Subgroups — C₂²×D₉×D₁₂ #13164700

Order 1728.

4322 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃×D₉	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄⋊(C₃⋊D₉)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×C₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#6195	C₂	1	2	yes	maximal, complemented
6	C₂×D₉×D₁₂	C₂	1	24	yes	maximal, direct product factor
7	C₂²×D₃×D₁₂	—	3	1	no	maximal
8	C₂²×D₄×D₉	—	3	1	no	maximal
9	C₂³×C₃⋊D₉	C₂²	1	2	yes	complemented
10	C₂³×D₃×C₉	C₂²	1	2	yes	complemented
11	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic
12	C₂²×D₃×D₉	—	2	16	no	—
13	C₂²×D₃×D₉	C₂²	1	24	yes	complemented
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₄⋊(C₃⋊D₉)	C₂²	1	12	yes	complemented
16	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₉×D₁₂	C₂²	1	12	yes	complemented
18	C₂×C₃×C₄×D₉	C₂²	1	12	yes	complemented
19	C₂×#6195	C₂²	1	24	yes	complemented
20	D₉×D₁₂	C₂²	1	64	yes	direct product factor
21	C₂³×D₃²	—	3	2	no	—
22	C₂²×C₄⋊(C₃⋊D₃)	—	3	1	no	—
23	C₂²×C₃×D₁₂	D₃	1	1	yes	characteristic
24	C₂²×C₃×C₄×D₃	—	3	1	no	—
25	C₂²×#626	—	3	2	no	—
26	C₂×D₃×D₁₂	—	3	24	no	—
27	C₂⁴×D₉	—	3	2	no	—
28	C₂²×D₄×C₉	—	3	1	no	—
29	C₂²×#611	—	3	2	no	—
30	C₂×D₄×D₉	—	3	24	no	—
31	C₂²×D₃₆	—	3	1	no	—
32	C₂²×D₃₆	—	6	1	no	—
33	C₂²×C₄×D₉	D₃	1	1	yes	characteristic, complemented
34	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
35	C₂²×C₃⋊D₉	—	2	8	no	—
36	C₂²×C₃⋊D₉	C₂³	1	12	yes	complemented
37	C₂²×D₃×C₉	—	2	8	no	—
38	C₂²×D₃×C₉	C₂³	1	12	yes	complemented
39	C₂²×C₃×D₉	D₄	1	8	yes	complemented
40	C₂²×C₃×D₉	C₂³	1	6	yes	—
41	C₂×D₃×D₉	—	2	96	no	—
42	C₂×D₃×D₉	C₂³	1	32	yes	complemented
43	C₂×C₃×C₄×C₉	C₂³	1	6	yes	complemented
44	C₄⋊(C₃⋊D₉)	C₂³	1	16	yes	complemented
45	C₂×C₃×Dic₉	C₂³	1	6	yes	complemented
46	C₉×D₁₂	C₂³	1	16	yes	complemented
47	C₃×C₄×D₉	C₂³	1	16	yes	complemented
48	#6195	C₂³	1	32	yes	complemented
49	C₂²×D₃×D₄	—	9	1	no	—
50	C₂³×D₁₂	—	9	1	no	—
51	C₂³×C₃⋊D₃	—	3	2	no	—
52	C₂³×C₃×D₃	—	3	1	no	—
53	C₂³×C₃×D₃	C₂×D₃	1	2	yes	—
54	C₂²×D₃²	—	3	24	no	—
55	C₂²×D₃²	—	6	16	no	—
56	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
57	C₂×C₄⋊(C₃⋊D₃)	—	3	12	no	—
58	C₂²×C₃×Dic₃	—	3	1	no	—
59	C₂×C₃×D₁₂	C₂×D₃	1	12	yes	—
60	C₂×C₃×C₄×D₃	—	3	12	no	—
61	C₂×#626	—	3	24	no	—
62	D₃×D₁₂	—	3	64	no	—
63	C₂⁴×C₉	—	3	2	no	—
64	C₂³×D₉	—	3	2	no	—
65	C₂³×D₉	—	3	24	no	—
66	C₂³×D₉	—	6	16	no	—
67	C₂³×D₉	—	6	2	no	—
68	C₂³×D₉	C₂×D₃	1	1	yes	characteristic
69	C₂×D₄×C₉	—	3	12	no	—
70	C₂²×C₄×C₉	—	2	1	no	—
71	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
72	C₂×#611	—	3	24	no	—
73	C₂²×Dic₉	C₂×D₃	1	1	yes	characteristic, complemented
74	D₄×D₉	—	3	64	no	—
75	C₂×D₃₆	—	3	12	no	—
76	C₂×D₃₆	—	6	12	no	—
77	C₂×C₄×D₉	C₂×D₃	1	12	yes	complemented
78	C₂²×C₃×C₉	C₂×D₄	1	4	yes	complemented
79	C₂²×C₃×C₉	C₂⁴	1	3	yes	—
80	C₂×C₃⋊D₉	—	2	24	no	—
81	C₂×C₃⋊D₉	C₂⁴	1	8	yes	complemented
82	C₂×D₃×C₉	—	2	24	no	—
83	C₂×D₃×C₉	C₂⁴	1	8	yes	complemented
84	C₂×C₃×D₉	C₂×D₄	1	24	yes	complemented
85	C₂×C₃×D₉	C₂⁴	1	4	yes	—
86	D₃×D₉	—	2	64	no	—
87	C₃×C₄×C₉	C₂⁴	1	4	yes	complemented
88	C₃×Dic₉	C₂⁴	1	4	yes	complemented
89	C₂⁴×D₃	—	9	2	no	—
90	C₂⁴×D₃	—	9	2	no	—
91	C₂²×C₃×D₄	—	3	1	no	—
92	C₂³×C₃×C₄	—	9	1	no	—
93	C₂²×#67	—	9	2	no	—
94	C₂×D₃×D₄	—	9	24	no	—
95	C₂²×D₁₂	—	9	2	no	—
96	C₂²×D₁₂	—	9	1	no	—
97	C₂²×D₁₂	—	9	1	no	—
98	C₂²×D₁₂	—	9	24	no	—
99	C₂²×D₁₂	—	18	1	no	—
100	C₂²×D₁₂	D₉	1	1	yes	characteristic, direct product factor
101	C₂²×C₄×D₃	—	3	1	no	—
102	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
103	C₂²×C₃⋊D₃	—	3	12	no	—
104	C₂²×C₃⋊D₃	—	6	8	no	—
105	C₂²×C₃×D₃	—	2	8	no	—
106	C₂²×C₃×D₃	—	3	8	no	—
107	C₂²×C₃×D₃	—	3	6	no	—
108	C₂²×C₃×D₃	C₂²×D₃	1	12	yes	—
109	C₂×D₃²	—	3	32	no	—
110	C₂×D₃²	—	6	96	no	—
111	C₂×C₃²×C₄	C₂²×D₃	1	6	yes	—
112	C₄⋊(C₃⋊D₃)	—	3	16	no	—
113	C₂×C₃×Dic₃	—	3	6	no	—
114	C₃×D₁₂	C₂²×D₃	1	16	yes	—
115	C₃×C₄×D₃	—	3	16	no	—
116	#626	—	3	32	no	—
117	C₂³×C₉	—	2	1	no	—
118	C₂³×C₉	—	3	12	no	—
119	C₂³×C₉	—	6	8	no	—
120	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
121	C₂²×D₉	—	3	12	no	—
122	C₂²×D₉	—	3	32	no	—
123	C₂²×D₉	—	6	12	no	—
124	C₂²×D₉	—	6	8	no	—
125	C₂²×D₉	—	6	96	no	—
126	C₂²×D₉	—	12	8	no	—
127	C₂²×D₉	D₁₂	1	8	yes	direct product factor
128	C₂²×D₉	C₂²×D₃	1	6	yes	—
129	D₄×C₉	—	3	16	no	—
130	C₂×C₄×C₉	—	2	6	no	—
131	C₂×C₄×C₉	C₂²×D₃	1	6	yes	complemented
132	#611	—	3	32	no	—
133	C₂×Dic₉	C₂²×D₃	1	6	yes	complemented
134	D₃₆	—	3	16	no	—
135	D₃₆	—	6	16	no	—
136	C₄×D₉	C₂²×D₃	1	16	yes	complemented
137	C₂³×D₄	—	27	1	no	Sylow
138	C₂×C₃×C₉	C₂²×D₄	1	6	yes	complemented
139	C₂×C₃×C₉	C₂⁵	1	1	yes	characteristic
140	C₃⋊D₉	—	2	8	no	—
141	D₃×C₉	—	2	8	no	—
142	C₃×D₉	C₂²×D₄	1	8	yes	complemented
143	C₂⁴×C₃	—	3	2	no	—
144	C₂⁴×C₃	—	9	1	no	—
145	C₂³×D₃	—	3	1	no	—
146	C₂³×D₃	—	9	24	no	—
147	C₂³×D₃	—	9	2	no	—
148	C₂³×D₃	—	9	2	no	—
149	C₂³×D₃	—	9	24	no	—
150	C₂³×D₃	—	18	2	no	—
151	C₂³×D₃	—	18	16	no	—
152	C₂³×D₃	—	18	16	no	—
153	C₂³×D₃	C₂×D₉	1	2	yes	complemented
154	C₂×C₃×D₄	—	3	12	no	—
155	C₂²×C₃×C₄	—	2	1	no	—
156	C₂²×C₃×C₄	—	9	1	no	—
157	C₂²×C₃×C₄	—	9	12	no	—
158	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic, complemented
159	C₂²×C₃×C₄	D₃²	1	1	yes	characteristic
160	C₂×#67	—	9	24	no	—
161	C₂²×Dic₃	—	3	1	no	—
162	D₃×D₄	—	9	64	no	—
163	C₂×D₁₂	—	9	24	no	—
164	C₂×D₁₂	—	9	12	no	—
165	C₂×D₁₂	—	9	12	no	—
166	C₂×D₁₂	—	9	64	no	—
167	C₂×D₁₂	—	18	12	no	—
168	C₂×D₁₂	C₂×D₉	1	12	yes	direct product factor
169	C₂×C₄×D₃	—	3	12	no	—
170	C₂²×C₃²	D₃×D₄	1	4	yes	—
171	C₂²×C₃²	C₂³×D₃	1	3	yes	—
172	C₂×C₃⋊D₃	—	3	8	no	—
173	C₂×C₃⋊D₃	—	6	24	no	—
174	C₂×C₃×D₃	—	2	24	no	—
175	C₂×C₃×D₃	—	3	24	no	—
176	C₂×C₃×D₃	—	3	4	no	—
177	C₂×C₃×D₃	C₂³×D₃	1	8	yes	—
178	D₃²	—	6	64	no	—
179	C₃²×C₄	C₂³×D₃	1	4	yes	—
180	C₃×Dic₃	—	3	4	no	—
181	C₂²×C₉	—	2	3	no	—
182	C₂²×C₉	—	2	4	no	—
183	C₂²×C₉	—	3	8	no	—
184	C₂²×C₉	—	6	24	no	—
185	C₂²×C₉	C₂×D₁₂	1	4	yes	complemented
186	C₂²×C₉	C₂³×D₃	1	3	yes	—
187	C₂×D₉	—	3	8	no	—
188	C₂×D₉	—	6	8	no	—
189	C₂×D₉	—	6	24	no	—
190	C₂×D₉	—	6	64	no	—
191	C₂×D₉	—	12	24	no	—
192	C₂×D₉	C₂×D₁₂	1	24	yes	direct product factor
193	C₂×D₉	C₂³×D₃	1	4	yes	—
194	C₄×C₉	—	2	4	no	—
195	C₄×C₉	C₂³×D₃	1	4	yes	complemented
196	Dic₉	C₂³×D₃	1	4	yes	complemented
197	C₂⁵	—	27	2	no	—
198	C₂²×D₄	—	3	1	no	—
199	C₂²×D₄	—	27	24	no	—
200	C₂²×D₄	—	27	2	no	—
201	C₂²×D₄	—	27	1	no	—
202	C₂³×C₄	—	9	1	no	—
203	C₃×C₉	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
204	C₂³×C₃	—	2	1	no	—
205	C₂³×C₃	—	3	12	no	—
206	C₂³×C₃	—	6	8	no	—
207	C₂³×C₃	—	9	8	no	—
208	C₂³×C₃	—	9	6	no	—
209	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
210	C₂³×C₃	C₂×D₃²	1	1	yes	characteristic
211	C₂²×D₃	—	2	8	no	—
212	C₂²×D₃	—	3	6	no	—
213	C₂²×D₃	—	3	8	no	—
214	C₂²×D₃	—	9	32	no	—
215	C₂²×D₃	—	9	12	no	—
216	C₂²×D₃	—	9	12	no	—
217	C₂²×D₃	—	9	32	no	—
218	C₂²×D₃	—	18	12	no	—
219	C₂²×D₃	—	18	96	no	—
220	C₂²×D₃	—	18	96	no	—
221	C₂²×D₃	—	18	8	no	—
222	C₂²×D₃	—	18	8	no	—
223	C₂²×D₃	—	36	8	no	—
224	C₂²×D₃	C₂²×D₉	1	12	yes	complemented
225	C₃×D₄	—	3	16	no	—
226	C₂×C₃×C₄	—	2	6	no	—
227	C₂×C₃×C₄	—	9	6	no	—
228	C₂×C₃×C₄	—	9	16	no	—
229	C₂×C₃×C₄	C₂²×D₉	1	6	yes	complemented
230	C₂×C₃×C₄	C₂×D₃²	1	6	yes	—
231	#67	—	9	32	no	—
232	C₂×Dic₃	—	3	6	no	—
233	D₁₂	—	9	32	no	—
234	D₁₂	—	9	16	no	—
235	D₁₂	—	9	16	no	—
236	D₁₂	—	18	16	no	—
237	D₁₂	C₂²×D₉	1	16	yes	direct product factor
238	C₄×D₃	—	3	16	no	—
239	C₂×C₃²	C₂×D₃×D₄	1	6	yes	—
240	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
241	C₃⋊D₃	—	6	8	no	—
242	C₃×D₃	—	2	8	no	—
243	C₃×D₃	—	3	8	no	—
244	C₂×C₉	—	2	6	no	—
245	C₂×C₉	—	2	1	no	—
246	C₂×C₉	—	6	8	no	—
247	C₂×C₉	C₂²×D₁₂	1	6	yes	complemented
248	C₂×C₉	C₂⁴×D₃	1	1	yes	characteristic
249	D₉	—	6	8	no	—
250	D₉	—	12	8	no	—
251	D₉	C₂²×D₁₂	1	8	yes	direct product factor
252	C₂⁴	—	3	2	no	—
253	C₂⁴	—	9	1	no	—
254	C₂⁴	—	27	24	no	—
255	C₂⁴	—	27	2	no	—
256	C₂⁴	—	54	16	no	—
257	C₂×D₄	—	3	12	no	—
258	C₂×D₄	—	27	64	no	—
259	C₂×D₄	—	27	24	no	—
260	C₂×D₄	—	27	12	no	—
261	C₂²×C₄	—	9	1	no	—
262	C₂²×C₄	—	9	12	no	—
263	C₂²×C₄	D₃×D₉	1	1	yes	characteristic, complemented
264	C₂²×C₃	—	2	3	no	—
265	C₂²×C₃	—	2	4	no	—
266	C₂²×C₃	—	3	8	no	—
267	C₂²×C₃	—	6	24	no	—
268	C₂²×C₃	—	9	4	no	—
269	C₂²×C₃	—	9	24	no	—
270	C₂²×C₃	D₄×D₉	1	4	yes	complemented
271	C₂²×C₃	C₂³×D₉	1	3	yes	—
272	C₂²×C₃	D₃×D₁₂	1	4	yes	—
273	C₂²×C₃	C₂²×D₃²	1	3	yes	—
274	C₂×D₃	—	2	24	no	—
275	C₂×D₃	—	3	24	no	—
276	C₂×D₃	—	3	4	no	—
277	C₂×D₃	—	9	8	no	—
278	C₂×D₃	—	9	8	no	—
279	C₂×D₃	—	18	8	no	—
280	C₂×D₃	—	18	64	no	—
281	C₂×D₃	—	18	64	no	—
282	C₂×D₃	—	18	24	no	—
283	C₂×D₃	—	18	24	no	—
284	C₂×D₃	—	36	24	no	—
285	C₂×D₃	C₂³×D₉	1	8	yes	complemented
286	C₃×C₄	—	2	4	no	—
287	C₃×C₄	—	9	4	no	—
288	C₃×C₄	C₂³×D₉	1	4	yes	complemented
289	C₃×C₄	C₂²×D₃²	1	4	yes	—
290	Dic₃	—	3	4	no	—
291	C₃²	C₂²×D₃×D₄	1	1	yes	characteristic
292	C₉	—	2	1	no	—
293	C₉	C₂³×D₁₂	1	1	yes	characteristic, complemented
294	C₂³	—	3	12	no	—
295	C₂³	—	6	8	no	—
296	C₂³	—	9	6	no	—
297	C₂³	—	9	8	no	—
298	C₂³	—	27	32	no	—
299	C₂³	—	27	12	no	—
300	C₂³	—	54	96	no	—
301	C₂³	—	54	8	no	—
302	C₂³	C₂×D₃×D₉	1	1	yes	characteristic
303	D₄	—	3	16	no	—
304	D₄	—	27	32	no	—
305	D₄	—	27	16	no	—
306	C₂×C₄	—	9	6	no	—
307	C₂×C₄	—	9	16	no	—
308	C₂×C₄	C₂×D₃×D₉	1	6	yes	complemented
309	C₂×C₃	—	2	1	no	—
310	C₂×C₃	—	2	6	no	—
311	C₂×C₃	—	6	8	no	—
312	C₂×C₃	—	9	8	no	—
313	C₂×C₃	C₂×D₄×D₉	1	6	yes	complemented
314	C₂×C₃	C₂⁴×D₉	1	1	yes	characteristic
315	C₂×C₃	C₂×D₃×D₁₂	1	6	yes	—
316	C₂×C₃	C₂³×D₃²	1	1	yes	characteristic
317	D₃	—	2	8	no	—
318	D₃	—	3	8	no	—
319	D₃	—	18	8	no	—
320	D₃	—	18	8	no	—
321	D₃	—	36	8	no	—
322	C₂²	—	3	8	no	—
323	C₂²	—	6	24	no	—
324	C₂²	—	9	4	no	—
325	C₂²	—	9	24	no	—
326	C₂²	—	27	8	no	—
327	C₂²	—	54	64	no	—
328	C₂²	—	54	24	no	—
329	C₂²	D₉×D₁₂	1	4	yes	direct product factor
330	C₂²	C₂²×D₃×D₉	1	3	yes	—
331	C₄	—	9	4	no	—
332	C₄	C₂²×D₃×D₉	1	4	yes	complemented
333	C₃	—	2	1	no	—
334	C₃	C₂²×D₄×D₉	1	1	yes	characteristic, complemented
335	C₃	C₂²×D₃×D₁₂	1	1	yes	characteristic
336	C₂	—	6	8	no	—
337	C₂	—	9	8	no	—
338	C₂	—	54	8	no	—
339	C₂	C₂×D₉×D₁₂	1	6	yes	direct product factor
340	C₂	C₂³×D₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×D₉
commutator, cosocle	C₂×C₃×C₉	C₂⁵
Frattini	C₂×C₃	C₂³×D₃²
Fitting	C₂²×C₃×C₄×C₉	C₂²
socle	C₂³×C₃²	C₂²×D₃
hypercenter	C₂²×C₄	D₃×D₉
hypocenter	C₃×C₉	C₂³×D₄
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×D₃×D₉	C₂	semidirect
2. C₂²×C₄⋊(C₃⋊D₉)	C₂	semidirect
3. C₂²×C₉×D₁₂	C₂	semidirect
4. C₂²×C₃×C₄×D₉	C₂	semidirect
5. C₂²×#6195	C₂	semidirect
6. C₂×D₉×D₁₂	C₂	direct (N × H)
9. C₂³×C₃⋊D₉	C₂²	semidirect
10. C₂³×D₃×C₉	C₂²	semidirect
13. C₂²×D₃×D₉	C₂²	semidirect
14. C₂²×C₃×C₄×C₉	C₂²	semidirect
15. C₂×C₄⋊(C₃⋊D₉)	C₂²	semidirect
16. C₂²×C₃×Dic₉	C₂²	semidirect
17. C₂×C₉×D₁₂	C₂²	semidirect
18. C₂×C₃×C₄×D₉	C₂²	semidirect
19. C₂×#6195	C₂²	semidirect
20. D₉×D₁₂	C₂²	direct (N × H)
33. C₂²×C₄×D₉	D₃	semidirect
36. C₂²×C₃⋊D₉	C₂³	semidirect
38. C₂²×D₃×C₉	C₂³	semidirect
39. C₂²×C₃×D₉	D₄	semidirect
42. C₂×D₃×D₉	C₂³	semidirect
43. C₂×C₃×C₄×C₉	C₂³	semidirect
44. C₄⋊(C₃⋊D₉)	C₂³	semidirect
45. C₂×C₃×Dic₉	C₂³	semidirect
46. C₉×D₁₂	C₂³	semidirect
47. C₃×C₄×D₉	C₂³	semidirect
48. #6195	C₂³	semidirect
71. C₂²×C₄×C₉	C₂×D₃	semidirect
73. C₂²×Dic₉	C₂×D₃	semidirect
77. C₂×C₄×D₉	C₂×D₃	semidirect
78. C₂²×C₃×C₉	C₂×D₄	semidirect
81. C₂×C₃⋊D₉	C₂⁴	semidirect
83. C₂×D₃×C₉	C₂⁴	semidirect
84. C₂×C₃×D₉	C₂×D₄	semidirect
87. C₃×C₄×C₉	C₂⁴	semidirect
88. C₃×Dic₉	C₂⁴	semidirect
100. C₂²×D₁₂	D₉	direct (N × H)
127. C₂²×D₉	D₁₂	direct (N × H)
131. C₂×C₄×C₉	C₂²×D₃	semidirect
133. C₂×Dic₉	C₂²×D₃	semidirect
136. C₄×D₉	C₂²×D₃	semidirect
138. C₂×C₃×C₉	C₂²×D₄	semidirect
142. C₃×D₉	C₂²×D₄	semidirect
153. C₂³×D₃	C₂×D₉	semidirect
158. C₂²×C₃×C₄	C₂×D₉	semidirect
168. C₂×D₁₂	C₂×D₉	direct (N × H)
185. C₂²×C₉	C₂×D₁₂	semidirect
192. C₂×D₉	C₂×D₁₂	direct (N × H)
195. C₄×C₉	C₂³×D₃	semidirect
196. Dic₉	C₂³×D₃	semidirect
203. C₃×C₉	C₂³×D₄	semidirect
224. C₂²×D₃	C₂²×D₉	semidirect
229. C₂×C₃×C₄	C₂²×D₉	semidirect
237. D₁₂	C₂²×D₉	direct (N × H)
247. C₂×C₉	C₂²×D₁₂	semidirect
251. D₉	C₂²×D₁₂	direct (N × H)
263. C₂²×C₄	D₃×D₉	semidirect
270. C₂²×C₃	D₄×D₉	semidirect
285. C₂×D₃	C₂³×D₉	semidirect
288. C₃×C₄	C₂³×D₉	semidirect
293. C₉	C₂³×D₁₂	semidirect
308. C₂×C₄	C₂×D₃×D₉	semidirect
313. C₂×C₃	C₂×D₄×D₉	semidirect
329. C₂²	D₉×D₁₂	direct (N × H)
332. C₄	C₂²×D₃×D₉	semidirect
334. C₃	C₂²×D₄×D₉	semidirect
339. C₂	C₂×D₉×D₁₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₃×D₉	2
C₂²×C₄⋊(C₃⋊D₉)	2
C₂²×C₉×D₁₂	2
C₂²×C₃×C₄×D₉	2
C₂²×#6195	2
C₂×D₉×D₁₂	2
C₂²×D₃×D₁₂	3
C₂²×D₄×D₉	3

Subgroups — C22×D9×D12 #13164700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₉×D₁₂ #13164700