Subgroups — #10588686⋊C₃ #13142711

Order 1728.

512 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3697⋊C₃	C₂	1	1	yes	maximal, characteristic
2	3₋¹⁺²×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	#63488⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63365⋊C₃	C₂	1	4	yes	maximal, complemented
5	C₃×#5006	—	3	1	no	maximal
6	#10588686	C₃	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
8	C₂×#611⋊C₃	C₂²	1	2	yes	—
9	#3697⋊C₃	—	2	1	no	—
10	#3697⋊C₃	—	2	1	no	—
11	#3697⋊C₃	—	2	1	no	—
12	#3697⋊C₃	—	2	1	no	—
13	C₂×C₄⋊AGL(1,ℤ/9)	C₄	1	1	yes	characteristic, complemented
14	C₂×C₄×AGL(1,ℤ/9)	C₄	1	2	yes	complemented
15	C₂×3₋¹⁺²⋊Q₈	C₄	1	1	yes	characteristic, complemented
16	C₄⋊C₄×3₋¹⁺²	—	2	1	no	—
17	C₂²⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
18	C₄²×3₋¹⁺²	—	2	1	no	—
19	#3676⋊C₃	C₂²	1	2	yes	—
20	C₄⋊(3₋¹⁺²⋊C₄)	—	2	1	no	—
21	C₄×3₋¹⁺²⋊C₄	—	2	1	no	—
22	C₂×C₃×#235	—	3	1	no	—
23	C₃²×#117	D₃	1	1	yes	characteristic
24	C₃×#926	—	3	1	no	—
25	C₂×#3697	C₂×C₃	1	1	yes	characteristic
26	C₃×#806	—	3	4	no	—
27	C₉×#117	—	2	1	no	—
28	C₉×#117	C₂×C₃	1	1	yes	characteristic, complemented
29	#63488	C₂×C₃	1	1	yes	characteristic, complemented
30	#63365	C₂×C₃	1	4	yes	complemented
31	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
32	C₂²×AGL(1,ℤ/9)	C₂×C₄	1	2	yes	—
33	C₂×C₄×3₋¹⁺²	—	2	2	no	—
34	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
37	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
38	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
39	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
40	#611⋊C₃	—	2	2	no	—
41	#611⋊C₃	—	2	2	no	—
42	C₂×3₋¹⁺²⋊C₄	—	2	2	no	—
43	C₂×3₋¹⁺²⋊C₄	C₂×C₄	1	2	yes	—
44	C₄⋊AGL(1,ℤ/9)	—	2	1	no	—
45	C₄⋊AGL(1,ℤ/9)	—	2	1	no	—
46	C₄×AGL(1,ℤ/9)	—	2	2	no	—
47	C₄×AGL(1,ℤ/9)	—	2	2	no	—
48	3₋¹⁺²⋊Q₈	—	2	1	no	—
49	3₋¹⁺²⋊Q₈	—	2	1	no	—
50	C₃×#410	—	9	1	no	—
51	#5006	—	3	1	no	—
52	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
53	C₂×C₃×#67	—	3	2	no	—
54	C₃×#235	—	6	1	no	—
55	C₃×#235	—	6	1	no	—
56	C₃×#235	—	6	1	no	—
57	C₃×#235	—	6	1	no	—
58	C₂×C₃×D₁₂	—	3	1	no	—
59	C₂×C₃×C₄×D₃	—	3	2	no	—
60	C₂×C₃×Dic₆	—	3	1	no	—
61	C₃²×C₄⋊C₄	—	2	1	no	—
62	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
63	C₃²×C₄²	—	2	1	no	—
64	C₃×#217	—	3	2	no	—
65	C₃×C₄⋊Dic₃	—	6	1	no	—
66	C₃×C₄×Dic₃	—	6	1	no	—
67	C₂²×C₄×C₉	—	2	1	no	—
68	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
69	C₂×#611	C₂²×C₃	1	2	yes	—
70	#3697	—	2	1	no	—
71	#3697	—	2	1	no	—
72	#3697	—	2	1	no	—
73	#3697	—	2	1	no	—
74	C₂×D₃₆	C₃×C₄	1	1	yes	characteristic, complemented
75	C₂×C₄×D₉	C₃×C₄	1	2	yes	complemented
76	C₂×Dic₁₈	C₃×C₄	1	1	yes	characteristic, complemented
77	C₉×C₄⋊C₄	—	2	2	no	—
78	C₉×C₄⋊C₄	—	2	1	no	—
79	C₉×C₂²⋊C₄	—	2	2	no	—
80	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₄²×C₉	—	2	2	no	—
82	C₄²×C₉	—	2	1	no	—
83	#3676	C₂²×C₃	1	2	yes	—
84	C₄⋊Dic₉	—	2	1	no	—
85	C₄×Dic₉	—	2	1	no	—
86	C₂²×3₋¹⁺²	—	4	1	no	—
87	C₂²×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
88	C₂²×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
89	C₂²×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
90	C₂×AGL(1,ℤ/9)	—	2	2	no	—
91	C₂×AGL(1,ℤ/9)	—	4	2	no	—
92	C₄×3₋¹⁺²	—	4	2	no	—
93	C₄×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
94	C₄×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
95	C₄×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
96	C₄×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
97	3₋¹⁺²⋊C₄	—	2	2	no	—
98	3₋¹⁺²⋊C₄	—	4	2	no	—
99	C₂×C₃×#41	—	9	1	no	—
100	C₂×#235	—	3	1	no	—
101	C₃×#117	—	3	1	no	—
102	C₃×#117	—	9	1	no	—
103	C₃×#117	C₃×D₃	1	1	yes	characteristic
104	#926	—	3	1	no	—
105	C₃×#99	—	9	4	no	—
106	#806	—	3	4	no	—
107	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
108	C₂²×C₃×D₃	—	3	2	no	—
109	C₂×C₃²×C₄	—	2	2	no	—
110	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
112	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
113	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
114	C₂×C₃²×C₄	#67	1	1	yes	characteristic
115	C₂×C₃²×C₄	#67	1	1	yes	characteristic
116	C₃×#67	—	6	2	no	—
117	C₃×#67	—	6	2	no	—
118	C₂×C₃×Dic₃	—	3	2	no	—
119	C₂×C₃×Dic₃	—	6	2	no	—
120	C₃×D₁₂	—	6	1	no	—
121	C₃×D₁₂	—	6	1	no	—
122	C₃×C₄×D₃	—	6	2	no	—
123	C₃×C₄×D₃	—	6	2	no	—
124	C₃×Dic₆	—	6	1	no	—
125	C₃×Dic₆	—	6	1	no	—
126	C₂³×C₉	—	2	1	no	—
127	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
128	C₂²×D₉	C₂×C₃×C₄	1	2	yes	—
129	C₂×C₄×C₉	—	2	4	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
140	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
141	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
142	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
143	#611	—	2	2	no	—
144	#611	—	2	2	no	—
145	C₂×Dic₉	—	2	2	no	—
146	C₂×Dic₉	C₂×C₃×C₄	1	2	yes	—
147	D₃₆	—	2	1	no	—
148	D₃₆	—	2	1	no	—
149	C₄×D₉	—	2	2	no	—
150	C₄×D₉	—	2	2	no	—
151	Dic₁₈	—	2	1	no	—
152	Dic₁₈	—	2	1	no	—
153	#410	—	9	1	no	Sylow
154	C₂×3₋¹⁺²	—	2	1	no	—
155	C₂×3₋¹⁺²	—	2	1	no	—
156	C₂×3₋¹⁺²	—	2	1	no	—
157	C₂×3₋¹⁺²	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	AGL(1,ℤ/9)	—	4	2	no	—
159	C₃×#41	—	18	1	no	—
160	C₃×#41	—	18	1	no	—
161	C₃×#41	—	18	1	no	—
162	C₃×#41	—	18	1	no	—
163	C₂×C₃×Q₈	—	9	1	no	—
164	C₂×C₃×D₄	—	9	1	no	—
165	C₂×C₃×D₄	—	9	2	no	—
166	C₂²×C₃×C₄	—	3	1	no	—
167	C₂²×C₃×C₄	—	9	2	no	—
168	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
169	C₂×#67	—	3	2	no	—
170	#235	—	6	1	no	—
171	#235	—	6	1	no	—
172	#235	—	6	1	no	—
173	#235	—	6	1	no	—
174	C₂×D₁₂	—	3	1	no	—
175	C₂×C₄×D₃	—	3	2	no	—
176	C₂×Dic₆	—	3	1	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	—	6	1	no	—
179	C₃×C₄⋊C₄	—	18	1	no	—
180	C₃×C₂²⋊C₄	—	3	2	no	—
181	C₃×C₂²⋊C₄	—	9	2	no	—
182	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
183	C₃×C₄²	—	2	1	no	—
184	C₃×C₄²	—	6	1	no	—
185	C₃×C₄²	—	18	1	no	—
186	#217	—	3	2	no	—
187	C₄⋊Dic₃	—	6	1	no	—
188	C₄×Dic₃	—	6	1	no	—
189	C₂²×C₃²	—	4	1	no	—
190	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
191	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
192	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
193	C₂×C₃×D₃	—	6	2	no	—
194	C₂×C₃×D₃	—	12	2	no	—
195	C₃²×C₄	—	4	2	no	—
196	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
197	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
198	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
199	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
200	C₃×Dic₃	—	6	2	no	—
201	C₃×Dic₃	—	12	2	no	—
202	C₂²×C₉	—	2	1	no	—
203	C₂²×C₉	—	2	1	no	—
204	C₂²×C₉	—	2	1	no	—
205	C₂²×C₉	—	4	1	no	—
206	C₂²×C₉	—	4	2	no	—
207	C₂²×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
208	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
209	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
210	C₂×D₉	—	2	2	no	—
211	C₂×D₉	—	4	2	no	—
212	C₄×C₉	—	2	1	no	—
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	2	1	no	—
215	C₄×C₉	—	2	1	no	—
216	C₄×C₉	—	4	4	no	—
217	C₄×C₉	—	4	2	no	—
218	C₄×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
219	C₄×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
220	C₄×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
221	C₄×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
222	Dic₉	—	2	2	no	—
223	Dic₉	—	4	2	no	—
224	C₂×#41	—	9	1	no	—
225	#117	—	9	1	no	—
226	#117	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
227	#99	—	9	4	no	—
228	3₋¹⁺²	#410	1	1	yes	characteristic, complemented, Sylow
229	C₂³×C₃	—	3	1	no	—
230	C₂³×C₃	—	9	2	no	—
231	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
232	C₂²×D₃	—	3	2	no	—
233	C₃×Q₈	—	18	1	no	—
234	C₃×Q₈	—	18	1	no	—
235	C₃×D₄	—	18	1	no	—
236	C₃×D₄	—	18	1	no	—
237	C₃×D₄	—	18	2	no	—
238	C₃×D₄	—	18	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	3	1	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	1	no	—
245	C₂×C₃×C₄	—	3	1	no	—
246	C₂×C₃×C₄	—	6	2	no	—
247	C₂×C₃×C₄	—	9	2	no	—
248	C₂×C₃×C₄	—	18	2	no	—
249	C₂×C₃×C₄	—	18	2	no	—
250	C₂×C₃×C₄	—	18	2	no	—
251	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
252	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
253	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
254	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
255	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
256	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
257	#67	—	6	2	no	—
258	#67	—	6	2	no	—
259	C₂×Dic₃	—	3	2	no	—
260	C₂×Dic₃	—	6	2	no	—
261	D₁₂	—	6	1	no	—
262	D₁₂	—	6	1	no	—
263	C₄×D₃	—	6	2	no	—
264	C₄×D₃	—	6	2	no	—
265	Dic₆	—	6	1	no	—
266	Dic₆	—	6	1	no	—
267	C₂×C₃²	—	2	1	no	—
268	C₂×C₃²	—	2	1	no	—
269	C₂×C₃²	—	2	1	no	—
270	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
271	C₃×D₃	—	12	2	no	—
272	C₂×C₉	—	2	2	no	—
273	C₂×C₉	—	2	1	no	—
274	C₂×C₉	—	2	1	no	—
275	C₂×C₉	—	2	1	no	—
276	C₂×C₉	—	2	1	no	—
277	C₂×C₉	—	4	1	no	—
278	C₂×C₉	—	4	1	no	—
279	C₂×C₉	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
280	D₉	—	4	2	no	—
281	#41	—	18	1	no	—
282	#41	—	18	1	no	—
283	#41	—	18	1	no	—
284	#41	—	18	1	no	—
285	C₂×Q₈	—	9	1	no	—
286	C₂×D₄	—	9	2	no	—
287	C₂×D₄	—	9	1	no	—
288	C₂²×C₄	—	9	2	no	—
289	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	18	1	no	—
292	C₂²⋊C₄	—	9	2	no	—
293	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
294	C₄²	—	2	1	no	—
295	C₄²	—	18	1	no	—
296	C₂²×C₃	—	3	1	no	—
297	C₂²×C₃	—	3	1	no	—
298	C₂²×C₃	—	3	1	no	—
299	C₂²×C₃	—	4	1	no	—
300	C₂²×C₃	—	12	1	no	—
301	C₂²×C₃	—	18	2	no	—
302	C₂²×C₃	—	36	2	no	—
303	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
304	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
305	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
306	C₂×D₃	—	6	2	no	—
307	C₂×D₃	—	12	2	no	—
308	C₃×C₄	—	3	1	no	—
309	C₃×C₄	—	3	1	no	—
310	C₃×C₄	—	3	1	no	—
311	C₃×C₄	—	3	1	no	—
312	C₃×C₄	—	4	2	no	—
313	C₃×C₄	—	12	2	no	—
314	C₃×C₄	—	18	2	no	—
315	C₃×C₄	—	36	2	no	—
316	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
317	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
318	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
319	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
320	Dic₃	—	6	2	no	—
321	Dic₃	—	12	2	no	—
322	C₃²	#5006	1	1	yes	characteristic
323	C₉	—	2	1	no	—
324	C₉	C₃×#410	1	1	yes	characteristic, complemented
325	C₂³	—	9	2	no	—
326	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
327	Q₈	—	18	1	no	—
328	Q₈	—	18	1	no	—
329	D₄	—	18	2	no	—
330	D₄	—	18	2	no	—
331	D₄	—	18	1	no	—
332	D₄	—	18	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	9	2	no	—
335	C₂×C₄	—	18	2	no	—
336	C₂×C₄	—	18	2	no	—
337	C₂×C₄	—	18	2	no	—
338	C₂×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
339	C₂×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
340	C₂×C₄	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
341	C₂×C₄	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
342	C₂×C₄	#611⋊C₃	1	1	yes	characteristic
343	C₂×C₄	#611⋊C₃	1	1	yes	characteristic
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	3	1	no	—
348	C₂×C₃	—	6	1	no	—
349	C₂×C₃	—	6	1	no	—
350	C₂×C₃	—	6	1	no	—
351	C₂×C₃	—	36	2	no	—
352	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
353	D₃	—	12	2	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	18	2	no	—
356	C₂²	—	36	2	no	—
357	C₂²	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
358	C₂²	C₂×C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
359	C₂²	C₂×#611⋊C₃	1	1	yes	characteristic
360	C₄	—	4	2	no	—
361	C₄	—	18	2	no	—
362	C₄	—	36	2	no	—
363	C₄	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
364	C₄	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
365	C₄	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
366	C₄	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
367	C₃	—	3	1	no	—
368	C₃	C₃×#5006	1	1	yes	characteristic
369	C₂	—	2	1	no	—
370	C₂	—	2	1	no	—
371	C₂	—	2	1	no	—
372	C₂	—	36	2	no	—
373	C₂	C₂×(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	(C₂×AGL(1,ℤ/9))⋊C₄
commutator	C₂²×C₉	C₂²×C₃×C₄
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	3₋¹⁺²×#117	C₂
socle	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄
prime radical	C₂×#3697⋊C₃	C₂
cosocle	C₂³×C₉	C₂³×C₃
hypercenter	#117	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#410
LCS	G ▷ C₂²×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. 3₋¹⁺²×#117	C₂	semidirect
3. #63488⋊C₃	C₂	semidirect
4. #63365⋊C₃	C₂	semidirect
6. #10588686	C₃	semidirect
13. C₂×C₄⋊AGL(1,ℤ/9)	C₄	semidirect
14. C₂×C₄×AGL(1,ℤ/9)	C₄	semidirect
15. C₂×3₋¹⁺²⋊Q₈	C₄	semidirect
28. C₉×#117	C₂×C₃	semidirect
29. #63488	C₂×C₃	semidirect
30. #63365	C₂×C₃	semidirect
74. C₂×D₃₆	C₃×C₄	semidirect
75. C₂×C₄×D₉	C₃×C₄	semidirect
76. C₂×Dic₁₈	C₃×C₄	semidirect
226. #117	AGL(1,ℤ/9)	semidirect
228. 3₋¹⁺²	#410	semidirect
324. C₉	C₃×#410	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3697⋊C₃	2
3₋¹⁺²×#117	2
#63488⋊C₃	2
#63365⋊C₃	2
C₃×#5006	3
#10588686	3

Subgroups — #10588686⋊C3 #13142711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588686⋊C₃ #13142711