Subgroups — C₂²×C₃×#904 #11918603

Order 1152.

3177 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	C₂²×C₃×#235	C₂	1	2	yes	maximal, complemented
2	C₂³×C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#904	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×#204	C₂	1	2	yes	maximal, complemented
7	C₂²×C₃×#135	—	3	1	no	maximal
8	C₂²×#904	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×#67	—	2	2	no	—
11	C₂×C₃×#235	—	2	12	no	—
12	C₂×C₃×#235	C₂²	1	24	yes	complemented
13	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×D₃	—	2	2	no	—
15	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃²×C₈	C₂²	1	12	yes	complemented
19	C₂×C₃×Dic₁₂	C₂²	1	12	yes	complemented
20	C₃×#904	C₂²	1	64	yes	direct product factor
21	C₂×C₃×D₂₄	C₂²	1	12	yes	complemented
22	C₂×C₃×#204	C₂²	1	24	yes	complemented
23	C₂²×C₃×#41	—	3	2	no	—
24	C₂²×#235	C₂×C₃	1	2	yes	complemented
25	C₂×C₃×#135	—	3	24	no	—
26	C₂²×C₃×Q₁₆	—	3	1	no	—
27	C₂²×C₃×SD₁₆	—	3	2	no	—
28	C₂²×C₃×D₈	—	3	1	no	—
29	C₂³×C₃×C₈	—	2	1	no	—
30	C₂³×C₃×C₈	D₃	1	1	yes	characteristic, complemented
31	C₂³×C₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂²×Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#904	C₂×C₃	1	24	yes	direct product factor
34	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂²×#204	C₂×C₃	1	2	yes	complemented
36	C₂⁴×C₃²	D₄	1	1	yes	characteristic
37	C₂³×C₃×D₃	—	2	2	no	—
38	C₂²×C₃²×C₄	D₄	1	6	yes	—
39	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
40	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
41	C₂²×C₃²×C₄	C₂³	1	6	yes	—
42	C₂×C₃×#67	—	2	24	no	—
43	C₂²×C₃×Dic₃	—	2	2	no	—
44	C₃×#235	—	2	48	no	—
45	C₃×#235	C₂³	1	32	yes	complemented
46	C₂×C₃×D₁₂	—	2	6	no	—
47	C₂×C₃×D₁₂	C₂³	1	12	yes	—
48	C₂×C₃×C₄×D₃	—	2	24	no	—
49	C₂×C₃×Dic₆	—	2	6	no	—
50	C₂×C₃×Dic₆	C₂³	1	12	yes	—
51	C₂×C₃²×C₈	C₂³	1	6	yes	—
52	C₂×C₃²×C₈	C₂³	1	6	yes	—
53	C₂×C₃²×C₈	C₂³	1	16	yes	complemented
54	C₃×Dic₁₂	C₂³	1	16	yes	complemented
55	C₃×D₂₄	C₂³	1	16	yes	complemented
56	C₃×#204	C₂³	1	32	yes	complemented
57	C₂²×#135	—	3	1	no	Sylow
58	C₂×C₃×#41	—	3	24	no	—
59	C₂×C₃×#41	—	6	12	no	—
60	C₂²×C₃×Q₈	—	3	2	no	—
61	C₂²×C₃×D₄	—	3	2	no	—
62	C₂²×C₃×D₄	—	6	2	no	—
63	C₂³×C₃×C₄	—	2	1	no	—
64	C₂³×C₃×C₄	—	6	2	no	—
65	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
66	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
67	C₂²×#67	—	2	2	no	—
68	C₂×#235	—	2	12	no	—
69	C₂×#235	C₂²×C₃	1	24	yes	complemented
70	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
71	C₂²×C₄×D₃	—	2	2	no	—
72	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
73	C₃×#135	—	3	64	no	—
74	C₂×C₃×Q₁₆	—	3	12	no	—
75	C₂×C₃×SD₁₆	—	3	24	no	—
76	C₂×C₃×D₈	—	3	12	no	—
77	C₂²×C₃×C₈	—	2	1	no	—
78	C₂²×C₃×C₈	—	2	1	no	—
79	C₂²×C₃×C₈	—	2	12	no	—
80	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₃×C₈	C₂×D₃	1	12	yes	complemented
83	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₃×C₈	C₂²×C₃	1	12	yes	complemented
86	C₂×Dic₁₂	C₂²×C₃	1	12	yes	complemented
87	#904	C₂²×C₃	1	64	yes	direct product factor
88	C₂×D₂₄	C₂²×C₃	1	12	yes	complemented
89	C₂×#204	C₂²×C₃	1	24	yes	complemented
90	C₂³×C₃²	—	2	4	no	—
91	C₂³×C₃²	C₂×D₄	1	6	yes	—
92	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₃×D₃	—	2	12	no	—
94	C₂²×C₃×D₃	—	4	8	no	—
95	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
96	C₂×C₃²×C₄	C₂×D₄	1	6	yes	—
97	C₂×C₃²×C₄	C₂×D₄	1	12	yes	—
98	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
99	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
100	C₃×#67	—	2	32	no	—
101	C₂×C₃×Dic₃	—	2	12	no	—
102	C₃×D₁₂	—	2	12	no	—
103	C₃×D₁₂	C₂⁴	1	8	yes	—
104	C₃×C₄×D₃	—	2	32	no	—
105	C₃×Dic₆	—	2	12	no	—
106	C₃×Dic₆	C₂⁴	1	8	yes	—
107	C₃²×C₈	C₂⁴	1	4	yes	—
108	C₃²×C₈	C₂⁴	1	4	yes	—
109	C₂²×#41	—	3	2	no	—
110	C₂×#135	—	3	24	no	—
111	C₂²×Q₁₆	—	3	1	no	—
112	C₂²×SD₁₆	—	3	2	no	—
113	C₂²×D₈	—	3	1	no	—
114	C₂³×C₈	C₃×D₃	1	1	yes	characteristic, complemented
115	C₂⁴×C₃	—	2	1	no	—
116	C₂⁴×C₃	—	6	2	no	—
117	C₂⁴×C₃	D₁₂	1	1	yes	characteristic
118	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
119	C₂³×D₃	—	2	2	no	—
120	C₃×#41	—	3	32	no	—
121	C₃×#41	—	6	48	no	—
122	C₂×C₃×Q₈	—	3	12	no	—
123	C₂×C₃×Q₈	—	6	6	no	—
124	C₂×C₃×D₄	—	3	12	no	—
125	C₂×C₃×D₄	—	6	24	no	—
126	C₂×C₃×D₄	—	6	6	no	—
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	2	6	no	—
129	C₂²×C₃×C₄	—	2	1	no	—
130	C₂²×C₃×C₄	—	2	6	no	—
131	C₂²×C₃×C₄	—	6	2	no	—
132	C₂²×C₃×C₄	—	6	24	no	—
133	C₂²×C₃×C₄	D₁₂	1	6	yes	—
134	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₃×D₄	1	6	yes	—
137	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
139	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
141	C₂×#67	—	2	24	no	—
142	C₂²×Dic₃	—	2	2	no	—
143	#235	—	2	48	no	—
144	#235	C₂³×C₃	1	32	yes	complemented
145	C₂×D₁₂	—	2	6	no	—
146	C₂×D₁₂	C₂³×C₃	1	12	yes	—
147	C₂×C₄×D₃	—	2	24	no	—
148	C₂×Dic₆	—	2	6	no	—
149	C₂×Dic₆	C₂³×C₃	1	12	yes	—
150	C₃×Q₁₆	—	3	16	no	—
151	C₃×SD₁₆	—	3	32	no	—
152	C₃×D₈	—	3	16	no	—
153	C₂×C₃×C₈	—	2	6	no	—
154	C₂×C₃×C₈	—	2	6	no	—
155	C₂×C₃×C₈	—	2	16	no	—
156	C₂×C₃×C₈	C₂²×D₃	1	6	yes	—
157	C₂×C₃×C₈	C₂²×D₃	1	6	yes	—
158	C₂×C₃×C₈	C₂²×D₃	1	16	yes	complemented
159	C₂×C₃×C₈	C₂³×C₃	1	6	yes	—
160	C₂×C₃×C₈	C₂³×C₃	1	6	yes	—
161	C₂×C₃×C₈	C₂³×C₃	1	16	yes	complemented
162	Dic₁₂	C₂³×C₃	1	16	yes	complemented
163	D₂₄	C₂³×C₃	1	16	yes	complemented
164	#204	C₂³×C₃	1	32	yes	complemented
165	C₂²×C₃²	—	2	12	no	—
166	C₂²×C₃²	#135	1	4	yes	complemented
167	C₂²×C₃²	C₂²×D₄	1	4	yes	—
168	C₂²×C₃²	C₂²×D₄	1	3	yes	—
169	C₂×C₃×D₃	—	2	8	no	—
170	C₂×C₃×D₃	—	4	24	no	—
171	C₃²×C₄	C₂²×D₄	1	3	yes	—
172	C₃²×C₄	C₂²×D₄	1	4	yes	—
173	C₃²×C₄	C₂⁵	1	1	yes	characteristic
174	C₃×Dic₃	—	2	8	no	—
175	C₂×#41	—	3	24	no	—
176	C₂×#41	—	6	12	no	—
177	C₂²×Q₈	—	3	2	no	—
178	C₂²×D₄	—	3	2	no	—
179	C₂²×D₄	—	6	2	no	—
180	C₂³×C₄	—	6	2	no	—
181	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
182	#135	—	3	64	no	—
183	C₂×Q₁₆	—	3	12	no	—
184	C₂×SD₁₆	—	3	24	no	—
185	C₂×D₈	—	3	12	no	—
186	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
187	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
188	C₂²×C₈	C₂×C₃×D₃	1	12	yes	complemented
189	C₂³×C₃	—	2	8	no	—
190	C₂³×C₃	—	2	4	no	—
191	C₂³×C₃	—	2	4	no	—
192	C₂³×C₃	—	2	6	no	—
193	C₂³×C₃	—	2	1	no	—
194	C₂³×C₃	—	6	12	no	—
195	C₂³×C₃	—	12	8	no	—
196	C₂³×C₃	C₂×D₁₂	1	6	yes	—
197	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
198	C₂³×C₃	C₂×C₃×D₄	1	6	yes	—
199	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
200	C₂²×D₃	—	2	12	no	—
201	C₂²×D₃	—	4	8	no	—
202	C₃×Q₈	—	3	8	no	—
203	C₃×Q₈	—	6	12	no	—
204	C₃×D₄	—	3	8	no	—
205	C₃×D₄	—	6	32	no	—
206	C₃×D₄	—	6	12	no	—
207	C₂×C₃×C₄	—	2	3	no	—
208	C₂×C₃×C₄	—	2	4	no	—
209	C₂×C₃×C₄	—	2	6	no	—
210	C₂×C₃×C₄	—	2	3	no	—
211	C₂×C₃×C₄	—	2	12	no	—
212	C₂×C₃×C₄	—	6	12	no	—
213	C₂×C₃×C₄	—	6	32	no	—
214	C₂×C₃×C₄	C₂×D₁₂	1	6	yes	—
215	C₂×C₃×C₄	C₂×D₁₂	1	3	yes	—
216	C₂×C₃×C₄	C₂×D₁₂	1	12	yes	—
217	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
218	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
219	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	—
220	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
221	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
222	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
223	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
224	#67	—	2	32	no	—
225	C₂×Dic₃	—	2	12	no	—
226	D₁₂	—	2	12	no	—
227	D₁₂	C₂⁴×C₃	1	8	yes	—
228	C₄×D₃	—	2	32	no	—
229	Dic₆	—	2	12	no	—
230	Dic₆	C₂⁴×C₃	1	8	yes	—
231	C₃×C₈	—	2	4	no	—
232	C₃×C₈	—	2	4	no	—
233	C₃×C₈	C₂³×D₃	1	4	yes	—
234	C₃×C₈	C₂³×D₃	1	4	yes	—
235	C₃×C₈	C₂⁴×C₃	1	4	yes	—
236	C₃×C₈	C₂⁴×C₃	1	4	yes	—
237	C₂×C₃²	—	2	4	no	—
238	C₂×C₃²	C₂×#135	1	6	yes	complemented
239	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
240	C₃×D₃	—	4	8	no	—
241	C₂⁴	—	6	2	no	—
242	C₂⁴	C₃×D₁₂	1	1	yes	characteristic
243	#41	—	3	32	no	—
244	#41	—	6	48	no	—
245	C₂×Q₈	—	3	12	no	—
246	C₂×Q₈	—	6	6	no	—
247	C₂×D₄	—	3	12	no	—
248	C₂×D₄	—	6	24	no	—
249	C₂×D₄	—	6	6	no	—
250	C₂²×C₄	—	6	2	no	—
251	C₂²×C₄	—	6	24	no	—
252	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
253	C₂²×C₄	C₃×D₁₂	1	6	yes	—
254	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
256	Q₁₆	—	3	16	no	—
257	SD₁₆	—	3	32	no	—
258	D₈	—	3	16	no	—
259	C₂×C₈	C₂²×C₃×D₃	1	6	yes	—
260	C₂×C₈	C₂²×C₃×D₃	1	6	yes	—
261	C₂×C₈	C₂²×C₃×D₃	1	16	yes	complemented
262	C₂²×C₃	—	2	24	no	—
263	C₂²×C₃	—	2	12	no	—
264	C₂²×C₃	—	2	12	no	—
265	C₂²×C₃	—	2	4	no	—
266	C₂²×C₃	—	2	4	no	—
267	C₂²×C₃	—	2	3	no	—
268	C₂²×C₃	—	6	8	no	—
269	C₂²×C₃	—	12	24	no	—
270	C₂²×C₃	#904	1	4	yes	direct product factor
271	C₂²×C₃	C₃×#135	1	4	yes	complemented
272	C₂²×C₃	C₂²×D₁₂	1	4	yes	—
273	C₂²×C₃	C₂²×D₁₂	1	3	yes	—
274	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
275	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
276	C₂×D₃	—	2	8	no	—
277	C₂×D₃	—	4	24	no	—
278	C₃×C₄	—	2	4	no	—
279	C₃×C₄	—	2	3	no	—
280	C₃×C₄	—	2	1	no	—
281	C₃×C₄	—	6	8	no	—
282	C₃×C₄	C₂²×D₁₂	1	4	yes	—
283	C₃×C₄	C₂²×D₁₂	1	3	yes	—
284	C₃×C₄	C₂²×C₃×D₄	1	3	yes	—
285	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
286	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
287	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
288	Dic₃	—	2	8	no	—
289	C₃²	C₂²×#135	1	1	yes	characteristic, complemented, Sylow
290	C₂³	—	2	4	no	—
291	C₂³	—	6	12	no	—
292	C₂³	—	12	8	no	—
293	C₂³	C₂×C₃×D₁₂	1	6	yes	—
294	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
295	Q₈	—	3	8	no	—
296	Q₈	—	6	12	no	—
297	D₄	—	3	8	no	—
298	D₄	—	6	32	no	—
299	D₄	—	6	12	no	—
300	C₂×C₄	—	6	12	no	—
301	C₂×C₄	—	6	32	no	—
302	C₂×C₄	C₂×C₃×D₁₂	1	6	yes	—
303	C₂×C₄	C₂×C₃×D₁₂	1	3	yes	—
304	C₂×C₄	C₂×C₃×D₁₂	1	12	yes	—
305	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
306	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
307	C₈	C₂³×C₃×D₃	1	4	yes	—
308	C₈	C₂³×C₃×D₃	1	4	yes	—
309	C₂×C₃	—	2	8	no	—
310	C₂×C₃	—	2	4	no	—
311	C₂×C₃	—	2	4	no	—
312	C₂×C₃	—	2	1	no	—
313	C₂×C₃	—	2	6	no	—
314	C₂×C₃	—	12	8	no	—
315	C₂×C₃	C₂×#904	1	6	yes	direct product factor
316	C₂×C₃	C₂×C₃×#135	1	6	yes	complemented
317	C₂×C₃	C₂³×D₁₂	1	1	yes	characteristic
318	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
319	D₃	—	4	8	no	—
320	C₂²	—	2	12	no	—
321	C₂²	—	6	8	no	—
322	C₂²	—	12	24	no	—
323	C₂²	C₃×#904	1	4	yes	direct product factor
324	C₂²	C₂²×C₃×D₁₂	1	4	yes	—
325	C₂²	C₂²×C₃×D₁₂	1	3	yes	—
326	C₄	—	6	8	no	—
327	C₄	C₂²×C₃×D₁₂	1	4	yes	—
328	C₄	C₂²×C₃×D₁₂	1	3	yes	—
329	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
330	C₃	—	2	1	no	—
331	C₃	C₂²×#904	1	1	yes	characteristic, direct product factor
332	C₃	C₂²×C₃×#135	1	1	yes	characteristic, complemented
333	C₂	—	2	4	no	—
334	C₂	—	12	8	no	—
335	C₂	C₂×C₃×#904	1	6	yes	direct product factor
336	C₂	C₂³×C₃×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	D₁₂
commutator, cosocle	C₃×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₂³×C₃²×C₈	C₂
socle	C₂³×C₃²	C₂×D₄
hypercenter	C₂³×C₃×C₈	D₃
hypocenter	C₃	C₂²×C₃×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ C₂³×C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#235	C₂	semidirect
2. C₂³×C₃²×C₈	C₂	semidirect
3. C₂²×C₃×Dic₁₂	C₂	semidirect
4. C₂×C₃×#904	C₂	direct (N × H)
5. C₂²×C₃×D₂₄	C₂	semidirect
6. C₂²×C₃×#204	C₂	semidirect
8. C₂²×#904	C₃	direct (N × H)
12. C₂×C₃×#235	C₂²	semidirect
18. C₂²×C₃²×C₈	C₂²	semidirect
19. C₂×C₃×Dic₁₂	C₂²	semidirect
20. C₃×#904	C₂²	direct (N × H)
21. C₂×C₃×D₂₄	C₂²	semidirect
22. C₂×C₃×#204	C₂²	semidirect
24. C₂²×#235	C₂×C₃	semidirect
30. C₂³×C₃×C₈	D₃	semidirect
31. C₂³×C₃×C₈	C₂×C₃	semidirect
32. C₂²×Dic₁₂	C₂×C₃	semidirect
33. C₂×#904	C₂×C₃	direct (N × H)
34. C₂²×D₂₄	C₂×C₃	semidirect
35. C₂²×#204	C₂×C₃	semidirect
45. C₃×#235	C₂³	semidirect
53. C₂×C₃²×C₈	C₂³	semidirect
54. C₃×Dic₁₂	C₂³	semidirect
55. C₃×D₂₄	C₂³	semidirect
56. C₃×#204	C₂³	semidirect
69. C₂×#235	C₂²×C₃	semidirect
82. C₂²×C₃×C₈	C₂×D₃	semidirect
85. C₂²×C₃×C₈	C₂²×C₃	semidirect
86. C₂×Dic₁₂	C₂²×C₃	semidirect
87. #904	C₂²×C₃	direct (N × H)
88. C₂×D₂₄	C₂²×C₃	semidirect
89. C₂×#204	C₂²×C₃	semidirect
114. C₂³×C₈	C₃×D₃	semidirect
144. #235	C₂³×C₃	semidirect
158. C₂×C₃×C₈	C₂²×D₃	semidirect
161. C₂×C₃×C₈	C₂³×C₃	semidirect
162. Dic₁₂	C₂³×C₃	semidirect
163. D₂₄	C₂³×C₃	semidirect
164. #204	C₂³×C₃	semidirect
166. C₂²×C₃²	#135	semidirect
188. C₂²×C₈	C₂×C₃×D₃	semidirect
238. C₂×C₃²	C₂×#135	semidirect
261. C₂×C₈	C₂²×C₃×D₃	semidirect
270. C₂²×C₃	#904	direct (N × H)
271. C₂²×C₃	C₃×#135	semidirect
289. C₃²	C₂²×#135	semidirect
315. C₂×C₃	C₂×#904	direct (N × H)
316. C₂×C₃	C₂×C₃×#135	semidirect
323. C₂²	C₃×#904	direct (N × H)
331. C₃	C₂²×#904	direct (N × H)
332. C₃	C₂²×C₃×#135	semidirect
335. C₂	C₂×C₃×#904	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×C₃×#235	2
C₂³×C₃²×C₈	2
C₂²×C₃×Dic₁₂	2
C₂×C₃×#904	2
C₂²×C₃×D₂₄	2
C₂²×C₃×#204	2
C₂²×C₃×#135	3
C₂²×#904	3

Subgroups — C22×C3×#904 #11918603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#904 #11918603