Subgroups — C₉×#5766 #13153462

Order 1728.

804 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#1007	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#942	C₂	1	2	yes	maximal, complemented
4	C₉×#919	C₂	1	2	yes	maximal, complemented
5	C₉×#918	C₂	1	4	yes	maximal, complemented
6	D₃×C₉×Q₁₆	C₂	1	2	yes	maximal, complemented
7	C₉×#904	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#901	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5766	C₃	1	1	yes	maximal, characteristic
10	C₉×#578	—	3	1	no	maximal
11	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
12	C₉×#239	—	2	2	no	—
13	C₉×#239	C₂²	1	4	yes	—
14	D₃×Q₈×C₉	—	2	2	no	—
15	D₃×Q₈×C₉	C₂²	1	4	yes	—
16	C₉×#235	—	2	4	no	—
17	C₉×#235	C₂²	1	1	yes	characteristic
18	C₉×#235	C₂²	1	2	yes	—
19	C₃×C₉×Q₁₆	C₂²	1	2	yes	—
20	C₃×C₉×Q₁₆	C₂²	1	2	yes	—
21	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
22	C₉×#216	C₂²	1	4	yes	—
23	C₉×#215	C₂²	1	4	yes	—
24	C₉×#208	C₂²	1	1	yes	characteristic
25	C₉×Dic₁₂	C₂²	1	1	yes	characteristic
26	C₉×D₂₄	C₂²	1	1	yes	characteristic
27	C₉×#204	C₂²	1	2	yes	—
28	C₉×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
29	D₃×C₈×C₉	C₂²	1	2	yes	—
30	C₃×#1007	C₂×C₃	1	2	yes	—
31	C₂×C₃²×Q₁₆	C₂×C₃	1	1	yes	characteristic
32	C₃×#942	C₂×C₃	1	2	yes	—
33	C₃×#919	C₂×C₃	1	2	yes	—
34	C₃×#918	C₂×C₃	1	4	yes	—
35	C₃×D₃×Q₁₆	C₂×C₃	1	2	yes	—
36	C₃×#904	C₂×C₃	1	1	yes	characteristic
37	C₃×#901	C₂×C₃	1	1	yes	characteristic
38	C₉×2₋¹⁺⁴	—	3	2	no	—
39	C₉×#137	—	3	2	no	—
40	C₉×#137	—	3	4	no	—
41	C₉×#135	—	3	2	no	—
42	C₉×#135	—	3	1	no	—
43	C₂×C₉×Q₁₆	—	2	1	no	—
44	C₂×C₉×Q₁₆	—	3	2	no	—
45	C₂×C₉×Q₁₆	D₃	1	1	yes	characteristic, complemented
46	C₉×#131	—	3	1	no	—
47	C₃×Q₈×C₉	—	2	2	no	—
48	C₃×Q₈×C₉	C₂³	1	4	yes	—
49	C₂×C₃×C₄×C₉	—	2	2	no	—
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₉×#67	—	2	2	no	—
52	C₉×#67	D₄	1	2	yes	—
53	C₉×D₁₂	—	2	4	no	—
54	C₉×D₁₂	D₄	1	1	yes	characteristic
55	C₉×D₁₂	C₂³	1	2	yes	—
56	C₄×D₃×C₉	—	2	4	no	—
57	C₄×D₃×C₉	—	2	2	no	—
58	C₄×D₃×C₉	—	2	4	no	—
59	C₄×D₃×C₉	C₂³	1	2	yes	—
60	C₉×Dic₆	—	2	4	no	—
61	C₉×Dic₆	D₄	1	1	yes	characteristic
62	C₉×Dic₆	C₂³	1	2	yes	—
63	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
64	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
65	C₉×C₃⋊C₈	C₂³	1	2	yes	—
66	C₃×#578	—	3	1	no	—
67	#5766	C₉	1	1	yes	characteristic, direct product factor
68	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
69	C₃×#239	—	2	2	no	—
70	C₃×#239	C₂²×C₃	1	4	yes	—
71	C₃×D₃×Q₈	—	2	2	no	—
72	C₃×D₃×Q₈	C₂²×C₃	1	4	yes	—
73	C₃×#235	—	2	4	no	—
74	C₃×#235	C₂²×C₃	1	1	yes	characteristic
75	C₃×#235	C₂²×C₃	1	2	yes	—
76	C₃²×Q₁₆	C₂²×C₃	1	2	yes	—
77	C₃²×Q₁₆	C₂²×C₃	1	2	yes	—
78	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
79	C₃×#216	C₂²×C₃	1	4	yes	—
80	C₃×#215	C₂²×C₃	1	4	yes	—
81	C₃×#208	C₂²×C₃	1	1	yes	characteristic
82	C₃×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
83	C₃×D₂₄	C₂²×C₃	1	1	yes	characteristic
84	C₃×#204	C₂²×C₃	1	2	yes	—
85	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
86	C₃×D₃×C₈	C₂²×C₃	1	2	yes	—
87	C₉×#41	—	3	1	no	—
88	C₉×#41	—	3	4	no	—
89	C₉×#41	—	3	2	no	—
90	C₉×#41	—	6	4	no	—
91	C₉×#41	—	6	2	no	—
92	C₂×Q₈×C₉	—	2	2	no	—
93	C₂×Q₈×C₉	—	3	4	no	—
94	C₂×Q₈×C₉	—	6	2	no	—
95	C₂×Q₈×C₉	C₂×D₃	1	2	yes	—
96	C₉×Q₁₆	—	2	2	no	—
97	C₉×Q₁₆	—	2	2	no	—
98	C₉×Q₁₆	—	3	4	no	—
99	C₉×Q₁₆	—	3	1	no	—
100	C₉×Q₁₆	C₂×D₃	1	2	yes	—
101	C₉×Q₁₆	C₂×D₃	1	2	yes	—
102	C₉×SD₁₆	—	3	4	no	—
103	C₉×SD₁₆	—	3	2	no	—
104	C₉×D₈	—	3	1	no	—
105	C₉×M₁₆	—	3	1	no	—
106	C₉×M₁₆	—	3	2	no	—
107	C₂×C₈×C₉	—	2	1	no	—
108	C₂×C₈×C₉	—	3	2	no	—
109	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
110	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
111	C₂×D₃×C₉	—	2	2	no	—
112	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
113	C₃×C₄×C₉	—	2	4	no	—
114	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
115	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
116	C₉×Dic₃	—	2	2	no	—
117	C₉×Dic₃	C₂×D₄	1	2	yes	—
118	C₃×2₋¹⁺⁴	—	3	2	no	—
119	#1007	C₂×C₉	1	2	yes	complemented
120	C₃×#137	—	3	2	no	—
121	C₃×#137	—	3	4	no	—
122	C₃×#135	—	3	2	no	—
123	C₃×#135	—	3	1	no	—
124	C₂×C₃×Q₁₆	—	2	1	no	—
125	C₂×C₃×Q₁₆	—	3	2	no	—
126	C₂×C₃×Q₁₆	C₂×C₉	1	1	yes	characteristic, complemented
127	C₂×C₃×Q₁₆	C₃×D₃	1	1	yes	characteristic
128	C₃×#131	—	3	1	no	—
129	#942	C₂×C₉	1	2	yes	complemented
130	#919	C₂×C₉	1	2	yes	complemented
131	#918	C₂×C₉	1	4	yes	complemented
132	D₃×Q₁₆	C₂×C₉	1	2	yes	complemented
133	#904	C₂×C₉	1	1	yes	characteristic, complemented
134	#901	C₂×C₉	1	1	yes	characteristic, complemented
135	C₃²×Q₈	—	2	2	no	—
136	C₃²×Q₈	C₂³×C₃	1	4	yes	—
137	C₂×C₃²×C₄	—	2	2	no	—
138	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
139	C₃×#67	—	2	2	no	—
140	C₃×#67	C₃×D₄	1	2	yes	—
141	C₃×D₁₂	—	2	4	no	—
142	C₃×D₁₂	C₃×D₄	1	1	yes	characteristic
143	C₃×D₁₂	C₂³×C₃	1	2	yes	—
144	C₃×C₄×D₃	—	2	4	no	—
145	C₃×C₄×D₃	—	2	2	no	—
146	C₃×C₄×D₃	—	2	4	no	—
147	C₃×C₄×D₃	C₂³×C₃	1	2	yes	—
148	C₃×Dic₆	—	2	4	no	—
149	C₃×Dic₆	C₃×D₄	1	1	yes	characteristic
150	C₃×Dic₆	C₂³×C₃	1	2	yes	—
151	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
152	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
153	C₃×C₃⋊C₈	C₂³×C₃	1	2	yes	—
154	Q₈×C₉	—	2	2	no	—
155	Q₈×C₉	—	2	4	no	—
156	Q₈×C₉	—	3	1	no	—
157	Q₈×C₉	—	3	2	no	—
158	Q₈×C₉	—	4	2	no	—
159	Q₈×C₉	—	6	4	no	—
160	Q₈×C₉	C₂²×D₃	1	4	yes	—
161	D₄×C₉	—	3	2	no	—
162	D₄×C₉	—	3	1	no	—
163	D₄×C₉	—	3	2	no	—
164	D₄×C₉	—	6	4	no	—
165	D₄×C₉	—	6	2	no	—
166	C₂×C₄×C₉	—	2	2	no	—
167	C₂×C₄×C₉	—	2	1	no	—
168	C₂×C₄×C₉	—	3	2	no	—
169	C₂×C₄×C₉	—	4	2	no	—
170	C₂×C₄×C₉	—	6	4	no	—
171	C₂×C₄×C₉	—	6	4	no	—
172	C₂×C₄×C₉	—	6	2	no	—
173	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
174	C₈×C₉	—	2	1	no	—
175	C₈×C₉	—	2	1	no	—
176	C₈×C₉	—	3	2	no	—
177	C₈×C₉	C₂²×D₃	1	1	yes	characteristic
178	C₈×C₉	C₂²×D₃	1	1	yes	characteristic
179	#578	—	3	1	no	Sylow
180	C₂×C₃×C₉	—	2	1	no	—
181	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
182	D₃×C₉	—	2	2	no	—
183	D₃×C₉	—	4	2	no	—
184	C₃×#41	—	3	1	no	—
185	C₃×#41	—	3	4	no	—
186	C₃×#41	—	3	2	no	—
187	C₃×#41	—	6	4	no	—
188	C₃×#41	—	6	2	no	—
189	C₂×C₃×Q₈	—	2	2	no	—
190	C₂×C₃×Q₈	—	3	4	no	—
191	C₂×C₃×Q₈	—	6	2	no	—
192	C₂×C₃×Q₈	C₂²×C₉	1	2	yes	—
193	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
194	#239	—	2	2	no	—
195	#239	C₂²×C₉	1	4	yes	—
196	D₃×Q₈	—	2	2	no	—
197	D₃×Q₈	C₂²×C₉	1	4	yes	—
198	#235	—	2	4	no	—
199	#235	C₂²×C₉	1	1	yes	characteristic
200	#235	C₂²×C₉	1	2	yes	—
201	C₃×Q₁₆	—	2	2	no	—
202	C₃×Q₁₆	—	2	2	no	—
203	C₃×Q₁₆	—	3	4	no	—
204	C₃×Q₁₆	—	3	1	no	—
205	C₃×Q₁₆	C₂²×C₉	1	2	yes	—
206	C₃×Q₁₆	C₂²×C₉	1	2	yes	—
207	C₃×Q₁₆	C₂×C₃×D₃	1	2	yes	—
208	C₃×Q₁₆	C₂×C₃×D₃	1	2	yes	—
209	C₃×SD₁₆	—	3	4	no	—
210	C₃×SD₁₆	—	3	2	no	—
211	C₃×D₈	—	3	1	no	—
212	C₃×M₁₆	—	3	1	no	—
213	C₃×M₁₆	—	3	2	no	—
214	C₂×C₃×C₈	—	2	1	no	—
215	C₂×C₃×C₈	—	3	2	no	—
216	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
217	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
218	#216	C₂²×C₉	1	4	yes	—
219	#215	C₂²×C₉	1	4	yes	—
220	#208	C₂²×C₉	1	1	yes	characteristic
221	Dic₁₂	C₂²×C₉	1	1	yes	characteristic
222	D₂₄	C₂²×C₉	1	1	yes	characteristic
223	#204	C₂²×C₉	1	2	yes	—
224	ΓL(1,𝔽₂₅)	C₂²×C₉	1	2	yes	—
225	D₃×C₈	C₂²×C₉	1	2	yes	—
226	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
227	C₂×C₃×D₃	—	2	2	no	—
228	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
229	C₃²×C₄	—	2	4	no	—
230	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
231	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
232	C₃×Dic₃	—	2	2	no	—
233	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
234	C₂²×C₉	—	2	1	no	—
235	C₂²×C₉	—	3	2	no	—
236	C₂²×C₉	—	6	2	no	—
237	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
238	C₄×C₉	—	2	4	no	—
239	C₄×C₉	—	2	1	no	—
240	C₄×C₉	—	2	1	no	—
241	C₄×C₉	—	3	2	no	—
242	C₄×C₉	—	4	4	no	—
243	C₄×C₉	—	6	2	no	—
244	C₄×C₉	D₃×D₄	1	1	yes	characteristic
245	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
246	2₋¹⁺⁴	—	3	2	no	—
247	#137	—	3	2	no	—
248	#137	—	3	4	no	—
249	#135	—	3	2	no	—
250	#135	—	3	1	no	—
251	C₂×Q₁₆	—	3	2	no	—
252	C₂×Q₁₆	D₃×C₉	1	1	yes	characteristic, complemented
253	#131	—	3	1	no	—
254	C₃×C₉	#578	1	1	yes	characteristic, complemented, Sylow
255	C₃×Q₈	—	2	2	no	—
256	C₃×Q₈	—	2	2	no	—
257	C₃×Q₈	—	2	4	no	—
258	C₃×Q₈	—	3	1	no	—
259	C₃×Q₈	—	3	2	no	—
260	C₃×Q₈	—	4	2	no	—
261	C₃×Q₈	—	6	4	no	—
262	C₃×Q₈	C₂³×C₉	1	4	yes	—
263	C₃×Q₈	C₂²×C₃×D₃	1	4	yes	—
264	C₃×D₄	—	3	2	no	—
265	C₃×D₄	—	3	2	no	—
266	C₃×D₄	—	3	1	no	—
267	C₃×D₄	—	6	4	no	—
268	C₃×D₄	—	6	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	3	2	no	—
273	C₂×C₃×C₄	—	4	2	no	—
274	C₂×C₃×C₄	—	6	4	no	—
275	C₂×C₃×C₄	—	6	4	no	—
276	C₂×C₃×C₄	—	6	2	no	—
277	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
279	#67	—	2	2	no	—
280	#67	D₄×C₉	1	2	yes	—
281	D₁₂	—	2	4	no	—
282	D₁₂	D₄×C₉	1	1	yes	characteristic
283	D₁₂	C₂³×C₉	1	2	yes	—
284	C₄×D₃	—	2	4	no	—
285	C₄×D₃	—	2	2	no	—
286	C₄×D₃	—	2	4	no	—
287	C₄×D₃	C₂³×C₉	1	2	yes	—
288	Dic₆	—	2	4	no	—
289	Dic₆	D₄×C₉	1	1	yes	characteristic
290	Dic₆	C₂³×C₉	1	2	yes	—
291	C₃×C₈	—	2	1	no	—
292	C₃×C₈	—	2	1	no	—
293	C₃×C₈	—	3	2	no	—
294	C₃×C₈	C₂³×C₉	1	1	yes	characteristic
295	C₃×C₈	C₂³×C₉	1	1	yes	characteristic
296	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
297	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
298	C₃⋊C₈	C₂³×C₉	1	2	yes	—
299	C₂×C₃²	—	2	1	no	—
300	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
301	C₃×D₃	—	2	2	no	—
302	C₃×D₃	—	4	2	no	—
303	C₂×C₉	—	2	2	no	—
304	C₂×C₉	—	2	1	no	—
305	C₂×C₉	—	2	1	no	—
306	C₂×C₉	—	6	2	no	—
307	C₂×C₉	—	12	2	no	—
308	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
309	#41	—	3	1	no	—
310	#41	—	3	4	no	—
311	#41	—	3	2	no	—
312	#41	—	6	4	no	—
313	#41	—	6	2	no	—
314	C₂×Q₈	—	3	4	no	—
315	C₂×Q₈	—	6	2	no	—
316	C₂×Q₈	C₂×D₃×C₉	1	2	yes	—
317	Q₁₆	—	3	4	no	—
318	Q₁₆	—	3	1	no	—
319	Q₁₆	C₂×D₃×C₉	1	2	yes	—
320	Q₁₆	C₂×D₃×C₉	1	2	yes	—
321	SD₁₆	—	3	4	no	—
322	SD₁₆	—	3	2	no	—
323	D₈	—	3	1	no	—
324	M₁₆	—	3	1	no	—
325	M₁₆	—	3	2	no	—
326	C₂×C₈	—	3	2	no	—
327	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	3	2	no	—
330	C₂²×C₃	—	6	2	no	—
331	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
332	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
333	C₂×D₃	—	2	2	no	—
334	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	4	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	3	2	no	—
340	C₃×C₄	—	4	4	no	—
341	C₃×C₄	—	6	2	no	—
342	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
343	C₃×C₄	C₂⁴×C₉	1	1	yes	characteristic
344	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
345	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
346	Dic₃	—	2	2	no	—
347	Dic₃	C₂×D₄×C₉	1	2	yes	—
348	C₃²	C₃×#578	1	1	yes	characteristic
349	C₉	—	2	1	no	—
350	C₉	#5766	1	1	yes	characteristic, direct product factor
351	Q₈	—	2	2	no	—
352	Q₈	—	3	1	no	—
353	Q₈	—	3	2	no	—
354	Q₈	—	6	4	no	—
355	Q₈	C₂²×D₃×C₉	1	4	yes	—
356	D₄	—	3	2	no	—
357	D₄	—	3	2	no	—
358	D₄	—	3	1	no	—
359	D₄	—	6	4	no	—
360	D₄	—	6	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	3	2	no	—
363	C₂×C₄	—	6	4	no	—
364	C₂×C₄	—	6	4	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
367	C₈	—	3	2	no	—
368	C₈	C₂²×D₃×C₉	1	1	yes	characteristic
369	C₈	C₂²×D₃×C₉	1	1	yes	characteristic
370	C₂×C₃	—	2	2	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	6	2	no	—
375	C₂×C₃	—	12	2	no	—
376	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
377	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
378	D₃	—	2	2	no	—
379	D₃	—	4	2	no	—
380	C₂²	—	3	2	no	—
381	C₂²	—	6	2	no	—
382	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
383	C₄	—	2	4	no	—
384	C₄	—	3	2	no	—
385	C₄	—	6	2	no	—
386	C₄	D₃×D₄×C₉	1	1	yes	characteristic
387	C₄	C₂³×D₃×C₉	1	1	yes	characteristic
388	C₃	—	2	1	no	—
389	C₃	C₉×#578	1	1	yes	characteristic, complemented
390	C₃	C₃×#5766	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	6	2	no	—
393	C₂	—	12	2	no	—
394	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	C₂×D₃×D₄
commutator	C₃×C₄	C₂⁴×C₉
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×Q₁₆	C₂
socle	C₂×C₃²	C₂²×C₃×D₄
prime radical	C₃×#5766	C₃
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₂×C₉×Q₁₆	D₃
hypocenter	C₃	C₉×#578
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₂×C₉×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₉×#1007	C₂	semidirect
2. C₂×C₃×C₉×Q₁₆	C₂	semidirect
3. C₉×#942	C₂	semidirect
4. C₉×#919	C₂	semidirect
5. C₉×#918	C₂	semidirect
6. D₃×C₉×Q₁₆	C₂	semidirect
7. C₉×#904	C₂	semidirect
8. C₉×#901	C₂	semidirect
45. C₂×C₉×Q₁₆	D₃	semidirect
67. #5766	C₉	direct (N × H)
119. #1007	C₂×C₉	semidirect
126. C₂×C₃×Q₁₆	C₂×C₉	semidirect
129. #942	C₂×C₉	semidirect
130. #919	C₂×C₉	semidirect
131. #918	C₂×C₉	semidirect
132. D₃×Q₁₆	C₂×C₉	semidirect
133. #904	C₂×C₉	semidirect
134. #901	C₂×C₉	semidirect
252. C₂×Q₁₆	D₃×C₉	semidirect
254. C₃×C₉	#578	semidirect
350. C₉	#5766	direct (N × H)
389. C₃	C₉×#578	semidirect

Maximal subgroups

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

subgroup	index
C₉×#1007	2
C₂×C₃×C₉×Q₁₆	2
C₉×#942	2
C₉×#919	2
C₉×#918	2
D₃×C₉×Q₁₆	2
C₉×#904	2
C₉×#901	2
C₃×#5766	3
C₉×#578	3

Subgroups — C9×#5766 #13153462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5766 #13153462