Subgroups — C₂²×C₃²×#237 #13181715

Order 1728.

6284 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×#67	C₂	1	2	yes	maximal, complemented
3	C₂³×C₃²×Dic₃	C₂	1	2	yes	maximal, complemented
4	C₂×C₃²×#237	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃²×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃²×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃²×#41	—	3	1	no	maximal
8	C₂²×C₃×#237	C₃	1	4	yes	maximal, direct product factor
9	C₂⁴×C₃³	C₂²	1	2	yes	—
10	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃³×D₄	C₂²	1	12	yes	complemented
12	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃²×#67	C₂²	1	24	yes	complemented
14	C₂²×C₃²×Dic₃	C₂²	1	2	yes	—
15	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×Dic₃	C₂²	1	24	yes	complemented
17	C₃²×#237	C₂²	1	64	yes	direct product factor
18	C₂×C₃²×C₄×D₃	C₂²	1	12	yes	complemented
19	C₂×C₃²×Dic₆	C₂²	1	12	yes	complemented
20	C₂×C₃²×#41	—	3	24	no	—
21	C₂²×C₃²×Q₈	—	3	1	no	—
22	C₂²×C₃²×D₄	—	2	4	no	—
23	C₂²×C₃²×D₄	—	3	2	no	—
24	C₂²×C₃²×D₄	D₃	1	1	yes	characteristic, complemented
25	C₂²×C₃²×D₄	C₂×C₃	1	4	yes	complemented
26	C₂³×C₃²×C₄	—	3	1	no	—
27	C₂³×C₃²×C₄	—	3	2	no	—
28	C₂²×C₃×#67	C₂×C₃	1	8	yes	complemented
29	C₂³×C₃×Dic₃	C₂×C₃	1	8	yes	complemented
30	C₂×C₃×#237	C₂×C₃	1	96	yes	direct product factor
31	C₂²×C₃×C₄×D₃	C₂×C₃	1	4	yes	complemented
32	C₂²×C₃×Dic₆	C₂×C₃	1	4	yes	complemented
33	C₂³×C₃³	—	2	8	no	—
34	C₂³×C₃³	C₂³	1	12	yes	—
35	C₂³×C₃³	C₂³	1	1	yes	characteristic
36	C₂²×C₃²×D₃	—	2	4	no	—
37	C₂²×C₃²×D₃	C₂³	1	6	yes	—
38	C₃³×D₄	C₂³	1	16	yes	complemented
39	C₂×C₃³×C₄	C₂³	1	6	yes	—
40	C₃²×#67	C₂³	1	32	yes	complemented
41	C₂×C₃²×Dic₃	C₂³	1	12	yes	—
42	C₂×C₃²×Dic₃	C₂³	1	6	yes	—
43	C₂×C₃²×Dic₃	C₂³	1	32	yes	complemented
44	C₃²×C₄×D₃	C₂³	1	16	yes	complemented
45	C₃²×Dic₆	C₂³	1	16	yes	complemented
46	C₂²×C₃×#41	—	3	4	no	—
47	C₂²×#237	C₃²	1	1	yes	characteristic, direct product factor
48	C₂⁴×C₃²	—	2	8	no	—
49	C₂⁴×C₃²	—	3	1	no	—
50	C₂⁴×C₃²	C₂×D₃	1	2	yes	—
51	C₂⁴×C₃²	C₂²×C₃	1	8	yes	—
52	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	—
53	C₃²×#41	—	3	64	no	—
54	C₂×C₃²×Q₈	—	3	12	no	—
55	C₂×C₃²×D₄	—	2	48	no	—
56	C₂×C₃²×D₄	—	3	24	no	—
57	C₂×C₃²×D₄	C₂×D₃	1	12	yes	complemented
58	C₂×C₃²×D₄	C₂²×C₃	1	48	yes	complemented
59	C₂²×C₃²×C₄	—	2	4	no	—
60	C₂²×C₃²×C₄	—	3	24	no	—
61	C₂²×C₃²×C₄	—	3	1	no	—
62	C₂²×C₃²×C₄	—	3	2	no	—
63	C₂²×C₃²×C₄	—	3	12	no	—
64	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
65	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
66	C₂×C₃×#67	C₂²×C₃	1	96	yes	complemented
67	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	—
68	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
69	C₂²×C₃×Dic₃	C₂²×C₃	1	96	yes	complemented
70	C₃×#237	C₂²×C₃	1	256	yes	direct product factor
71	C₂×C₃×C₄×D₃	C₂²×C₃	1	48	yes	complemented
72	C₂×C₃×Dic₆	C₂²×C₃	1	48	yes	complemented
73	C₂²×C₃³	—	2	24	no	—
74	C₂²×C₃³	#41	1	4	yes	complemented
75	C₂²×C₃³	C₂⁴	1	8	yes	—
76	C₂²×C₃³	C₂⁴	1	3	yes	—
77	C₂×C₃²×D₃	—	2	12	no	—
78	C₂×C₃²×D₃	C₂⁴	1	4	yes	—
79	C₃³×C₄	C₂⁴	1	4	yes	—
80	C₃²×Dic₃	C₂⁴	1	8	yes	—
81	C₃²×Dic₃	C₂⁴	1	4	yes	—
82	C₂×C₃×#41	—	3	96	no	—
83	C₂²×C₃×Q₈	—	3	4	no	—
84	C₂²×C₃×D₄	—	2	4	no	—
85	C₂²×C₃×D₄	—	3	8	no	—
86	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
87	C₂²×C₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
88	C₂³×C₃×C₄	—	3	8	no	—
89	C₂³×C₃×C₄	—	3	4	no	—
90	C₂²×#67	C₂×C₃²	1	2	yes	complemented
91	C₂³×Dic₃	C₂×C₃²	1	2	yes	complemented
92	C₂×#237	C₂×C₃²	1	24	yes	direct product factor
93	C₂²×C₄×D₃	C₂×C₃²	1	1	yes	characteristic, complemented
94	C₂²×Dic₆	C₂×C₃²	1	1	yes	characteristic, complemented
95	C₂³×C₃²	—	2	8	no	—
96	C₂³×C₃²	—	2	4	no	—
97	C₂³×C₃²	—	2	48	no	—
98	C₂³×C₃²	—	2	32	no	—
99	C₂³×C₃²	—	3	6	no	—
100	C₂³×C₃²	—	4	32	no	—
101	C₂³×C₃²	—	6	4	no	—
102	C₂³×C₃²	C₂²×D₃	1	12	yes	—
103	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
104	C₂³×C₃²	C₂³×C₃	1	48	yes	—
105	C₂³×C₃²	C₂³×C₃	1	4	yes	—
106	C₂²×C₃×D₃	—	2	16	no	—
107	C₂²×C₃×D₃	C₂³×C₃	1	24	yes	—
108	C₃²×Q₈	—	3	16	no	—
109	C₃²×D₄	—	2	64	no	—
110	C₃²×D₄	—	3	32	no	—
111	C₃²×D₄	C₂²×D₃	1	16	yes	complemented
112	C₃²×D₄	C₂³×C₃	1	64	yes	complemented
113	C₂×C₃²×C₄	—	2	24	no	—
114	C₂×C₃²×C₄	—	3	6	no	—
115	C₂×C₃²×C₄	—	3	12	no	—
116	C₂×C₃²×C₄	—	3	32	no	—
117	C₂×C₃²×C₄	—	3	16	no	—
118	C₂×C₃²×C₄	C₂²×D₃	1	6	yes	—
119	C₂×C₃²×C₄	C₂³×C₃	1	24	yes	—
120	C₃×#67	C₂³×C₃	1	128	yes	complemented
121	C₂×C₃×Dic₃	C₂³×C₃	1	48	yes	—
122	C₂×C₃×Dic₃	C₂³×C₃	1	24	yes	—
123	C₂×C₃×Dic₃	C₂³×C₃	1	128	yes	complemented
124	C₃×C₄×D₃	C₂³×C₃	1	64	yes	complemented
125	C₃×Dic₆	C₂³×C₃	1	64	yes	complemented
126	C₂²×#41	—	3	1	no	Sylow
127	C₂×C₃³	—	2	8	no	—
128	C₂×C₃³	C₂×#41	1	6	yes	complemented
129	C₂×C₃³	C₂⁵	1	1	yes	characteristic
130	C₃²×D₃	—	2	4	no	—
131	C₂⁴×C₃	—	2	8	no	—
132	C₂⁴×C₃	—	3	4	no	—
133	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	—
134	C₂⁴×C₃	C₂²×C₃²	1	2	yes	—
135	C₂³×D₃	C₂²×C₃²	1	1	yes	characteristic
136	C₃×#41	—	3	256	no	—
137	C₂×C₃×Q₈	—	3	48	no	—
138	C₂×C₃×D₄	—	2	48	no	—
139	C₂×C₃×D₄	—	3	96	no	—
140	C₂×C₃×D₄	C₂×C₃×D₃	1	48	yes	complemented
141	C₂×C₃×D₄	C₂²×C₃²	1	12	yes	complemented
142	C₂²×C₃×C₄	—	2	4	no	—
143	C₂²×C₃×C₄	—	3	4	no	—
144	C₂²×C₃×C₄	—	3	8	no	—
145	C₂²×C₃×C₄	—	3	96	no	—
146	C₂²×C₃×C₄	—	3	48	no	—
147	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
148	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
149	C₂×#67	C₂²×C₃²	1	24	yes	complemented
150	C₂²×Dic₃	C₂²×C₃²	1	2	yes	—
151	C₂²×Dic₃	C₂²×C₃²	1	1	yes	characteristic
152	C₂²×Dic₃	C₂²×C₃²	1	24	yes	complemented
153	#237	C₂²×C₃²	1	64	yes	direct product factor
154	C₂×C₄×D₃	C₂²×C₃²	1	12	yes	complemented
155	C₂×Dic₆	C₂²×C₃²	1	12	yes	complemented
156	C₂²×C₃²	—	2	24	no	—
157	C₂²×C₃²	—	2	12	no	—
158	C₂²×C₃²	—	2	32	no	—
159	C₂²×C₃²	—	2	16	no	—
160	C₂²×C₃²	—	2	96	no	—
161	C₂²×C₃²	—	3	4	no	—
162	C₂²×C₃²	—	4	96	no	—
163	C₂²×C₃²	—	6	12	no	—
164	C₂²×C₃²	#237	1	4	yes	direct product factor
165	C₂²×C₃²	C₃×#41	1	16	yes	complemented
166	C₂²×C₃²	C₂³×D₃	1	8	yes	—
167	C₂²×C₃²	C₂³×D₃	1	3	yes	—
168	C₂²×C₃²	C₂⁴×C₃	1	32	yes	—
169	C₂²×C₃²	C₂⁴×C₃	1	12	yes	—
170	C₂×C₃×D₃	—	2	48	no	—
171	C₂×C₃×D₃	C₂⁴×C₃	1	16	yes	—
172	C₃²×C₄	—	2	16	no	—
173	C₃²×C₄	—	3	4	no	—
174	C₃²×C₄	—	3	8	no	—
175	C₃²×C₄	C₂³×D₃	1	4	yes	—
176	C₃²×C₄	C₂⁴×C₃	1	16	yes	—
177	C₃×Dic₃	C₂⁴×C₃	1	32	yes	—
178	C₃×Dic₃	C₂⁴×C₃	1	16	yes	—
179	C₂×#41	—	3	24	no	—
180	C₂²×Q₈	—	3	1	no	—
181	C₂²×D₄	—	3	2	no	—
182	C₂²×D₄	C₃²×D₃	1	1	yes	characteristic, complemented
183	C₂³×C₄	—	3	2	no	—
184	C₂³×C₄	—	3	1	no	—
185	C₃³	C₂²×#41	1	1	yes	characteristic, complemented, Sylow
186	C₂³×C₃	—	2	32	no	—
187	C₂³×C₃	—	2	8	no	—
188	C₂³×C₃	—	2	4	no	—
189	C₂³×C₃	—	2	48	no	—
190	C₂³×C₃	—	3	24	no	—
191	C₂³×C₃	—	4	32	no	—
192	C₂³×C₃	—	6	16	no	—
193	C₂³×C₃	C₂²×C₃×D₃	1	48	yes	—
194	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
195	C₂³×C₃	C₂³×C₃²	1	12	yes	—
196	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
197	C₂²×D₃	—	2	4	no	—
198	C₂²×D₃	C₂³×C₃²	1	6	yes	—
199	C₃×Q₈	—	3	64	no	—
200	C₃×D₄	—	2	64	no	—
201	C₃×D₄	—	3	128	no	—
202	C₃×D₄	C₂²×C₃×D₃	1	64	yes	complemented
203	C₃×D₄	C₂³×C₃²	1	16	yes	complemented
204	C₂×C₃×C₄	—	2	24	no	—
205	C₂×C₃×C₄	—	3	24	no	—
206	C₂×C₃×C₄	—	3	48	no	—
207	C₂×C₃×C₄	—	3	128	no	—
208	C₂×C₃×C₄	—	3	64	no	—
209	C₂×C₃×C₄	C₂²×C₃×D₃	1	24	yes	—
210	C₂×C₃×C₄	C₂³×C₃²	1	6	yes	—
211	#67	C₂³×C₃²	1	32	yes	complemented
212	C₂×Dic₃	C₂³×C₃²	1	12	yes	—
213	C₂×Dic₃	C₂³×C₃²	1	6	yes	—
214	C₂×Dic₃	C₂³×C₃²	1	32	yes	complemented
215	C₄×D₃	C₂³×C₃²	1	16	yes	complemented
216	Dic₆	C₂³×C₃²	1	16	yes	complemented
217	C₂×C₃²	—	2	8	no	—
218	C₂×C₃²	—	2	24	no	—
219	C₂×C₃²	—	2	4	no	—
220	C₂×C₃²	—	2	32	no	—
221	C₂×C₃²	—	4	32	no	—
222	C₂×C₃²	—	6	4	no	—
223	C₂×C₃²	C₂×#237	1	6	yes	direct product factor
224	C₂×C₃²	C₂×C₃×#41	1	24	yes	complemented
225	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
226	C₂×C₃²	C₂⁵×C₃	1	4	yes	—
227	C₃×D₃	—	2	16	no	—
228	C₂⁴	—	3	1	no	—
229	C₂⁴	C₂×C₃²×D₃	1	2	yes	—
230	#41	—	3	64	no	—
231	C₂×Q₈	—	3	12	no	—
232	C₂×D₄	—	3	24	no	—
233	C₂×D₄	C₂×C₃²×D₃	1	12	yes	complemented
234	C₂²×C₄	—	3	1	no	—
235	C₂²×C₄	—	3	2	no	—
236	C₂²×C₄	—	3	24	no	—
237	C₂²×C₄	—	3	12	no	—
238	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
239	C₂²×C₃	—	2	96	no	—
240	C₂²×C₃	—	2	24	no	—
241	C₂²×C₃	—	2	12	no	—
242	C₂²×C₃	—	2	32	no	—
243	C₂²×C₃	—	2	16	no	—
244	C₂²×C₃	—	3	16	no	—
245	C₂²×C₃	—	4	96	no	—
246	C₂²×C₃	—	6	48	no	—
247	C₂²×C₃	C₃×#237	1	16	yes	direct product factor
248	C₂²×C₃	C₃²×#41	1	4	yes	complemented
249	C₂²×C₃	C₂³×C₃×D₃	1	32	yes	—
250	C₂²×C₃	C₂³×C₃×D₃	1	12	yes	—
251	C₂²×C₃	C₂⁴×C₃²	1	8	yes	—
252	C₂²×C₃	C₂⁴×C₃²	1	3	yes	—
253	C₂×D₃	—	2	12	no	—
254	C₂×D₃	C₂⁴×C₃²	1	4	yes	—
255	C₃×C₄	—	2	16	no	—
256	C₃×C₄	—	3	16	no	—
257	C₃×C₄	—	3	32	no	—
258	C₃×C₄	C₂³×C₃×D₃	1	16	yes	—
259	C₃×C₄	C₂⁴×C₃²	1	4	yes	—
260	Dic₃	C₂⁴×C₃²	1	8	yes	—
261	Dic₃	C₂⁴×C₃²	1	4	yes	—
262	C₃²	—	2	4	no	—
263	C₃²	C₂²×#237	1	1	yes	characteristic, direct product factor
264	C₃²	C₂²×C₃×#41	1	4	yes	complemented
265	C₂³	—	2	8	no	—
266	C₂³	—	3	6	no	—
267	C₂³	—	6	4	no	—
268	C₂³	C₂²×C₃²×D₃	1	12	yes	—
269	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
270	Q₈	—	3	16	no	—
271	D₄	—	3	32	no	—
272	D₄	C₂²×C₃²×D₃	1	16	yes	complemented
273	C₂×C₄	—	3	6	no	—
274	C₂×C₄	—	3	12	no	—
275	C₂×C₄	—	3	32	no	—
276	C₂×C₄	—	3	16	no	—
277	C₂×C₄	C₂²×C₃²×D₃	1	6	yes	—
278	C₂×C₃	—	2	32	no	—
279	C₂×C₃	—	2	8	no	—
280	C₂×C₃	—	2	24	no	—
281	C₂×C₃	—	2	4	no	—
282	C₂×C₃	—	4	32	no	—
283	C₂×C₃	—	6	16	no	—
284	C₂×C₃	C₂×C₃×#237	1	24	yes	direct product factor
285	C₂×C₃	C₂×C₃²×#41	1	6	yes	complemented
286	C₂×C₃	C₂⁴×C₃×D₃	1	4	yes	—
287	C₂×C₃	C₂⁵×C₃²	1	1	yes	characteristic
288	D₃	—	2	4	no	—
289	C₂²	—	2	24	no	—
290	C₂²	—	3	4	no	—
291	C₂²	—	6	12	no	—
292	C₂²	C₃²×#237	1	4	yes	direct product factor
293	C₂²	C₂³×C₃²×D₃	1	8	yes	—
294	C₂²	C₂³×C₃²×D₃	1	3	yes	—
295	C₄	—	3	4	no	—
296	C₄	—	3	8	no	—
297	C₄	C₂³×C₃²×D₃	1	4	yes	—
298	C₃	—	2	4	no	—
299	C₃	C₂²×C₃×#237	1	4	yes	direct product factor
300	C₃	C₂²×C₃²×#41	1	1	yes	characteristic, complemented
301	C₂	—	2	8	no	—
302	C₂	—	6	4	no	—
303	C₂	C₂×C₃²×#237	1	6	yes	direct product factor
304	C₂	C₂⁴×C₃²×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃²	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂⁵×C₃²
Frattini	C₂	C₂⁴×C₃²×D₃
Fitting	C₂²×C₃³×D₄	C₂
socle	C₂³×C₃³	C₂³
hypercenter	C₂²×C₃²×D₄	D₃
hypocenter	C₃	C₂²×C₃²×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃² ◁ C₂²×C₃²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×D₄	C₂	semidirect
2. C₂²×C₃²×#67	C₂	semidirect
3. C₂³×C₃²×Dic₃	C₂	semidirect
4. C₂×C₃²×#237	C₂	direct (N × H)
5. C₂²×C₃²×C₄×D₃	C₂	semidirect
6. C₂²×C₃²×Dic₆	C₂	semidirect
8. C₂²×C₃×#237	C₃	direct (N × H)
11. C₂×C₃³×D₄	C₂²	semidirect
13. C₂×C₃²×#67	C₂²	semidirect
16. C₂²×C₃²×Dic₃	C₂²	semidirect
17. C₃²×#237	C₂²	direct (N × H)
18. C₂×C₃²×C₄×D₃	C₂²	semidirect
19. C₂×C₃²×Dic₆	C₂²	semidirect
24. C₂²×C₃²×D₄	D₃	semidirect
25. C₂²×C₃²×D₄	C₂×C₃	semidirect
28. C₂²×C₃×#67	C₂×C₃	semidirect
29. C₂³×C₃×Dic₃	C₂×C₃	semidirect
30. C₂×C₃×#237	C₂×C₃	direct (N × H)
31. C₂²×C₃×C₄×D₃	C₂×C₃	semidirect
32. C₂²×C₃×Dic₆	C₂×C₃	semidirect
38. C₃³×D₄	C₂³	semidirect
40. C₃²×#67	C₂³	semidirect
43. C₂×C₃²×Dic₃	C₂³	semidirect
44. C₃²×C₄×D₃	C₂³	semidirect
45. C₃²×Dic₆	C₂³	semidirect
47. C₂²×#237	C₃²	direct (N × H)
57. C₂×C₃²×D₄	C₂×D₃	semidirect
58. C₂×C₃²×D₄	C₂²×C₃	semidirect
66. C₂×C₃×#67	C₂²×C₃	semidirect
69. C₂²×C₃×Dic₃	C₂²×C₃	semidirect
70. C₃×#237	C₂²×C₃	direct (N × H)
71. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
72. C₂×C₃×Dic₆	C₂²×C₃	semidirect
74. C₂²×C₃³	#41	semidirect
86. C₂²×C₃×D₄	C₃×D₃	semidirect
87. C₂²×C₃×D₄	C₂×C₃²	semidirect
90. C₂²×#67	C₂×C₃²	semidirect
91. C₂³×Dic₃	C₂×C₃²	semidirect
92. C₂×#237	C₂×C₃²	direct (N × H)
93. C₂²×C₄×D₃	C₂×C₃²	semidirect
94. C₂²×Dic₆	C₂×C₃²	semidirect
111. C₃²×D₄	C₂²×D₃	semidirect
112. C₃²×D₄	C₂³×C₃	semidirect
120. C₃×#67	C₂³×C₃	semidirect
123. C₂×C₃×Dic₃	C₂³×C₃	semidirect
124. C₃×C₄×D₃	C₂³×C₃	semidirect
125. C₃×Dic₆	C₂³×C₃	semidirect
128. C₂×C₃³	C₂×#41	semidirect
140. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
141. C₂×C₃×D₄	C₂²×C₃²	semidirect
149. C₂×#67	C₂²×C₃²	semidirect
152. C₂²×Dic₃	C₂²×C₃²	semidirect
153. #237	C₂²×C₃²	direct (N × H)
154. C₂×C₄×D₃	C₂²×C₃²	semidirect
155. C₂×Dic₆	C₂²×C₃²	semidirect
164. C₂²×C₃²	#237	direct (N × H)
165. C₂²×C₃²	C₃×#41	semidirect
182. C₂²×D₄	C₃²×D₃	semidirect
185. C₃³	C₂²×#41	semidirect
202. C₃×D₄	C₂²×C₃×D₃	semidirect
203. C₃×D₄	C₂³×C₃²	semidirect
211. #67	C₂³×C₃²	semidirect
214. C₂×Dic₃	C₂³×C₃²	semidirect
215. C₄×D₃	C₂³×C₃²	semidirect
216. Dic₆	C₂³×C₃²	semidirect
223. C₂×C₃²	C₂×#237	direct (N × H)
224. C₂×C₃²	C₂×C₃×#41	semidirect
233. C₂×D₄	C₂×C₃²×D₃	semidirect
247. C₂²×C₃	C₃×#237	direct (N × H)
248. C₂²×C₃	C₃²×#41	semidirect
263. C₃²	C₂²×#237	direct (N × H)
264. C₃²	C₂²×C₃×#41	semidirect
272. D₄	C₂²×C₃²×D₃	semidirect
284. C₂×C₃	C₂×C₃×#237	direct (N × H)
285. C₂×C₃	C₂×C₃²×#41	semidirect
292. C₂²	C₃²×#237	direct (N × H)
299. C₃	C₂²×C₃×#237	direct (N × H)
300. C₃	C₂²×C₃²×#41	semidirect
303. C₂	C₂×C₃²×#237	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃³×D₄	2
C₂²×C₃²×#67	2
C₂³×C₃²×Dic₃	2
C₂×C₃²×#237	2
C₂²×C₃²×C₄×D₃	2
C₂²×C₃²×Dic₆	2
C₂²×C₃²×#41	3
C₂²×C₃×#237	3

Subgroups — C22×C32×#237 #13181715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃²×#237 #13181715