C₃	1	1	yes	characteristic, complemented
29	#64110	C₂×C₃	1	8	yes	direct product factor
30	C₂×#3743	C₂×C₃	1	2	yes	complemented
31	C₂×C₈×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
32	C₂×C₃×#208	—	3	4	no	—
33	C₃×#901	—	3	32	no	—
34	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
35	C₂×C₃×D₃×C₈	—	3	8	no	—
36	C₂³×C₃³	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	2	yes	—
38	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃³×C₄	C₂×C₄	1	2	yes	—
40	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
41	C₂×C₃³×C₄	C₂³	1	2	yes	—
42	C₃×#638	C₂×C₄	1	8	yes	—
43	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
44	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	4	yes	—
45	C₃×C₄×C₃⋊D₃	C₂×C₄	1	4	yes	—
46	C₃×C₄×C₃⋊D₃	C₂³	1	4	yes	—
47	C₃×#634	C₂×C₄	1	4	yes	—
48	C₃³×C₈	C₂³	1	2	yes	—
49	C₃³×C₈	C₂³	1	2	yes	—
50	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	4	yes	—
51	C₂×C₃×#131	—	9	1	no	—
52	C₂×#901	—	3	4	no	—
53	C₂²×C₃²×C₄	—	2	4	no	—
54	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
55	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
56	C₂×#638	C₃×C₄	1	2	yes	—
57	#3828	C₃×C₄	1	4	yes	—
58	#3828	C₂²×C₃	1	4	yes	—
59	C₂×C₄⋊(C₃⋊D₃)	C₃×C₄	1	1	yes	characteristic
60	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
61	C₂×#634	C₃×C₄	1	1	yes	characteristic
62	C₂×C₃×#67	—	3	8	no	—
63	C₃×#235	—	3	16	no	—
64	C₃×#235	—	3	16	no	—
65	C₂×C₃×D₁₂	—	3	4	no	—
66	C₂×C₃×C₄×D₃	—	3	8	no	—
67	C₂×C₃×Dic₆	—	3	4	no	—
68	C₂×C₃²×C₈	—	2	4	no	—
69	C₂×C₃²×C₈	—	2	4	no	—
70	C₂×C₃²×C₈	—	2	16	no	—
71	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
72	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
73	C₂×C₃²×C₈	C₂×D₃	1	16	yes	complemented
74	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	complemented
77	#3748	C₂²×C₃	1	4	yes	complemented
78	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
79	#3743	C₂²×C₃	1	8	yes	complemented
80	C₈×C₃⋊D₃	C₂²×C₃	1	8	yes	complemented
81	C₃×#208	—	3	16	no	—
82	C₂×C₃×C₃⋊C₈	—	3	8	no	—
83	C₃×ΓL(1,𝔽₂₅)	—	3	32	no	—
84	C₃×D₃×C₈	—	3	32	no	—
85	C₂²×C₃³	—	2	2	no	—
86	C₂²×C₃³	C₂²×C₄	1	2	yes	—
87	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃×C₃⋊D₃	—	2	4	no	—
89	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	4	yes	—
90	C₃³×C₄	C₂²×C₄	1	2	yes	—
91	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
92	C₃³×C₄	C₂⁴	1	1	yes	characteristic
93	C₃×C₃⋊Dic₃	C₂²×C₄	1	4	yes	—
94	C₂×C₃×#41	—	9	1	no	—
95	C₂×#235	—	3	4	no	—
96	C₃×#131	—	9	8	no	—
97	C₂×C₃×M₁₆	—	9	1	no	—
98	C₂×C₃×M₁₆	—	9	2	no	—
99	C₂²×C₃×C₈	—	2	4	no	—
100	C₂²×C₃×C₈	—	9	2	no	—
101	C₂²×C₃×C₈	C₃×D₃	1	4	yes	complemented
102	C₂²×C₃×C₈	C₃⋊D₃	1	1	yes	characteristic, complemented
103	C₂×#208	—	3	4	no	—
104	#901	—	3	32	no	—
105	C₂×ΓL(1,𝔽₂₅)	—	3	8	no	—
106	C₂×D₃×C₈	—	3	8	no	—
107	C₂³×C₃²	—	2	4	no	—
108	C₂³×C₃²	C₄×D₃	1	4	yes	—
109	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
110	C₂²×C₃⋊D₃	C₂×C₃×C₄	1	2	yes	—
111	C₂²×C₃×D₃	—	3	8	no	—
112	C₂×C₃²×C₄	—	2	4	no	—
113	C₂×C₃²×C₄	—	2	8	no	—
114	C₂×C₃²×C₄	—	2	4	no	—
115	C₂×C₃²×C₄	—	2	8	no	—
116	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
117	C₂×C₃²×C₄	C₄×D₃	1	8	yes	—
118	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
120	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
121	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
122	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
124	#638	C₂×C₃×C₄	1	8	yes	—
125	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
126	C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	1	4	yes	—
127	C₄×C₃⋊D₃	C₂×C₃×C₄	1	4	yes	—
128	C₄×C₃⋊D₃	C₂³×C₃	1	4	yes	—
129	#634	C₂×C₃×C₄	1	4	yes	—
130	C₃×#67	—	3	32	no	—
131	C₂×C₃×Dic₃	—	3	8	no	—
132	C₃×D₁₂	—	3	16	no	—
133	C₃×C₄×D₃	—	3	16	no	—
134	C₃×C₄×D₃	—	3	16	no	—
135	C₃×Dic₆	—	3	16	no	—
136	C₃²×C₈	—	2	8	no	—
137	C₃²×C₈	—	2	8	no	—
138	C₃²×C₈	C₂²×D₃	1	8	yes	—
139	C₃²×C₈	C₂²×D₃	1	8	yes	—
140	C₃²×C₈	C₂³×C₃	1	2	yes	—
141	C₃²×C₈	C₂³×C₃	1	2	yes	—
142	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	4	yes	—
143	C₃×C₃⋊C₈	—	3	16	no	—
144	C₂×#131	—	9	1	no	Sylow
145	C₂×C₃³	—	2	2	no	—
146	C₂×C₃³	#131	1	2	yes	complemented
147	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
148	C₃×C₃⋊D₃	—	2	4	no	—
149	C₃×#41	—	9	4	no	—
150	C₃×#41	—	9	4	no	—
151	C₂×C₃×Q₈	—	9	1	no	—
152	C₂×C₃×D₄	—	9	2	no	—
153	C₂×C₃×D₄	—	9	1	no	—
154	C₂²×C₃×C₄	—	2	4	no	—
155	C₂²×C₃×C₄	—	9	2	no	—
156	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
157	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
158	C₂×#67	—	3	8	no	—
159	#235	—	3	16	no	—
160	#235	—	3	16	no	—
161	C₂×D₁₂	—	3	4	no	—
162	C₂×C₄×D₃	—	3	8	no	—
163	C₂×Dic₆	—	3	4	no	—
164	C₃×M₁₆	—	9	4	no	—
165	C₃×M₁₆	—	9	8	no	—
166	C₂×C₃×C₈	—	2	4	no	—
167	C₂×C₃×C₈	—	2	4	no	—
168	C₂×C₃×C₈	—	2	16	no	—
169	C₂×C₃×C₈	—	9	2	no	—
170	C₂×C₃×C₈	—	9	8	no	—
171	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
172	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
173	C₂×C₃×C₈	C₂×C₃×D₃	1	16	yes	complemented
174	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
175	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
176	C₂×C₃×C₈	C₂×C₃⋊D₃	1	4	yes	complemented
177	#208	—	3	16	no	—
178	C₂×C₃⋊C₈	—	3	8	no	—
179	ΓL(1,𝔽₂₅)	—	3	32	no	—
180	D₃×C₈	—	3	32	no	—
181	C₂²×C₃²	—	2	16	no	—
182	C₂²×C₃²	—	2	8	no	—
183	C₂²×C₃²	—	2	2	no	—
184	C₂²×C₃²	—	2	8	no	—
185	C₂²×C₃²	—	2	4	no	—
186	C₂²×C₃²	C₂×C₄×D₃	1	8	yes	—
187	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
188	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
189	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
190	C₂×C₃⋊D₃	—	2	4	no	—
191	C₂×C₃⋊D₃	C₂²×C₃×C₄	1	4	yes	—
192	C₂×C₃×D₃	—	3	16	no	—
193	C₂×C₃×D₃	—	6	16	no	—
194	C₃²×C₄	—	2	4	no	—
195	C₃²×C₄	—	2	8	no	—
196	C₃²×C₄	—	2	4	no	—
197	C₃²×C₄	C₂×C₄×D₃	1	8	yes	—
198	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
199	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
200	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
201	C₃²×C₄	C₂³×D₃	1	4	yes	—
202	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
203	C₃⋊Dic₃	C₂²×C₃×C₄	1	4	yes	—
204	C₃×Dic₃	—	3	16	no	—
205	C₂×#41	—	9	1	no	—
206	#131	—	9	8	no	—
207	C₂×M₁₆	—	9	1	no	—
208	C₂×M₁₆	—	9	2	no	—
209	C₂²×C₈	—	9	2	no	—
210	C₂²×C₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
211	C₃³	C₂×#131	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₃	—	2	4	no	—
213	C₂³×C₃	—	9	2	no	—
214	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
215	C₂³×C₃	C₄×C₃⋊D₃	1	1	yes	characteristic
216	C₂²×D₃	—	3	8	no	—
217	C₃×Q₈	—	9	4	no	—
218	C₃×D₄	—	9	8	no	—
219	C₃×D₄	—	9	4	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	2	8	no	—
222	C₂×C₃×C₄	—	2	4	no	—
223	C₂×C₃×C₄	—	2	8	no	—
224	C₂×C₃×C₄	—	9	2	no	—
225	C₂×C₃×C₄	—	9	4	no	—
226	C₂×C₃×C₄	—	9	4	no	—
227	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
228	C₂×C₃×C₄	C₃×C₄×D₃	1	8	yes	—
229	C₂×C₃×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
230	C₂×C₃×C₄	C₄×C₃⋊D₃	1	2	yes	—
231	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
232	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
233	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
235	#67	—	3	32	no	—
236	C₂×Dic₃	—	3	8	no	—
237	D₁₂	—	3	16	no	—
238	C₄×D₃	—	3	16	no	—
239	C₄×D₃	—	3	16	no	—
240	Dic₆	—	3	16	no	—
241	C₃×C₈	—	2	8	no	—
242	C₃×C₈	—	2	8	no	—
243	C₃×C₈	—	9	4	no	—
244	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
245	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
246	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	—
247	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	—
248	C₃⋊C₈	—	3	16	no	—
249	C₂×C₃²	—	2	16	no	—
250	C₂×C₃²	—	2	2	no	—
251	C₂×C₃²	—	2	8	no	—
252	C₂×C₃²	—	2	8	no	—
253	C₂×C₃²	—	2	4	no	—
254	C₂×C₃²	#901	1	8	yes	complemented
255	C₂×C₃²	C₃×#131	1	2	yes	complemented
256	C₂×C₃²	C₂²×C₄×D₃	1	4	yes	—
257	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
258	C₃⋊D₃	—	2	4	no	—
259	C₃×D₃	—	6	16	no	—
260	#41	—	9	4	no	—
261	#41	—	9	4	no	—
262	C₂×Q₈	—	9	1	no	—
263	C₂×D₄	—	9	2	no	—
264	C₂×D₄	—	9	1	no	—
265	C₂²×C₄	—	9	2	no	—
266	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
267	M₁₆	—	9	4	no	—
268	M₁₆	—	9	8	no	—
269	C₂×C₈	—	9	2	no	—
270	C₂×C₈	—	9	8	no	—
271	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
272	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
273	C₂×C₈	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
274	C₂²×C₃	—	2	16	no	—
275	C₂²×C₃	—	2	8	no	—
276	C₂²×C₃	—	2	2	no	—
277	C₂²×C₃	—	2	8	no	—
278	C₂²×C₃	—	2	4	no	—
279	C₂²×C₃	—	9	4	no	—
280	C₂²×C₃	—	18	4	no	—
281	C₂²×C₃	C₂×C₃×C₄×D₃	1	8	yes	—
282	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
283	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	2	yes	—
284	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
285	C₂×D₃	—	3	16	no	—
286	C₂×D₃	—	6	16	no	—
287	C₃×C₄	—	2	4	no	—
288	C₃×C₄	—	2	4	no	—
289	C₃×C₄	—	2	8	no	—
290	C₃×C₄	—	9	4	no	—
291	C₃×C₄	C₂×C₃×C₄×D₃	1	8	yes	—
292	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
293	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
294	C₃×C₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
295	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
296	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
297	Dic₃	—	3	16	no	—
298	C₃²	—	2	4	no	—
299	C₃²	C₂×#901	1	4	yes	complemented
300	C₃²	C₂×C₃×#131	1	1	yes	characteristic, complemented
301	C₂³	—	9	2	no	—
302	C₂³	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
303	Q₈	—	9	4	no	—
304	D₄	—	9	8	no	—
305	D₄	—	9	4	no	—
306	C₂×C₄	—	9	2	no	—
307	C₂×C₄	—	9	4	no	—
308	C₂×C₄	—	9	4	no	—
309	C₂×C₄	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
310	C₂×C₄	C₃×C₄×C₃⋊D₃	1	2	yes	—
311	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
312	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
313	C₈	—	9	4	no	—
314	C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
315	C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
316	C₂×C₃	—	2	16	no	—
317	C₂×C₃	—	2	2	no	—
318	C₂×C₃	—	2	8	no	—
319	C₂×C₃	—	2	8	no	—
320	C₂×C₃	—	2	4	no	—
321	C₂×C₃	—	18	4	no	—
322	C₂×C₃	C₃×#901	1	8	yes	complemented
323	C₂×C₃	#64110	1	2	yes	direct product factor
324	C₂×C₃	C₂²×C₃×C₄×D₃	1	4	yes	—
325	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
326	D₃	—	6	16	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	9	4	no	—
329	C₂²	—	18	4	no	—
330	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	2	yes	—
331	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
332	C₄	—	9	4	no	—
333	C₄	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
334	C₄	C₂×C₃×C₄×C₃⋊D₃	1	2	yes	—
335	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
336	C₃	—	2	4	no	—
337	C₃	C₂×C₃×#901	1	4	yes	complemented
338	C₃	C₂×#64110	1	1	yes	characteristic, direct product factor
339	C₂	—	2	2	no	—
340	C₂	—	18	4	no	—
341	C₂	C₃×#64110	1	2	yes	direct product factor
342	C₂	C₂²×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂×C₃⋊D₃
commutator	C₂×C₃²	C₂³×C₃×C₄
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×C₈	C₂
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂×C₃×#3828	C₂
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₂²×C₃×C₈	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#131
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₂²×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃³×C₈	C₂	semidirect
3. C₂×C₃×#3748	C₂	semidirect
4. C₃×#64110	C₂	direct (N × H)
5. C₂×C₃×#3743	C₂	semidirect
6. C₂×C₃×C₈×C₃⋊D₃	C₂	semidirect
7. C₂×#64110	C₃	direct (N × H)
18. C₂×C₃³×C₈	C₂²	semidirect
19. C₃×#3748	C₂²	semidirect
21. C₃×#3743	C₂²	semidirect
22. C₃×C₈×C₃⋊D₃	C₂²	semidirect
26. C₂²×C₃²×C₈	D₃	semidirect
27. C₂²×C₃²×C₈	C₂×C₃	semidirect
28. C₂×#3748	C₂×C₃	semidirect
29. #64110	C₂×C₃	direct (N × H)
30. C₂×#3743	C₂×C₃	semidirect
31. C₂×C₈×C₃⋊D₃	C₂×C₃	semidirect
73. C₂×C₃²×C₈	C₂×D₃	semidirect
76. C₂×C₃²×C₈	C₂²×C₃	semidirect
77. #3748	C₂²×C₃	semidirect
79. #3743	C₂²×C₃	semidirect
80. C₈×C₃⋊D₃	C₂²×C₃	semidirect
101. C₂²×C₃×C₈	C₃×D₃	semidirect
102. C₂²×C₃×C₈	C₃⋊D₃	semidirect
146. C₂×C₃³	#131	semidirect
173. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
176. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
210. C₂²×C₈	C₃×C₃⋊D₃	semidirect
211. C₃³	C₂×#131	semidirect
254. C₂×C₃²	#901	semidirect
255. C₂×C₃²	C₃×#131	semidirect
273. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
299. C₃²	C₂×#901	semidirect
300. C₃²	C₂×C₃×#131	semidirect
322. C₂×C₃	C₃×#901	semidirect
323. C₂×C₃	#64110	direct (N × H)
337. C₃	C₂×C₃×#901	semidirect
338. C₃	C₂×#64110	direct (N × H)
341. C₂	C₃×#64110	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×#3828	2
C₂²×C₃³×C₈	2
C₂×C₃×#3748	2
C₃×#64110	2
C₂×C₃×#3743	2
C₂×C₃×C₈×C₃⋊D₃	2
C₂×#64110	3
C₂×C₃×#901	3

Subgroups — C2×C3×#64110 #13179489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64110 #13179489