Subgroups — C₉×Dic₃×SD₁₆ #13143338

Order 1728.

434 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₉×#835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#832	C₂	1	1	yes	maximal, characteristic
6	C₉×#817	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×Dic₃×SD₁₆	C₃	1	1	yes	maximal, characteristic
9	C₄×C₉×SD₁₆	—	3	1	no	maximal
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₉×Dic₃	—	2	1	no	—
13	C₃×C₉×SD₁₆	C₄	1	4	yes	complemented
14	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
15	C₉×#217	—	2	1	no	—
16	C₉×C₄⋊Dic₃	—	2	1	no	—
17	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₄×C₉×Dic₃	—	2	1	no	—
20	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃²×SD₁₆	C₂×C₃	1	1	yes	characteristic
23	C₃×Q₈×Dic₃	C₂×C₃	1	1	yes	characteristic
24	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
25	C₃×#835	C₂×C₃	1	1	yes	characteristic
26	C₃×#832	C₂×C₃	1	1	yes	characteristic
27	C₃×#817	C₂×C₃	1	1	yes	characteristic
28	C₃×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic
29	C₂×C₉×SD₁₆	—	2	1	no	—
30	C₂×C₉×SD₁₆	D₃	1	1	yes	characteristic
31	C₄×Q₈×C₉	—	3	1	no	—
32	C₄×D₄×C₉	—	3	1	no	—
33	C₉×#106	—	3	1	no	—
34	C₉×#103	—	3	1	no	—
35	C₉×#102	—	3	1	no	—
36	C₄×C₈×C₉	—	3	1	no	—
37	C₂³×C₃×C₉	—	2	1	no	—
38	C₃×Q₈×C₉	—	2	1	no	—
39	C₃×Q₈×C₉	C₂×C₄	1	2	yes	complemented
40	C₃×D₄×C₉	—	2	1	no	—
41	C₃×D₄×C₉	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×C₉	—	2	1	no	—
43	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
44	C₂×C₉×Dic₃	—	2	1	no	—
45	C₂×C₉×Dic₃	—	2	1	no	—
46	C₂×C₉×Dic₃	—	4	2	no	—
47	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
48	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
49	C₃×C₈×C₉	C₂×C₄	1	2	yes	complemented
50	C₉×C₃⋊C₈	—	2	1	no	—
51	C₃×C₄×SD₁₆	—	3	1	no	—
52	Dic₃×SD₁₆	C₉	1	1	yes	characteristic, direct product factor
53	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
54	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
55	C₂²×C₃×Dic₃	—	2	1	no	—
56	C₃²×SD₁₆	C₃×C₄	1	4	yes	—
57	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
58	C₃×#217	—	2	1	no	—
59	C₃×C₄⋊Dic₃	—	2	1	no	—
60	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
61	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
62	C₃×C₄×Dic₃	—	2	1	no	—
63	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
65	C₂×Q₈×C₉	—	2	1	no	—
66	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
67	C₂×D₄×C₉	—	2	1	no	—
68	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
69	C₂²×C₄×C₉	—	6	1	no	—
70	C₉×SD₁₆	—	2	4	no	—
71	C₉×SD₁₆	Dic₃	1	4	yes	direct product factor
72	C₂×C₈×C₉	—	2	1	no	—
73	C₂×C₈×C₉	—	3	1	no	—
74	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
75	C₉×C₄⋊C₄	—	3	1	no	—
76	C₉×C₄⋊C₄	—	3	1	no	—
77	C₉×C₄⋊C₄	—	6	1	no	—
78	C₉×C₂²⋊C₄	—	6	1	no	—
79	C₄²×C₉	—	3	1	no	—
80	C₄²×C₉	—	6	1	no	—
81	C₂²×C₃×C₉	—	2	2	no	—
82	C₂²×C₃×C₉	—	4	1	no	—
83	C₂²×C₃×C₉	—	4	1	no	—
84	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
85	C₃×C₄×C₉	—	2	2	no	—
86	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
87	C₃×C₄×C₉	#41	1	1	yes	characteristic
88	C₉×Dic₃	—	2	1	no	—
89	C₉×Dic₃	—	4	1	no	—
90	C₉×Dic₃	—	4	1	no	—
91	C₉×Dic₃	SD₁₆	1	2	yes	direct product factor
92	C₂×C₃×SD₁₆	—	2	1	no	—
93	C₂×C₃×SD₁₆	C₂×C₉	1	1	yes	characteristic
94	C₂×C₃×SD₁₆	C₃×D₃	1	1	yes	characteristic
95	C₃×C₄×Q₈	—	3	1	no	—
96	C₃×C₄×D₄	—	3	1	no	—
97	Q₈×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
98	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic
99	C₃×#106	—	3	1	no	—
100	C₃×#103	—	3	1	no	—
101	C₃×#102	—	3	1	no	—
102	C₃×C₄×C₈	—	3	1	no	—
103	#835	C₂×C₉	1	1	yes	characteristic, complemented
104	#832	C₂×C₉	1	1	yes	characteristic
105	#817	C₂×C₉	1	1	yes	characteristic, complemented
106	C₈×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
107	C₂³×C₃²	—	2	1	no	—
108	C₃²×Q₈	—	2	1	no	—
109	C₃²×Q₈	C₂×C₃×C₄	1	2	yes	—
110	C₃²×D₄	—	2	1	no	—
111	C₃²×D₄	C₂×C₃×C₄	1	2	yes	—
112	C₂×C₃²×C₄	—	2	1	no	—
113	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
114	C₂×C₃×Dic₃	—	2	1	no	—
115	C₂×C₃×Dic₃	—	2	1	no	—
116	C₂×C₃×Dic₃	—	4	2	no	—
117	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
118	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
119	C₂³×C₉	—	2	1	no	—
120	C₂³×C₉	—	4	1	no	—
121	C₃²×C₈	C₂×C₃×C₄	1	2	yes	—
122	C₃×C₃⋊C₈	—	2	1	no	—
123	Q₈×C₉	—	2	1	no	—
124	Q₈×C₉	—	2	2	no	—
125	Q₈×C₉	—	4	1	no	—
126	Q₈×C₉	C₂×Dic₃	1	2	yes	complemented
127	D₄×C₉	—	2	1	no	—
128	D₄×C₉	—	2	2	no	—
129	D₄×C₉	—	4	1	no	—
130	D₄×C₉	C₂×Dic₃	1	2	yes	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	3	1	no	—
134	C₂×C₄×C₉	—	3	1	no	—
135	C₂×C₄×C₉	—	4	1	no	—
136	C₂×C₄×C₉	—	6	1	no	—
137	C₂×C₄×C₉	—	6	1	no	—
138	C₂×C₄×C₉	—	12	2	no	—
139	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
140	C₈×C₉	—	2	2	no	—
141	C₈×C₉	—	6	1	no	—
142	C₈×C₉	C₂×Dic₃	1	2	yes	complemented
143	C₄×SD₁₆	—	3	1	no	Sylow
144	C₂×C₃×C₉	—	4	2	no	—
145	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
146	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
147	C₂×C₃×C₉	#135	1	1	yes	characteristic
148	C₂×C₃×Q₈	—	2	1	no	—
149	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
150	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
151	C₂×C₃×D₄	—	2	1	no	—
152	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
153	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
154	C₂²×C₃×C₄	—	6	1	no	—
155	C₂²×Dic₃	—	2	1	no	—
156	C₃×SD₁₆	—	2	4	no	—
157	C₃×SD₁₆	C₄×C₉	1	4	yes	complemented
158	C₃×SD₁₆	C₃×Dic₃	1	4	yes	—
159	C₂×C₃×C₈	—	2	1	no	—
160	C₂×C₃×C₈	—	3	1	no	—
161	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
162	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
163	C₃×C₄⋊C₄	—	3	1	no	—
164	C₃×C₄⋊C₄	—	3	1	no	—
165	C₃×C₄⋊C₄	—	6	1	no	—
166	C₃×C₂²⋊C₄	—	6	1	no	—
167	C₃×C₄²	—	3	1	no	—
168	C₃×C₄²	—	6	1	no	—
169	#217	—	2	1	no	—
170	C₄⋊Dic₃	—	2	1	no	—
171	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
172	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
173	C₄×Dic₃	—	2	1	no	—
174	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
175	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
176	C₂²×C₃²	—	2	2	no	—
177	C₂²×C₃²	—	4	1	no	—
178	C₂²×C₃²	—	4	1	no	—
179	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
180	C₃²×C₄	—	2	2	no	—
181	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
182	C₃²×C₄	C₃×#41	1	1	yes	characteristic
183	C₃×Dic₃	—	2	1	no	—
184	C₃×Dic₃	—	4	1	no	—
185	C₃×Dic₃	—	4	1	no	—
186	C₃×Dic₃	C₃×SD₁₆	1	2	yes	—
187	C₂²×C₉	—	2	2	no	—
188	C₂²×C₉	—	2	1	no	—
189	C₂²×C₉	—	4	2	no	—
190	C₂²×C₉	—	4	1	no	—
191	C₂²×C₉	—	4	1	no	—
192	C₂²×C₉	—	8	1	no	—
193	C₂²×C₉	—	8	1	no	—
194	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
195	C₄×C₉	—	2	2	no	—
196	C₄×C₉	—	2	1	no	—
197	C₄×C₉	—	2	1	no	—
198	C₄×C₉	—	3	2	no	—
199	C₄×C₉	—	4	2	no	—
200	C₄×C₉	—	6	1	no	—
201	C₄×C₉	—	12	1	no	—
202	C₄×C₉	—	12	1	no	—
203	C₄×C₉	#237	1	1	yes	characteristic
204	C₄×C₉	C₂²×Dic₃	1	1	yes	characteristic
205	C₂×SD₁₆	D₃×C₉	1	1	yes	characteristic
206	C₄×Q₈	—	3	1	no	—
207	C₄×D₄	—	3	1	no	—
208	#106	—	3	1	no	—
209	#103	—	3	1	no	—
210	#102	—	3	1	no	—
211	C₄×C₈	—	3	1	no	—
212	C₃×C₉	C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
213	C₂³×C₃	—	2	1	no	—
214	C₂³×C₃	—	2	1	no	—
215	C₂³×C₃	—	4	1	no	—
216	C₃×Q₈	—	2	1	no	—
217	C₃×Q₈	—	2	1	no	—
218	C₃×Q₈	—	2	2	no	—
219	C₃×Q₈	—	4	1	no	—
220	C₃×Q₈	C₂×C₄×C₉	1	2	yes	complemented
221	C₃×Q₈	C₂×C₃×Dic₃	1	2	yes	—
222	C₃×D₄	—	2	1	no	—
223	C₃×D₄	—	2	1	no	—
224	C₃×D₄	—	2	2	no	—
225	C₃×D₄	—	4	1	no	—
226	C₃×D₄	C₂×C₄×C₉	1	2	yes	—
227	C₃×D₄	C₂×C₃×Dic₃	1	2	yes	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	3	1	no	—
232	C₂×C₃×C₄	—	3	1	no	—
233	C₂×C₃×C₄	—	4	1	no	—
234	C₂×C₃×C₄	—	6	1	no	—
235	C₂×C₃×C₄	—	6	1	no	—
236	C₂×C₃×C₄	—	12	2	no	—
237	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
239	C₂×Dic₃	—	2	1	no	—
240	C₂×Dic₃	—	2	1	no	—
241	C₂×Dic₃	—	4	2	no	—
242	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
243	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
244	C₃×C₈	—	2	2	no	—
245	C₃×C₈	—	6	1	no	—
246	C₃×C₈	C₂×C₄×C₉	1	2	yes	complemented
247	C₃×C₈	C₂×C₃×Dic₃	1	2	yes	—
248	C₃⋊C₈	—	2	1	no	—
249	C₂×C₃²	—	4	2	no	—
250	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
251	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
252	C₂×C₃²	C₃×#135	1	1	yes	characteristic
253	C₂×C₉	—	2	1	no	—
254	C₂×C₉	—	2	1	no	—
255	C₂×C₉	—	2	1	no	—
256	C₂×C₉	—	4	2	no	—
257	C₂×C₉	—	8	2	no	—
258	C₂×C₉	D₃×SD₁₆	1	1	yes	characteristic
259	C₂×C₉	#916	1	1	yes	characteristic
260	C₂×C₉	D₄×Dic₃	1	1	yes	characteristic
261	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
262	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
263	C₂²×C₄	—	6	1	no	—
264	SD₁₆	C₉×Dic₃	1	4	yes	direct product factor
265	C₂×C₈	—	3	1	no	—
266	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
267	C₄⋊C₄	—	3	1	no	—
268	C₄⋊C₄	—	3	1	no	—
269	C₄⋊C₄	—	6	1	no	—
270	C₂²⋊C₄	—	6	1	no	—
271	C₄²	—	3	1	no	—
272	C₄²	—	6	1	no	—
273	C₂²×C₃	—	2	2	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	4	2	no	—
277	C₂²×C₃	—	4	1	no	—
278	C₂²×C₃	—	4	1	no	—
279	C₂²×C₃	—	4	1	no	—
280	C₂²×C₃	—	4	1	no	—
281	C₂²×C₃	—	8	1	no	—
282	C₂²×C₃	—	8	1	no	—
283	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
284	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	2	2	no	—
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	—	3	2	no	—
290	C₃×C₄	—	4	2	no	—
291	C₃×C₄	—	6	1	no	—
292	C₃×C₄	—	12	1	no	—
293	C₃×C₄	—	12	1	no	—
294	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
295	C₃×C₄	C₉×#41	1	1	yes	characteristic
296	C₃×C₄	C₃×#237	1	1	yes	characteristic
297	C₃×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
298	Dic₃	—	2	1	no	—
299	Dic₃	—	4	1	no	—
300	Dic₃	—	4	1	no	—
301	Dic₃	C₉×SD₁₆	1	2	yes	direct product factor
302	C₃²	C₃×C₄×SD₁₆	1	1	yes	characteristic
303	C₉	—	2	1	no	—
304	C₉	Dic₃×SD₁₆	1	1	yes	characteristic, direct product factor
305	C₂³	—	2	1	no	—
306	Q₈	—	2	1	no	—
307	Q₈	C₂×C₉×Dic₃	1	2	yes	complemented
308	D₄	—	2	1	no	—
309	D₄	C₂×C₉×Dic₃	1	2	yes	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	3	1	no	—
312	C₂×C₄	—	3	1	no	—
313	C₂×C₄	—	6	1	no	—
314	C₂×C₄	—	6	1	no	—
315	C₂×C₄	—	12	2	no	—
316	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
317	C₈	—	6	1	no	—
318	C₈	C₂×C₉×Dic₃	1	2	yes	complemented
319	C₂×C₃	—	2	1	no	—
320	C₂×C₃	—	2	1	no	—
321	C₂×C₃	—	2	1	no	—
322	C₂×C₃	—	4	2	no	—
323	C₂×C₃	—	4	2	no	—
324	C₂×C₃	—	8	2	no	—
325	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
326	C₂×C₃	C₂×C₉×SD₁₆	1	1	yes	characteristic
327	C₂×C₃	C₉×#135	1	1	yes	characteristic
328	C₂×C₃	C₃×D₃×SD₁₆	1	1	yes	characteristic
329	C₂×C₃	C₃×#916	1	1	yes	characteristic
330	C₂×C₃	C₃×D₄×Dic₃	1	1	yes	characteristic
331	C₂²	—	2	2	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	1	no	—
334	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
335	C₄	—	2	2	no	—
336	C₄	—	3	2	no	—
337	C₄	—	6	1	no	—
338	C₄	—	12	1	no	—
339	C₄	—	12	1	no	—
340	C₄	C₉×#237	1	1	yes	characteristic
341	C₄	C₂²×C₉×Dic₃	1	1	yes	characteristic
342	C₃	—	2	1	no	—
343	C₃	C₄×C₉×SD₁₆	1	1	yes	characteristic, complemented
344	C₃	C₃×Dic₃×SD₁₆	1	1	yes	characteristic
345	C₂	—	4	2	no	—
346	C₂	D₃×C₉×SD₁₆	1	1	yes	characteristic
347	C₂	C₉×#916	1	1	yes	characteristic
348	C₂	D₄×C₉×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×SD₁₆	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃²×D₄	C₂²×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₉×SD₁₆	D₃
hypocenter	C₃	C₄×C₉×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₂×C₉×SD₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×C₉×Dic₃	C₂	semidirect
4. C₉×#835	C₂	semidirect
6. C₉×#817	C₂	semidirect
7. C₈×C₉×Dic₃	C₂	semidirect
13. C₃×C₉×SD₁₆	C₄	semidirect
39. C₃×Q₈×C₉	C₂×C₄	semidirect
49. C₃×C₈×C₉	C₂×C₄	semidirect
52. Dic₃×SD₁₆	C₉	direct (N × H)
71. C₉×SD₁₆	Dic₃	direct (N × H)
91. C₉×Dic₃	SD₁₆	direct (N × H)
97. Q₈×Dic₃	C₂×C₉	semidirect
103. #835	C₂×C₉	semidirect
105. #817	C₂×C₉	semidirect
106. C₈×Dic₃	C₂×C₉	semidirect
126. Q₈×C₉	C₂×Dic₃	semidirect
142. C₈×C₉	C₂×Dic₃	semidirect
157. C₃×SD₁₆	C₄×C₉	semidirect
212. C₃×C₉	C₄×SD₁₆	semidirect
220. C₃×Q₈	C₂×C₄×C₉	semidirect
246. C₃×C₈	C₂×C₄×C₉	semidirect
264. SD₁₆	C₉×Dic₃	direct (N × H)
301. Dic₃	C₉×SD₁₆	direct (N × H)
304. C₉	Dic₃×SD₁₆	direct (N × H)
307. Q₈	C₂×C₉×Dic₃	semidirect
318. C₈	C₂×C₉×Dic₃	semidirect
343. C₃	C₄×C₉×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×SD₁₆	2
Q₈×C₉×Dic₃	2
D₄×C₉×Dic₃	2
C₉×#835	2
C₉×#832	2
C₉×#817	2
C₈×C₉×Dic₃	2
C₃×Dic₃×SD₁₆	3
C₄×C₉×SD₁₆	3

Subgroups — C9×Dic3×SD16 #13143338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₃×SD₁₆ #13143338