Subgroups — #10589829⋊C₃ #13153332

Order 1728.

874 conjugacy classes of subgroups.

The subgroup lattice has 355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×AGL(1,ℤ/9)	C₂	1	2	yes	maximal, complemented
2	3₋¹⁺²×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#63508⋊C₃	C₂	1	2	yes	maximal, complemented
4	#63458⋊C₃	C₂	1	4	yes	maximal, complemented
5	#63455⋊C₃	C₂	1	2	yes	maximal
6	#63450⋊C₃	C₂	1	2	yes	maximal, complemented
7	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
8	C₄×3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5727	—	3	1	no	maximal
10	#10589829	C₃	1	1	yes	maximal, characteristic, complemented
11	C₂×Q₈×3₋¹⁺²	C₂²	1	2	yes	—
12	Q₈×AGL(1,ℤ/9)	—	2	8	no	—
13	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
14	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	4	yes	—
15	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	2	yes	—
16	C₂×3₋¹⁺²⋊Q₈	C₂²	1	4	yes	—
17	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
19	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
20	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
21	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	4	yes	—
22	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
23	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
24	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
25	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	4	yes	—
26	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
27	C₄×3₋¹⁺²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×D₃×Q₈	—	3	2	no	—
29	C₃²×C₄⋊Q₈	D₃	1	1	yes	characteristic
30	C₃×#946	—	3	2	no	—
31	C₃×#896	—	3	4	no	—
32	C₃×#893	—	3	2	no	—
33	C₃×#888	—	3	2	no	—
34	C₃×C₄×D₁₂	—	3	1	no	—
35	C₃×C₄×Dic₆	—	3	1	no	—
36	C₂×Q₈×D₉	C₂×C₃	1	2	yes	complemented
37	C₉×C₄⋊Q₈	—	2	1	no	—
38	C₉×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
39	#63508	C₂×C₃	1	2	yes	complemented
40	#63458	C₂×C₃	1	4	yes	complemented
41	#63455	C₂×C₃	1	2	yes	—
42	#63450	C₂×C₃	1	2	yes	complemented
43	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic
44	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂²×AGL(1,ℤ/9)	C₂³	1	2	yes	—
46	Q₈×3₋¹⁺²	—	2	4	no	—
47	C₂×C₄×3₋¹⁺²	C₂³	1	4	yes	—
48	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
49	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
50	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
51	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
52	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
53	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
54	C₄⋊AGL(1,ℤ/9)	Q₈	1	4	yes	complemented
55	C₄×AGL(1,ℤ/9)	—	2	4	no	—
56	C₄×AGL(1,ℤ/9)	—	2	8	no	—
57	3₋¹⁺²⋊Q₈	—	2	8	no	—
58	3₋¹⁺²⋊Q₈	D₄	1	4	yes	complemented
59	C₃×D₄×Q₈	—	9	1	no	—
60	#5727	—	3	1	no	—
61	C₂×C₃²×Q₈	C₂×D₃	1	2	yes	—
62	C₃×D₃×Q₈	—	6	8	no	—
63	C₂×C₃×D₁₂	—	3	1	no	—
64	C₂×C₃×C₄×D₃	—	3	4	no	—
65	C₂×C₃×C₄×D₃	—	3	2	no	—
66	C₂×C₃×Dic₆	—	3	1	no	—
67	C₂×C₃×Dic₆	—	3	4	no	—
68	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
69	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
70	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
71	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
72	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
73	C₃×C₄⋊Dic₃	—	3	1	no	—
74	C₃×C₄⋊Dic₃	—	3	1	no	—
75	C₃×Dic₃⋊C₄	—	3	4	no	—
76	C₃×Dic₃⋊C₄	—	3	2	no	—
77	C₃×C₄×Dic₃	—	3	2	no	—
78	C₂×Q₈×C₉	—	2	2	no	—
79	C₂×Q₈×C₉	C₂²×C₃	1	2	yes	—
80	Q₈×D₉	—	2	8	no	—
81	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
83	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
84	C₂×Dic₁₈	C₂²×C₃	1	4	yes	—
85	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
86	C₉×C₄⋊C₄	—	2	2	no	—
87	C₉×C₄⋊C₄	—	2	2	no	—
88	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₄²×C₉	—	2	1	no	—
91	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
92	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
93	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
94	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
95	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
96	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
97	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
98	C₄×Dic₉	C₂²×C₃	1	2	yes	—
99	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
100	C₂×AGL(1,ℤ/9)	—	2	2	no	—
101	C₂×AGL(1,ℤ/9)	—	2	2	no	—
102	C₂×AGL(1,ℤ/9)	C₂×Q₈	1	4	yes	complemented
103	C₄×3₋¹⁺²	—	2	4	no	—
104	C₄×3₋¹⁺²	—	2	1	no	—
105	C₄×3₋¹⁺²	C₂×D₄	1	2	yes	—
106	C₄×3₋¹⁺²	C₂×Q₈	1	2	yes	complemented
107	3₋¹⁺²⋊C₄	—	2	2	no	—
108	3₋¹⁺²⋊C₄	—	2	2	no	—
109	3₋¹⁺²⋊C₄	C₂×D₄	1	4	yes	—
110	C₂²×C₃×Q₈	—	9	2	no	—
111	C₂×D₃×Q₈	—	3	2	no	—
112	C₃×C₄⋊Q₈	—	3	1	no	—
113	C₃×C₄⋊Q₈	—	9	2	no	—
114	C₃×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic
115	C₃×C₂²⋊Q₈	—	9	4	no	—
116	C₃×C₂²⋊Q₈	—	9	2	no	—
117	C₃×C₄×Q₈	—	9	1	no	—
118	C₃×C₄×D₄	—	9	1	no	—
119	C₃×C₄×D₄	—	9	2	no	—
120	#946	—	3	2	no	—
121	#896	—	3	4	no	—
122	#893	—	3	2	no	—
123	#888	—	3	2	no	—
124	C₄×D₁₂	—	3	1	no	—
125	C₄×Dic₆	—	3	1	no	—
126	C₂²×C₃×D₃	—	3	2	no	—
127	C₃²×Q₈	—	2	4	no	—
128	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
130	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
132	C₂×C₃×Dic₃	—	3	2	no	—
133	C₂×C₃×Dic₃	—	3	2	no	—
134	C₂×C₃×Dic₃	—	3	2	no	—
135	C₃×D₁₂	—	3	4	no	—
136	C₃×C₄×D₃	—	6	8	no	—
137	C₃×C₄×D₃	—	6	4	no	—
138	C₃×Dic₆	—	3	4	no	—
139	C₃×Dic₆	—	6	8	no	—
140	C₂²×D₉	C₂³×C₃	1	2	yes	—
141	Q₈×C₉	—	2	4	no	—
142	Q₈×C₉	—	4	4	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	4	no	—
147	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₄×C₉	C₂³×C₃	1	4	yes	—
149	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
150	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
151	C₂×Dic₉	C₂³×C₃	1	2	yes	—
152	C₂×Dic₉	C₂³×C₃	1	2	yes	—
153	C₂×Dic₉	C₂³×C₃	1	2	yes	—
154	D₃₆	C₃×Q₈	1	4	yes	complemented
155	C₄×D₉	—	2	4	no	—
156	C₄×D₉	—	2	8	no	—
157	Dic₁₈	—	2	8	no	—
158	Dic₁₈	C₃×D₄	1	4	yes	complemented
159	D₄×Q₈	—	9	1	no	Sylow
160	C₂×3₋¹⁺²	C₂²×D₄	1	1	yes	characteristic
161	C₂×3₋¹⁺²	C₂²×Q₈	1	1	yes	characteristic
162	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
163	AGL(1,ℤ/9)	—	2	4	no	—
164	C₂×C₃×Q₈	—	3	2	no	—
165	C₂×C₃×Q₈	—	9	1	no	—
166	C₂×C₃×Q₈	—	9	4	no	—
167	C₂×C₃×Q₈	—	18	8	no	—
168	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
169	C₂×C₃×D₄	—	9	1	no	—
170	C₂²×C₃×C₄	—	9	2	no	—
171	C₂²×C₃×C₄	—	9	4	no	—
172	D₃×Q₈	—	6	8	no	—
173	C₂×D₁₂	—	3	1	no	—
174	C₂×C₄×D₃	—	3	2	no	—
175	C₂×C₄×D₃	—	3	4	no	—
176	C₂×Dic₆	—	3	1	no	—
177	C₂×Dic₆	—	3	4	no	—
178	C₃×C₄⋊C₄	—	3	2	no	—
179	C₃×C₄⋊C₄	—	3	2	no	—
180	C₃×C₄⋊C₄	—	9	2	no	—
181	C₃×C₄⋊C₄	—	9	4	no	—
182	C₃×C₄⋊C₄	—	9	1	no	—
183	C₃×C₄⋊C₄	—	9	1	no	—
184	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
185	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
186	C₃×C₂²⋊C₄	—	9	2	no	—
187	C₃×C₂²⋊C₄	—	9	4	no	—
188	C₃×C₄²	—	3	1	no	—
189	C₃×C₄²	—	9	2	no	—
190	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
191	(C₂×D₃)⋊C₄	—	3	2	no	—
192	(C₂×D₃)⋊C₄	—	3	4	no	—
193	C₄⋊Dic₃	—	3	1	no	—
194	C₄⋊Dic₃	—	3	1	no	—
195	Dic₃⋊C₄	—	3	2	no	—
196	Dic₃⋊C₄	—	3	4	no	—
197	C₄×Dic₃	—	3	2	no	—
198	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
199	C₂×C₃×D₃	—	3	4	no	—
200	C₂×C₃×D₃	—	6	2	no	—
201	C₂×C₃×D₃	—	6	2	no	—
202	C₃²×C₄	—	2	4	no	—
203	C₃²×C₄	—	2	1	no	—
204	C₃²×C₄	D₃×D₄	1	2	yes	—
205	C₃²×C₄	D₃×Q₈	1	2	yes	—
206	C₃×Dic₃	—	3	4	no	—
207	C₃×Dic₃	—	6	2	no	—
208	C₃×Dic₃	—	6	2	no	—
209	C₂²×C₉	—	2	1	no	—
210	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
211	C₂×D₉	—	2	2	no	—
212	C₂×D₉	—	2	2	no	—
213	C₂×D₉	C₂×C₃×Q₈	1	4	yes	complemented
214	C₄×C₉	—	2	2	no	—
215	C₄×C₉	—	2	4	no	—
216	C₄×C₉	—	2	1	no	—
217	C₄×C₉	—	2	2	no	—
218	C₄×C₉	—	2	2	no	—
219	C₄×C₉	—	4	4	no	—
220	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
221	C₄×C₉	C₂×C₃×Q₈	1	2	yes	complemented
222	Dic₉	—	2	2	no	—
223	Dic₉	—	2	2	no	—
224	Dic₉	C₂×C₃×D₄	1	4	yes	—
225	C₂²×Q₈	—	9	2	no	—
226	C₄⋊Q₈	—	9	2	no	—
227	C₄⋊Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
228	C₂²⋊Q₈	—	9	2	no	—
229	C₂²⋊Q₈	—	9	4	no	—
230	C₄×Q₈	—	9	1	no	—
231	C₄×D₄	—	9	2	no	—
232	C₄×D₄	—	9	1	no	—
233	3₋¹⁺²	D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₃	—	9	2	no	—
235	C₂²×D₃	—	3	2	no	—
236	C₃×Q₈	—	2	4	no	—
237	C₃×Q₈	—	6	4	no	—
238	C₃×Q₈	—	9	4	no	—
239	C₃×Q₈	—	18	8	no	—
240	C₃×D₄	—	9	4	no	—
241	C₂×C₃×C₄	—	3	1	no	—
242	C₂×C₃×C₄	—	3	1	no	—
243	C₂×C₃×C₄	—	3	1	no	—
244	C₂×C₃×C₄	—	3	4	no	—
245	C₂×C₃×C₄	—	9	2	no	—
246	C₂×C₃×C₄	—	9	2	no	—
247	C₂×C₃×C₄	—	9	2	no	—
248	C₂×C₃×C₄	—	18	4	no	—
249	C₂×C₃×C₄	—	18	8	no	—
250	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
254	C₂×Dic₃	—	3	2	no	—
255	C₂×Dic₃	—	3	2	no	—
256	C₂×Dic₃	—	3	2	no	—
257	D₁₂	—	3	4	no	—
258	C₄×D₃	—	6	8	no	—
259	C₄×D₃	—	6	4	no	—
260	Dic₆	—	3	4	no	—
261	Dic₆	—	6	8	no	—
262	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
263	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
264	C₂×C₃²	#1007	1	1	yes	characteristic
265	C₃×D₃	—	6	4	no	—
266	C₂×C₉	—	2	1	no	—
267	C₂×C₉	—	2	1	no	—
268	C₂×C₉	—	2	1	no	—
269	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
270	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
271	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
272	D₉	—	2	4	no	—
273	C₂×Q₈	—	9	1	no	—
274	C₂×Q₈	—	9	4	no	—
275	C₂×Q₈	—	18	8	no	—
276	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	2	yes	—
277	C₂×D₄	—	9	1	no	—
278	C₂²×C₄	—	9	4	no	—
279	C₂²×C₄	—	9	2	no	—
280	C₄⋊C₄	—	9	1	no	—
281	C₄⋊C₄	—	9	2	no	—
282	C₄⋊C₄	—	9	1	no	—
283	C₄⋊C₄	—	9	4	no	—
284	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
285	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
286	C₂²⋊C₄	—	9	4	no	—
287	C₂²⋊C₄	—	9	2	no	—
288	C₄²	—	9	2	no	—
289	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
290	C₂²×C₃	—	3	1	no	—
291	C₂²×C₃	—	9	4	no	—
292	C₂²×C₃	—	18	2	no	—
293	C₂²×C₃	—	18	2	no	—
294	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
295	C₂×D₃	—	3	4	no	—
296	C₂×D₃	—	6	2	no	—
297	C₂×D₃	—	6	2	no	—
298	C₃×C₄	—	2	4	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	3	2	no	—
301	C₃×C₄	—	3	2	no	—
302	C₃×C₄	—	6	4	no	—
303	C₃×C₄	—	6	1	no	—
304	C₃×C₄	—	9	4	no	—
305	C₃×C₄	—	18	2	no	—
306	C₃×C₄	—	18	2	no	—
307	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
308	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
309	Dic₃	—	3	4	no	—
310	Dic₃	—	6	2	no	—
311	Dic₃	—	6	2	no	—
312	C₃²	#5727	1	1	yes	characteristic
313	C₉	—	2	1	no	—
314	C₉	C₃×D₄×Q₈	1	1	yes	characteristic, complemented
315	C₂³	—	9	2	no	—
316	Q₈	—	2	4	no	—
317	Q₈	—	9	4	no	—
318	Q₈	—	18	8	no	—
319	D₄	—	9	4	no	—
320	C₂×C₄	—	9	2	no	—
321	C₂×C₄	—	9	2	no	—
322	C₂×C₄	—	9	2	no	—
323	C₂×C₄	—	18	8	no	—
324	C₂×C₄	—	18	4	no	—
325	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
326	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	4	yes	—
327	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
328	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
329	C₂×C₃	—	3	1	no	—
330	C₂×C₃	—	3	1	no	—
331	C₂×C₃	—	3	1	no	—
332	C₂×C₃	—	18	4	no	—
333	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
334	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
335	C₂×C₃	C₃×#1007	1	1	yes	characteristic
336	D₃	—	6	4	no	—
337	C₂²	—	9	4	no	—
338	C₂²	—	18	2	no	—
339	C₂²	—	18	2	no	—
340	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	2	1	no	—
343	C₄	—	9	4	no	—
344	C₄	—	18	2	no	—
345	C₄	—	18	2	no	—
346	C₄	D₄×AGL(1,ℤ/9)	1	2	yes	—
347	C₄	Q₈×AGL(1,ℤ/9)	1	2	yes	complemented
348	C₃	—	3	1	no	—
349	C₃	C₃×#5727	1	1	yes	characteristic
350	C₂	—	18	4	no	—
351	C₂	C₂×D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
352	C₂	C₂×Q₈×AGL(1,ℤ/9)	1	1	yes	characteristic
353	C₂	#11722630	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×AGL(1,ℤ/9)
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini, socle	C₂²×C₃	C₂³×C₃×D₃
Fitting	3₋¹⁺²×C₄⋊Q₈	C₂
prime radical	C₂×C₄⋊AGL(1,ℤ/9)	C₂²
hypercenter	C₄⋊Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×D₄×Q₈
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×AGL(1,ℤ/9)	C₂	semidirect
2. 3₋¹⁺²×C₄⋊Q₈	C₂	semidirect
3. #63508⋊C₃	C₂	semidirect
4. #63458⋊C₃	C₂	semidirect
6. #63450⋊C₃	C₂	semidirect
8. C₄×3₋¹⁺²⋊Q₈	C₂	semidirect
10. #10589829	C₃	semidirect
36. C₂×Q₈×D₉	C₂×C₃	semidirect
38. C₉×C₄⋊Q₈	C₂×C₃	semidirect
39. #63508	C₂×C₃	semidirect
40. #63458	C₂×C₃	semidirect
42. #63450	C₂×C₃	semidirect
44. C₄×Dic₁₈	C₂×C₃	semidirect
54. C₄⋊AGL(1,ℤ/9)	Q₈	semidirect
58. 3₋¹⁺²⋊Q₈	D₄	semidirect
102. C₂×AGL(1,ℤ/9)	C₂×Q₈	semidirect
106. C₄×3₋¹⁺²	C₂×Q₈	semidirect
154. D₃₆	C₃×Q₈	semidirect
158. Dic₁₈	C₃×D₄	semidirect
213. C₂×D₉	C₂×C₃×Q₈	semidirect
221. C₄×C₉	C₂×C₃×Q₈	semidirect
227. C₄⋊Q₈	AGL(1,ℤ/9)	semidirect
233. 3₋¹⁺²	D₄×Q₈	semidirect
314. C₉	C₃×D₄×Q₈	semidirect
347. C₄	Q₈×AGL(1,ℤ/9)	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×AGL(1,ℤ/9)	2
3₋¹⁺²×C₄⋊Q₈	2
#63508⋊C₃	2
#63458⋊C₃	2
#63455⋊C₃	2
#63450⋊C₃	2
C₄×C₄⋊AGL(1,ℤ/9)	2
C₄×3₋¹⁺²⋊Q₈	2
C₃×#5727	3
#10589829	3

Subgroups — #10589829⋊C3 #13153332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589829⋊C₃ #13153332