Subgroups — C₂×#11720882 #13150099

Order 1728.

962 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88532	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#88425	C₂	1	2	yes	maximal, complemented
5	#11720882	C₂	1	8	yes	maximal, direct product factor
6	C₂×#88421	C₂	1	2	yes	maximal, complemented
7	C₂×#63823	—	3	1	no	maximal
8	C₂×#63512	—	3	1	no	maximal
9	C₂³×C₃×D₉	—	2	1	no	—
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₉×#67	—	2	1	no	—
12	C₉×#235	—	2	2	no	—
13	C₉×#235	C₂²	1	4	yes	complemented
14	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₄×D₃×C₉	—	2	1	no	—
16	C₂×C₃×D₃₆	—	2	2	no	—
17	C₂×C₃×D₃₆	—	2	1	no	—
18	C₂×C₃×D₃₆	C₂²	1	2	yes	—
19	C₂×C₃×D₃₆	C₂²	1	4	yes	complemented
20	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
21	#88532	C₂²	1	4	yes	complemented
22	C₂×C₃⋊(C₉⋊C₈)	C₂²	1	2	yes	complemented
23	#88425	C₂²	1	8	yes	complemented
24	#88421	C₂²	1	8	yes	complemented
25	C₂×C₃×#235	D₃	1	1	yes	characteristic
26	C₂²×C₃×D₁₂	—	3	1	no	—
27	C₂×#3748	—	3	1	no	—
28	C₂×#3715	—	3	2	no	—
29	#63823	—	3	8	no	—
30	C₂×#3713	—	3	2	no	—
31	C₂×C₉×#41	—	3	1	no	—
32	C₂²×D₃₆	D₃	1	1	yes	characteristic, complemented
33	#63512	—	3	8	no	—
34	C₂×#3675	—	3	2	no	—
35	C₂×#3673	—	3	2	no	—
36	C₂×#3667	—	3	1	no	—
37	C₂×#3667	—	6	1	no	—
38	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
39	C₂²×D₃×C₉	—	2	1	no	—
40	C₂²×C₃×D₉	—	2	2	no	—
41	C₂²×C₃×D₉	—	2	4	no	—
42	C₂²×C₃×D₉	—	4	4	no	—
43	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
44	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
45	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
47	C₉×#67	—	2	4	no	—
48	C₂×C₉×Dic₃	—	2	1	no	—
49	C₉×D₁₂	—	2	1	no	—
50	C₉×D₁₂	C₂³	1	2	yes	complemented
51	C₄×D₃×C₉	—	2	4	no	—
52	C₃×D₃₆	—	2	2	no	—
53	C₃×D₃₆	—	2	4	no	—
54	C₃×D₃₆	C₂³	1	4	yes	—
55	C₉×Dic₆	—	2	1	no	—
56	C₉×Dic₆	C₂³	1	2	yes	complemented
57	C₃⋊(C₉⋊C₈)	C₂³	1	4	yes	complemented
58	C₂×#949	—	9	1	no	—
59	C₂×#932	—	9	1	no	—
60	C₂³×C₃×D₃	—	6	1	no	—
61	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
62	C₂×C₃×#67	—	2	1	no	—
63	C₃×#235	—	2	2	no	—
64	C₃×#235	C₂×D₃	1	4	yes	—
65	C₂×C₃×D₁₂	—	3	2	no	—
66	C₂×C₃×D₁₂	—	3	4	no	—
67	C₂×C₃×D₁₂	—	6	1	no	—
68	C₂×C₃×D₁₂	—	6	2	no	—
69	C₂×C₃×D₁₂	C₂×D₃	1	1	yes	characteristic
70	C₂×C₃×C₄×D₃	—	2	1	no	—
71	C₂×C₃×Dic₆	C₂×D₃	1	1	yes	characteristic
72	C₂³×D₉	—	2	1	no	—
73	#3748	—	3	4	no	—
74	C₂×C₃⋊(C₃⋊C₈)	—	3	2	no	—
75	#3715	—	3	8	no	—
76	#3713	—	3	8	no	—
77	C₉×#41	—	3	4	no	—
78	C₉×#41	—	6	2	no	—
79	C₂×Q₈×C₉	—	3	1	no	—
80	C₂×D₄×C₉	—	3	1	no	—
81	C₂×D₄×C₉	—	6	1	no	—
82	C₂²×C₄×C₉	—	2	1	no	—
83	C₂²×C₄×C₉	—	6	1	no	—
84	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
85	C₂×D₃₆	—	2	2	no	—
86	C₂×D₃₆	—	2	1	no	—
87	C₂×D₃₆	C₂×D₃	1	2	yes	—
88	C₂×D₃₆	C₂×D₃	1	4	yes	complemented
89	#3675	—	3	8	no	—
90	#3673	—	3	8	no	—
91	#3667	—	3	4	no	—
92	#3667	—	6	4	no	—
93	C₂×C₉⋊C₈	—	3	2	no	—
94	C₂×C₉⋊C₈	—	6	2	no	—
95	C₂²×C₃×C₉	—	2	2	no	—
96	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
97	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
98	C₂×D₃×C₉	—	2	2	no	—
99	C₂×D₃×C₉	—	4	2	no	—
100	C₂×C₃×D₉	—	2	4	no	—
101	C₂×C₃×D₉	—	4	8	no	—
102	C₂×C₃×D₉	—	4	4	no	—
103	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
104	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
105	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
106	C₉×Dic₃	—	2	2	no	—
107	C₂×C₃×#41	—	3	1	no	—
108	C₂²×C₃×D₄	—	9	1	no	—
109	C₂×#235	D₉	1	1	yes	characteristic, complemented
110	C₂²×D₁₂	—	3	1	no	—
111	#949	—	9	8	no	—
112	C₂×#215	—	9	2	no	—
113	C₂×#214	—	9	2	no	—
114	#932	—	9	8	no	—
115	C₂×#213	—	9	2	no	—
116	C₂×#213	—	9	2	no	—
117	C₂×#208	—	9	1	no	—
118	C₂×#208	—	9	1	no	—
119	C₂×#208	—	18	1	no	—
120	C₂³×C₃²	#67	1	1	yes	characteristic
121	C₂²×C₃×D₃	—	2	1	no	—
122	C₂²×C₃×D₃	—	6	4	no	—
123	C₂²×C₃×D₃	—	6	2	no	—
124	C₂²×C₃×D₃	—	12	4	no	—
125	C₂×C₃²×C₄	#67	1	1	yes	characteristic
126	C₂×C₃²×C₄	#67	1	2	yes	—
127	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
129	C₃×#67	—	2	4	no	—
130	C₂×C₃×Dic₃	—	2	1	no	—
131	C₃×D₁₂	—	2	1	no	—
132	C₃×D₁₂	—	3	4	no	—
133	C₃×D₁₂	—	6	2	no	—
134	C₃×D₁₂	—	6	4	no	—
135	C₃×D₁₂	C₂²×D₃	1	2	yes	—
136	C₃×C₄×D₃	—	2	4	no	—
137	C₃×Dic₆	—	2	1	no	—
138	C₃×Dic₆	C₂²×D₃	1	2	yes	—
139	C₂³×C₉	—	2	1	no	—
140	C₂³×C₉	—	6	1	no	—
141	C₂³×C₉	#67	1	1	yes	characteristic
142	C₂²×D₉	—	2	2	no	—
143	C₂²×D₉	—	2	4	no	—
144	C₂²×D₉	—	4	4	no	—
145	C₃⋊(C₃⋊C₈)	—	3	4	no	—
146	Q₈×C₉	—	3	2	no	—
147	Q₈×C₉	—	6	1	no	—
148	D₄×C₉	—	3	2	no	—
149	D₄×C₉	—	6	4	no	—
150	D₄×C₉	—	6	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	2	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	2	2	no	—
155	C₂×C₄×C₉	—	6	1	no	—
156	C₂×C₄×C₉	—	6	4	no	—
157	C₂×C₄×C₉	#67	1	1	yes	characteristic
158	C₂×C₄×C₉	#67	1	2	yes	—
159	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
160	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
161	D₃₆	—	2	2	no	—
162	D₃₆	—	2	4	no	—
163	D₃₆	C₂²×D₃	1	4	yes	—
164	C₉⋊C₈	—	3	4	no	—
165	C₉⋊C₈	—	6	4	no	—
166	C₂×AGL(1,ℤ/8)	—	27	1	no	Sylow
167	C₂×C₃×C₉	—	2	2	no	—
168	C₂×C₃×C₉	AGL(1,ℤ/8)	1	2	yes	complemented
169	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
170	D₃×C₉	—	4	2	no	—
171	C₃×D₉	—	4	4	no	—
172	C₂⁴×C₃	—	18	1	no	—
173	C₂³×D₃	—	6	1	no	—
174	C₃×#41	—	3	4	no	—
175	C₃×#41	—	6	2	no	—
176	C₂×C₃×Q₈	—	3	1	no	—
177	C₂×C₃×D₄	—	3	1	no	—
178	C₂×C₃×D₄	—	6	1	no	—
179	C₂×C₃×D₄	—	9	2	no	—
180	C₂×C₃×D₄	—	9	4	no	—
181	C₂×C₃×D₄	—	18	1	no	—
182	C₂×C₃×D₄	—	18	2	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	6	1	no	—
185	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
186	C₂²×C₃×C₄	D₃²	1	1	yes	characteristic
187	C₂×#67	—	2	1	no	—
188	#235	—	2	2	no	—
189	#235	C₂×D₉	1	4	yes	complemented
190	C₂×D₁₂	—	3	2	no	—
191	C₂×D₁₂	—	3	4	no	—
192	C₂×D₁₂	—	6	1	no	—
193	C₂×D₁₂	—	6	2	no	—
194	C₂×D₁₂	C₂×D₉	1	1	yes	characteristic, complemented
195	C₂×C₄×D₃	—	2	1	no	—
196	C₂×Dic₆	C₂×D₉	1	1	yes	characteristic, complemented
197	#215	—	9	8	no	—
198	#214	—	9	8	no	—
199	#213	—	9	8	no	—
200	#213	—	9	8	no	—
201	#208	—	9	4	no	—
202	#208	—	9	4	no	—
203	#208	—	18	4	no	—
204	C₂×C₃⋊C₈	—	9	2	no	—
205	C₂×C₃⋊C₈	—	9	2	no	—
206	C₂×C₃⋊C₈	—	18	2	no	—
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	C₂×#67	1	2	yes	—
209	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
210	C₂×C₃×D₃	—	2	2	no	—
211	C₂×C₃×D₃	—	4	2	no	—
212	C₂×C₃×D₃	—	6	4	no	—
213	C₂×C₃×D₃	—	12	8	no	—
214	C₂×C₃×D₃	—	12	4	no	—
215	C₃²×C₄	C₂×#67	1	1	yes	characteristic
216	C₃²×C₄	C₂×#67	1	2	yes	—
217	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
218	C₃×Dic₃	—	2	2	no	—
219	C₂²×C₉	—	2	2	no	—
220	C₂²×C₉	—	2	1	no	—
221	C₂²×C₉	—	2	2	no	—
222	C₂²×C₉	—	4	2	no	—
223	C₂²×C₉	—	6	2	no	—
224	C₂²×C₉	—	12	2	no	—
225	C₂²×C₉	C₂×#67	1	2	yes	—
226	C₂²×C₉	C₂×#67	1	1	yes	characteristic
227	C₂×D₉	—	2	4	no	—
228	C₂×D₉	—	4	8	no	—
229	C₂×D₉	—	4	4	no	—
230	C₄×C₉	—	2	1	no	—
231	C₄×C₉	—	2	2	no	—
232	C₄×C₉	—	2	1	no	—
233	C₄×C₉	—	6	2	no	—
234	C₄×C₉	C₂×#67	1	2	yes	—
235	C₄×C₉	C₂×#67	1	1	yes	characteristic
236	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
237	C₂×#41	—	3	1	no	—
238	C₂²×D₄	—	9	1	no	—
239	AGL(1,ℤ/8)	—	27	8	no	—
240	C₂×SD₁₆	—	27	2	no	—
241	C₂×D₈	—	27	2	no	—
242	C₂×M₁₆	—	27	1	no	—
243	C₃×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
244	C₂³×C₃	—	2	1	no	—
245	C₂³×C₃	—	6	1	no	—
246	C₂³×C₃	—	18	4	no	—
247	C₂³×C₃	—	18	2	no	—
248	C₂³×C₃	—	36	4	no	—
249	C₂³×C₃	#611	1	1	yes	characteristic
250	C₂³×C₃	#625	1	1	yes	characteristic
251	C₂²×D₃	—	2	1	no	—
252	C₂²×D₃	—	6	4	no	—
253	C₂²×D₃	—	6	2	no	—
254	C₂²×D₃	—	12	4	no	—
255	C₃×Q₈	—	3	2	no	—
256	C₃×Q₈	—	6	1	no	—
257	C₃×D₄	—	3	2	no	—
258	C₃×D₄	—	6	4	no	—
259	C₃×D₄	—	6	1	no	—
260	C₃×D₄	—	9	4	no	—
261	C₃×D₄	—	18	2	no	—
262	C₃×D₄	—	18	4	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	6	1	no	—
268	C₂×C₃×C₄	—	6	4	no	—
269	C₂×C₃×C₄	#611	1	1	yes	characteristic
270	C₂×C₃×C₄	#611	1	2	yes	—
271	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
273	C₂×C₃×C₄	#625	1	1	yes	characteristic
274	C₂×C₃×C₄	#625	1	2	yes	—
275	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×D₃²	1	2	yes	—
277	#67	—	2	4	no	—
278	C₂×Dic₃	—	2	1	no	—
279	D₁₂	—	2	1	no	—
280	D₁₂	—	3	4	no	—
281	D₁₂	—	6	4	no	—
282	D₁₂	—	6	2	no	—
283	D₁₂	C₂²×D₉	1	2	yes	complemented
284	C₄×D₃	—	2	4	no	—
285	Dic₆	—	2	1	no	—
286	Dic₆	C₂²×D₉	1	2	yes	complemented
287	C₃⋊C₈	—	9	4	no	—
288	C₃⋊C₈	—	9	4	no	—
289	C₃⋊C₈	—	18	4	no	—
290	C₂×C₃²	—	2	2	no	—
291	C₂×C₃²	#949	1	2	yes	—
292	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
293	C₃×D₃	—	4	2	no	—
294	C₃×D₃	—	12	4	no	—
295	C₂×C₉	—	2	2	no	—
296	C₂×C₉	—	2	1	no	—
297	C₂×C₉	—	2	2	no	—
298	C₂×C₉	—	4	2	no	—
299	C₂×C₉	—	12	2	no	—
300	C₂×C₉	#932	1	2	yes	complemented
301	C₂×C₉	C₂²×#67	1	1	yes	characteristic
302	D₉	—	4	4	no	—
303	C₂⁴	—	18	1	no	—
304	#41	—	3	4	no	—
305	#41	—	6	2	no	—
306	C₂×Q₈	—	3	1	no	—
307	C₂×D₄	—	3	1	no	—
308	C₂×D₄	—	6	1	no	—
309	C₂×D₄	—	9	2	no	—
310	C₂×D₄	—	9	4	no	—
311	C₂×D₄	—	18	2	no	—
312	C₂×D₄	—	18	1	no	—
313	C₂²×C₄	—	6	1	no	—
314	C₂²×C₄	D₃×D₉	1	1	yes	characteristic
315	SD₁₆	—	27	8	no	—
316	D₈	—	27	8	no	—
317	M₁₆	—	27	4	no	—
318	C₂×C₈	—	27	2	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	4	2	no	—
324	C₂²×C₃	—	6	2	no	—
325	C₂²×C₃	—	12	2	no	—
326	C₂²×C₃	—	18	4	no	—
327	C₂²×C₃	—	36	8	no	—
328	C₂²×C₃	—	36	4	no	—
329	C₂²×C₃	C₂×#611	1	2	yes	—
330	C₂²×C₃	C₂×#611	1	1	yes	characteristic
331	C₂²×C₃	C₂×#625	1	2	yes	—
332	C₂²×C₃	C₂×#625	1	1	yes	characteristic
333	C₂×D₃	—	2	2	no	—
334	C₂×D₃	—	4	2	no	—
335	C₂×D₃	—	6	4	no	—
336	C₂×D₃	—	12	8	no	—
337	C₂×D₃	—	12	4	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	2	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	6	2	no	—
342	C₃×C₄	C₂×#611	1	1	yes	characteristic
343	C₃×C₄	C₂×#611	1	2	yes	—
344	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
345	C₃×C₄	C₂×#625	1	2	yes	—
346	C₃×C₄	C₂×#625	1	1	yes	characteristic
347	C₃×C₄	C₂²×D₃²	1	1	yes	characteristic
348	Dic₃	—	2	2	no	—
349	C₃²	C₂×#949	1	1	yes	characteristic
350	C₉	—	2	1	no	—
351	C₉	C₂×#932	1	1	yes	characteristic, complemented
352	C₂³	—	6	1	no	—
353	C₂³	—	18	4	no	—
354	C₂³	—	18	2	no	—
355	C₂³	—	36	4	no	—
356	C₂³	#6194	1	1	yes	characteristic
357	Q₈	—	3	2	no	—
358	Q₈	—	6	1	no	—
359	D₄	—	3	2	no	—
360	D₄	—	6	4	no	—
361	D₄	—	6	1	no	—
362	D₄	—	9	4	no	—
363	D₄	—	18	4	no	—
364	D₄	—	18	2	no	—
365	C₂×C₄	—	6	1	no	—
366	C₂×C₄	—	6	4	no	—
367	C₂×C₄	#6194	1	2	yes	—
368	C₂×C₄	#6194	1	1	yes	characteristic
369	C₂×C₄	C₂×D₃×D₉	1	2	yes	—
370	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
371	C₈	—	27	4	no	—
372	C₂×C₃	—	2	2	no	—
373	C₂×C₃	—	2	2	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	4	2	no	—
377	C₂×C₃	—	12	2	no	—
378	C₂×C₃	—	36	4	no	—
379	C₂×C₃	#63512	1	2	yes	complemented
380	C₂×C₃	C₂²×#611	1	1	yes	characteristic
381	C₂×C₃	#63823	1	2	yes	—
382	C₂×C₃	C₂²×#625	1	1	yes	characteristic
383	D₃	—	4	2	no	—
384	D₃	—	12	4	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	6	2	no	—
387	C₂²	—	12	2	no	—
388	C₂²	—	18	4	no	—
389	C₂²	—	36	8	no	—
390	C₂²	—	36	4	no	—
391	C₂²	C₂×#6194	1	2	yes	—
392	C₂²	C₂×#6194	1	1	yes	characteristic
393	C₄	—	6	2	no	—
394	C₄	C₂×#6194	1	2	yes	—
395	C₄	C₂×#6194	1	1	yes	characteristic
396	C₄	C₂²×D₃×D₉	1	1	yes	characteristic
397	C₃	—	2	1	no	—
398	C₃	C₂×#63512	1	1	yes	characteristic, complemented
399	C₃	C₂×#63823	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	12	2	no	—
402	C₂	—	36	4	no	—
403	C₂	#11720882	1	2	yes	direct product factor
404	C₂	C₂²×#6194	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#6194
commutator, cosocle	C₃×C₄×C₉	C₂⁴
Frattini	C₃×C₄	C₂²×D₃²
Fitting	C₂²×C₃×C₄×C₉	C₂²
socle	C₂²×C₃²	C₂×#67
hypercenter	C₂²×C₄	D₃×D₉
hypocenter	C₃×C₉	C₂×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄×C₉ ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#235	C₂	semidirect
2. C₂²×C₃×D₃₆	C₂	semidirect
3. C₂×#88532	C₂	semidirect
4. C₂×#88425	C₂	semidirect
5. #11720882	C₂	direct (N × H)
6. C₂×#88421	C₂	semidirect
13. C₉×#235	C₂²	semidirect
14. C₂×C₉×D₁₂	C₂²	semidirect
19. C₂×C₃×D₃₆	C₂²	semidirect
20. C₂×C₉×Dic₆	C₂²	semidirect
21. #88532	C₂²	semidirect
22. C₂×C₃⋊(C₉⋊C₈)	C₂²	semidirect
23. #88425	C₂²	semidirect
24. #88421	C₂²	semidirect
32. C₂²×D₃₆	D₃	semidirect
50. C₉×D₁₂	C₂³	semidirect
56. C₉×Dic₆	C₂³	semidirect
57. C₃⋊(C₉⋊C₈)	C₂³	semidirect
88. C₂×D₃₆	C₂×D₃	semidirect
109. C₂×#235	D₉	semidirect
168. C₂×C₃×C₉	AGL(1,ℤ/8)	semidirect
189. #235	C₂×D₉	semidirect
194. C₂×D₁₂	C₂×D₉	semidirect
196. C₂×Dic₆	C₂×D₉	semidirect
243. C₃×C₉	C₂×AGL(1,ℤ/8)	semidirect
283. D₁₂	C₂²×D₉	semidirect
286. Dic₆	C₂²×D₉	semidirect
300. C₂×C₉	#932	semidirect
351. C₉	C₂×#932	semidirect
379. C₂×C₃	#63512	semidirect
398. C₃	C₂×#63512	semidirect
403. C₂	#11720882	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×C₉×#235	2
C₂²×C₃×D₃₆	2
C₂×#88532	2
C₂×#88425	2
#11720882	2
C₂×#88421	2
C₂×#63823	3
C₂×#63512	3

Subgroups — C2×#11720882 #13150099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11720882 #13150099