Subgroups — C₂×C₃×#64113 #13179492

Order 1728.

1900 conjugacy classes of subgroups.

The subgroup lattice has 338 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	2	yes	maximal, complemented
2	C₂²×C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3746	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64113	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3745	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3744	C₂	1	2	yes	maximal, complemented
7	C₂×#64113	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#904	—	3	4	no	maximal
9	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×#638	—	2	2	no	—
11	C₃×#3828	—	2	4	no	—
12	C₃×#3828	C₂²	1	8	yes	complemented
13	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
14	C₂×C₃×C₄×C₃⋊D₃	—	2	2	no	—
15	C₂×C₃×#634	C₂²	1	2	yes	—
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×#3746	C₂²	1	4	yes	complemented
20	C₃×#3745	C₂²	1	4	yes	complemented
21	C₃×#3744	C₂²	1	8	yes	complemented
22	C₂×#3828	C₂×C₃	1	2	yes	complemented
23	C₂×C₃×#235	—	3	8	no	—
24	C₂²×C₃²×C₈	—	2	4	no	—
25	C₂²×C₃²×C₈	D₃	1	4	yes	complemented
26	C₂²×C₃²×C₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#3746	C₂×C₃	1	1	yes	characteristic, complemented
28	#64113	C₂×C₃	1	8	yes	direct product factor
29	C₂×#3745	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×#3744	C₂×C₃	1	2	yes	complemented
31	C₂×C₃×Dic₁₂	—	3	4	no	—
32	C₃×#904	—	3	32	no	—
33	C₂×C₃×D₂₄	—	3	4	no	—
34	C₂×C₃×#204	—	3	8	no	—
35	C₂³×C₃³	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
37	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
38	C₂×C₃³×C₄	D₄	1	2	yes	—
39	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
40	C₂×C₃³×C₄	C₂³	1	2	yes	—
41	C₃×#638	—	2	8	no	—
42	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
43	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
44	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	4	yes	—
45	C₃×C₄×C₃⋊D₃	—	2	8	no	—
46	C₃×#634	—	2	2	no	—
47	C₃×#634	C₂³	1	4	yes	—
48	C₃³×C₈	C₂³	1	2	yes	—
49	C₃³×C₈	C₂³	1	2	yes	—
50	C₂×C₃×#135	—	9	1	no	—
51	C₂×#904	—	3	4	no	—
52	C₂²×C₃²×C₄	—	2	4	no	—
53	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
54	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
55	C₂×#638	—	2	2	no	—
56	#3828	—	2	4	no	—
57	#3828	C₂²×C₃	1	8	yes	complemented
58	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
59	C₂×C₄×C₃⋊D₃	—	2	2	no	—
60	C₂×#634	C₂²×C₃	1	2	yes	—
61	C₂×C₃×#67	—	6	8	no	—
62	C₃×#235	—	3	32	no	—
63	C₃×#235	—	6	16	no	—
64	C₂×C₃×D₁₂	—	3	8	no	—
65	C₂×C₃×C₄×D₃	—	6	8	no	—
66	C₂×C₃×Dic₆	—	3	8	no	—
67	C₂×C₃²×C₈	—	2	4	no	—
68	C₂×C₃²×C₈	—	2	4	no	—
69	C₂×C₃²×C₈	—	2	16	no	—
70	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
71	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
72	C₂×C₃²×C₈	C₂×D₃	1	16	yes	complemented
73	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	complemented
76	#3746	C₂²×C₃	1	4	yes	complemented
77	#3745	C₂²×C₃	1	4	yes	complemented
78	#3744	C₂²×C₃	1	8	yes	complemented
79	C₃×Dic₁₂	—	3	16	no	—
80	C₃×D₂₄	—	3	16	no	—
81	C₃×#204	—	3	32	no	—
82	C₂²×C₃³	—	2	2	no	—
83	C₂²×C₃³	C₂×D₄	1	2	yes	—
84	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃×C₃⋊D₃	—	2	4	no	—
86	C₂×C₃×C₃⋊D₃	—	4	4	no	—
87	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
88	C₃³×C₄	C₂×D₄	1	2	yes	—
89	C₃³×C₄	C₂⁴	1	1	yes	characteristic
90	C₃×C₃⋊Dic₃	—	2	4	no	—
91	C₂×C₃×#41	—	9	2	no	—
92	C₂×#235	—	3	8	no	—
93	C₃×#135	—	9	8	no	—
94	C₂×C₃×Q₁₆	—	9	1	no	—
95	C₂×C₃×SD₁₆	—	9	2	no	—
96	C₂×C₃×D₈	—	9	1	no	—
97	C₂²×C₃×C₈	—	2	4	no	—
98	C₂²×C₃×C₈	C₃×D₃	1	4	yes	complemented
99	C₂²×C₃×C₈	C₃⋊D₃	1	1	yes	characteristic, complemented
100	C₂×Dic₁₂	—	3	4	no	—
101	#904	—	3	32	no	—
102	C₂×D₂₄	—	3	4	no	—
103	C₂×#204	—	3	8	no	—
104	C₂³×C₃²	—	2	4	no	—
105	C₂³×C₃²	D₁₂	1	4	yes	—
106	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
107	C₂²×C₃⋊D₃	—	2	2	no	—
108	C₂²×C₃×D₃	—	6	8	no	—
109	C₂×C₃²×C₄	—	2	4	no	—
110	C₂×C₃²×C₄	—	2	8	no	—
111	C₂×C₃²×C₄	—	2	4	no	—
112	C₂×C₃²×C₄	—	2	8	no	—
113	C₂×C₃²×C₄	D₁₂	1	8	yes	—
114	C₂×C₃²×C₄	D₁₂	1	4	yes	—
115	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
117	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
118	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
119	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
120	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
121	#638	—	2	8	no	—
122	C₂×C₃⋊Dic₃	—	2	2	no	—
123	C₄⋊(C₃⋊D₃)	—	2	2	no	—
124	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	4	yes	—
125	C₄×C₃⋊D₃	—	2	8	no	—
126	#634	—	2	2	no	—
127	#634	C₂³×C₃	1	4	yes	—
128	C₃×#67	—	6	32	no	—
129	C₂×C₃×Dic₃	—	6	8	no	—
130	C₃×D₁₂	—	3	16	no	—
131	C₃×D₁₂	—	6	8	no	—
132	C₃×C₄×D₃	—	6	32	no	—
133	C₃×Dic₆	—	3	16	no	—
134	C₃×Dic₆	—	6	8	no	—
135	C₃²×C₈	—	2	8	no	—
136	C₃²×C₈	—	2	8	no	—
137	C₃²×C₈	C₂²×D₃	1	8	yes	—
138	C₃²×C₈	C₂²×D₃	1	8	yes	—
139	C₃²×C₈	C₂³×C₃	1	2	yes	—
140	C₃²×C₈	C₂³×C₃	1	2	yes	—
141	C₂×#135	—	9	1	no	Sylow
142	C₂×C₃³	—	2	2	no	—
143	C₂×C₃³	#135	1	2	yes	complemented
144	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
145	C₃×C₃⋊D₃	—	4	4	no	—
146	C₃×#41	—	9	8	no	—
147	C₃×#41	—	18	4	no	—
148	C₂×C₃×Q₈	—	9	2	no	—
149	C₂×C₃×D₄	—	9	2	no	—
150	C₂×C₃×D₄	—	18	2	no	—
151	C₂²×C₃×C₄	—	2	4	no	—
152	C₂²×C₃×C₄	—	18	2	no	—
153	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
154	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
155	C₂×#67	—	6	8	no	—
156	#235	—	3	32	no	—
157	#235	—	6	16	no	—
158	C₂×D₁₂	—	3	8	no	—
159	C₂×C₄×D₃	—	6	8	no	—
160	C₂×Dic₆	—	3	8	no	—
161	C₃×Q₁₆	—	9	4	no	—
162	C₃×SD₁₆	—	9	8	no	—
163	C₃×D₈	—	9	4	no	—
164	C₂×C₃×C₈	—	2	4	no	—
165	C₂×C₃×C₈	—	2	4	no	—
166	C₂×C₃×C₈	—	2	16	no	—
167	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
168	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
169	C₂×C₃×C₈	C₂×C₃×D₃	1	16	yes	complemented
170	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
171	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
172	C₂×C₃×C₈	C₂×C₃⋊D₃	1	4	yes	complemented
173	Dic₁₂	—	3	16	no	—
174	D₂₄	—	3	16	no	—
175	#204	—	3	32	no	—
176	C₂²×C₃²	—	2	16	no	—
177	C₂²×C₃²	—	2	8	no	—
178	C₂²×C₃²	—	2	2	no	—
179	C₂²×C₃²	—	2	8	no	—
180	C₂²×C₃²	—	2	4	no	—
181	C₂²×C₃²	C₂×D₁₂	1	8	yes	—
182	C₂²×C₃²	C₂×D₁₂	1	4	yes	—
183	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
184	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
185	C₂×C₃⋊D₃	—	2	4	no	—
186	C₂×C₃⋊D₃	—	4	4	no	—
187	C₂×C₃×D₃	—	6	16	no	—
188	C₂×C₃×D₃	—	12	16	no	—
189	C₃²×C₄	—	2	4	no	—
190	C₃²×C₄	—	2	4	no	—
191	C₃²×C₄	—	2	8	no	—
192	C₃²×C₄	C₂×D₁₂	1	4	yes	—
193	C₃²×C₄	C₂×D₁₂	1	8	yes	—
194	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
195	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
196	C₃²×C₄	C₂³×D₃	1	4	yes	—
197	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
198	C₃⋊Dic₃	—	2	4	no	—
199	C₃×Dic₃	—	6	16	no	—
200	C₂×#41	—	9	2	no	—
201	#135	—	9	8	no	—
202	C₂×Q₁₆	—	9	1	no	—
203	C₂×SD₁₆	—	9	2	no	—
204	C₂×D₈	—	9	1	no	—
205	C₂²×C₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
206	C₃³	C₂×#135	1	1	yes	characteristic, complemented, Sylow
207	C₂³×C₃	—	2	4	no	—
208	C₂³×C₃	—	18	2	no	—
209	C₂³×C₃	C₃×D₁₂	1	4	yes	—
210	C₂³×C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
211	C₂²×D₃	—	6	8	no	—
212	C₃×Q₈	—	9	4	no	—
213	C₃×Q₈	—	18	2	no	—
214	C₃×D₄	—	9	4	no	—
215	C₃×D₄	—	18	8	no	—
216	C₃×D₄	—	18	2	no	—
217	C₂×C₃×C₄	—	2	4	no	—
218	C₂×C₃×C₄	—	2	8	no	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	2	8	no	—
221	C₂×C₃×C₄	—	18	2	no	—
222	C₂×C₃×C₄	—	18	8	no	—
223	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
224	C₂×C₃×C₄	C₃×D₁₂	1	8	yes	—
225	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
226	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
228	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
229	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
231	#67	—	6	32	no	—
232	C₂×Dic₃	—	6	8	no	—
233	D₁₂	—	3	16	no	—
234	D₁₂	—	6	8	no	—
235	C₄×D₃	—	6	32	no	—
236	Dic₆	—	3	16	no	—
237	Dic₆	—	6	8	no	—
238	C₃×C₈	—	2	8	no	—
239	C₃×C₈	—	2	8	no	—
240	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
241	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
242	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	—
243	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	—
244	C₂×C₃²	—	2	16	no	—
245	C₂×C₃²	—	2	2	no	—
246	C₂×C₃²	—	2	8	no	—
247	C₂×C₃²	—	2	8	no	—
248	C₂×C₃²	—	2	4	no	—
249	C₂×C₃²	#904	1	8	yes	complemented
250	C₂×C₃²	C₃×#135	1	2	yes	complemented
251	C₂×C₃²	C₂²×D₁₂	1	4	yes	—
252	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
253	C₃⋊D₃	—	4	4	no	—
254	C₃×D₃	—	12	16	no	—
255	#41	—	9	8	no	—
256	#41	—	18	4	no	—
257	C₂×Q₈	—	9	2	no	—
258	C₂×D₄	—	9	2	no	—
259	C₂×D₄	—	18	2	no	—
260	C₂²×C₄	—	18	2	no	—
261	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
262	Q₁₆	—	9	4	no	—
263	SD₁₆	—	9	8	no	—
264	D₈	—	9	4	no	—
265	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
266	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
267	C₂×C₈	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
268	C₂²×C₃	—	2	16	no	—
269	C₂²×C₃	—	2	8	no	—
270	C₂²×C₃	—	2	2	no	—
271	C₂²×C₃	—	2	8	no	—
272	C₂²×C₃	—	2	4	no	—
273	C₂²×C₃	—	18	4	no	—
274	C₂²×C₃	—	36	4	no	—
275	C₂²×C₃	C₂×C₃×D₁₂	1	8	yes	—
276	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
277	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
278	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
279	C₂×D₃	—	6	16	no	—
280	C₂×D₃	—	12	16	no	—
281	C₃×C₄	—	2	4	no	—
282	C₃×C₄	—	2	8	no	—
283	C₃×C₄	—	2	4	no	—
284	C₃×C₄	—	18	4	no	—
285	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
286	C₃×C₄	C₂×C₃×D₁₂	1	8	yes	—
287	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
288	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
289	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
290	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
291	Dic₃	—	6	16	no	—
292	C₃²	—	2	4	no	—
293	C₃²	C₂×#904	1	4	yes	complemented
294	C₃²	C₂×C₃×#135	1	1	yes	characteristic, complemented
295	C₂³	—	18	2	no	—
296	C₂³	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
297	Q₈	—	9	4	no	—
298	Q₈	—	18	2	no	—
299	D₄	—	9	4	no	—
300	D₄	—	18	8	no	—
301	D₄	—	18	2	no	—
302	C₂×C₄	—	18	2	no	—
303	C₂×C₄	—	18	8	no	—
304	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
305	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
306	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
307	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
308	C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
309	C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
310	C₂×C₃	—	2	16	no	—
311	C₂×C₃	—	2	2	no	—
312	C₂×C₃	—	2	8	no	—
313	C₂×C₃	—	2	8	no	—
314	C₂×C₃	—	2	4	no	—
315	C₂×C₃	—	36	4	no	—
316	C₂×C₃	C₃×#904	1	8	yes	complemented
317	C₂×C₃	#64113	1	2	yes	direct product factor
318	C₂×C₃	C₂²×C₃×D₁₂	1	4	yes	—
319	C₂×C₃	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
320	D₃	—	12	16	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	18	4	no	—
323	C₂²	—	36	4	no	—
324	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
325	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
326	C₄	—	18	4	no	—
327	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
328	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
329	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
330	C₃	—	2	4	no	—
331	C₃	C₂×C₃×#904	1	4	yes	complemented
332	C₃	C₂×#64113	1	1	yes	characteristic, direct product factor
333	C₂	—	2	2	no	—
334	C₂	—	36	4	no	—
335	C₂	C₃×#64113	1	2	yes	direct product factor
336	C₂	C₂²×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×C₈	C₂
socle	C₂²×C₃³	C₂×D₄
hypercenter	C₂²×C₃×C₈	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#135
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3828	C₂	semidirect
2. C₂²×C₃³×C₈	C₂	semidirect
3. C₂×C₃×#3746	C₂	semidirect
4. C₃×#64113	C₂	direct (N × H)
5. C₂×C₃×#3745	C₂	semidirect
6. C₂×C₃×#3744	C₂	semidirect
7. C₂×#64113	C₃	direct (N × H)
12. C₃×#3828	C₂²	semidirect
18. C₂×C₃³×C₈	C₂²	semidirect
19. C₃×#3746	C₂²	semidirect
20. C₃×#3745	C₂²	semidirect
21. C₃×#3744	C₂²	semidirect
22. C₂×#3828	C₂×C₃	semidirect
25. C₂²×C₃²×C₈	D₃	semidirect
26. C₂²×C₃²×C₈	C₂×C₃	semidirect
27. C₂×#3746	C₂×C₃	semidirect
28. #64113	C₂×C₃	direct (N × H)
29. C₂×#3745	C₂×C₃	semidirect
30. C₂×#3744	C₂×C₃	semidirect
57. #3828	C₂²×C₃	semidirect
72. C₂×C₃²×C₈	C₂×D₃	semidirect
75. C₂×C₃²×C₈	C₂²×C₃	semidirect
76. #3746	C₂²×C₃	semidirect
77. #3745	C₂²×C₃	semidirect
78. #3744	C₂²×C₃	semidirect
98. C₂²×C₃×C₈	C₃×D₃	semidirect
99. C₂²×C₃×C₈	C₃⋊D₃	semidirect
143. C₂×C₃³	#135	semidirect
169. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
172. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
205. C₂²×C₈	C₃×C₃⋊D₃	semidirect
206. C₃³	C₂×#135	semidirect
249. C₂×C₃²	#904	semidirect
250. C₂×C₃²	C₃×#135	semidirect
267. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
293. C₃²	C₂×#904	semidirect
294. C₃²	C₂×C₃×#135	semidirect
316. C₂×C₃	C₃×#904	semidirect
317. C₂×C₃	#64113	direct (N × H)
331. C₃	C₂×C₃×#904	semidirect
332. C₃	C₂×#64113	direct (N × H)
335. C₂	C₃×#64113	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×#3746	2
C₃×#64113	2
C₂×C₃×#3745	2
C₂×C₃×#3744	2
C₂×#64113	3
C₂×C₃×#904	3

Subgroups — C2×C3×#64113 #13179492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64113 #13179492