Subgroups — #10589681⋊C₃ #13152740

Order 1728.

719 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	#63508⋊C₃	C₂	1	2	yes	maximal, complemented
3	#63458⋊C₃	C₂	1	4	yes	maximal, complemented
4	C₄⋊C₄×AGL(1,ℤ/9)	C₂	1	2	yes	maximal, complemented
5	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
6	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	2	yes	maximal
7	#63432⋊C₃	C₂	1	2	yes	maximal, complemented
8	#63431⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5579	—	3	1	no	maximal
10	#10589681	C₃	1	1	yes	maximal, characteristic, complemented
11	C₂×Q₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
13	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	2	yes	—
14	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	4	yes	—
15	C₂×3₋¹⁺²⋊Q₈	C₂²	1	2	yes	—
16	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
18	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
19	C₄²×3₋¹⁺²	C₂²	1	2	yes	—
20	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
21	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	4	yes	—
22	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
23	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
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	4	yes	—
27	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic
28	C₃×#946	—	3	2	no	—
29	C₃×#896	—	3	4	no	—
30	C₃×D₃×C₄⋊C₄	—	3	2	no	—
31	C₃×C₄×D₁₂	—	3	2	no	—
32	C₃×C₄×D₁₂	—	3	1	no	—
33	C₃×#870	—	3	2	no	—
34	C₃×#869	—	3	1	no	—
35	C₄×Q₈×C₉	—	2	1	no	—
36	C₄×Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
37	#63508	C₂×C₃	1	2	yes	complemented
38	#63458	C₂×C₃	1	4	yes	complemented
39	C₄⋊C₄×D₉	C₂×C₃	1	2	yes	complemented
40	C₄×D₃₆	C₂×C₃	1	2	yes	—
41	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic
42	#63432	C₂×C₃	1	2	yes	complemented
43	#63431	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×AGL(1,ℤ/9)	C₂³	1	2	yes	—
45	Q₈×3₋¹⁺²	—	2	2	no	—
46	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
47	C₂×C₄×3₋¹⁺²	C₂³	1	2	yes	—
48	C₂×C₄×3₋¹⁺²	C₂³	1	2	yes	—
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	4	yes	—
52	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
53	C₄⋊AGL(1,ℤ/9)	Q₈	1	4	yes	complemented
54	C₄×AGL(1,ℤ/9)	—	2	4	no	—
55	C₄×AGL(1,ℤ/9)	—	4	4	no	—
56	3₋¹⁺²⋊Q₈	—	4	2	no	—
57	C₃×#554	—	9	1	no	—
58	#5579	—	3	1	no	—
59	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
60	C₂×C₃×D₁₂	—	3	1	no	—
61	C₂×C₃×C₄×D₃	—	3	2	no	—
62	C₂×C₃×C₄×D₃	—	3	4	no	—
63	C₂×C₃×Dic₆	—	3	2	no	—
64	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
65	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
66	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
67	C₃²×C₄²	C₂×D₃	1	2	yes	—
68	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
69	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
70	C₃×C₄⋊Dic₃	—	3	2	no	—
71	C₃×C₄⋊Dic₃	—	3	2	no	—
72	C₃×C₄⋊Dic₃	—	3	1	no	—
73	C₃×Dic₃⋊C₄	—	3	4	no	—
74	C₃×Dic₃⋊C₄	—	3	4	no	—
75	C₂×Q₈×C₉	—	2	1	no	—
76	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
77	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
79	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
80	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
81	C₉×C₄⋊C₄	—	2	1	no	—
82	C₉×C₄⋊C₄	—	2	2	no	—
83	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₄²×C₉	—	2	1	no	—
86	C₄²×C₉	—	2	2	no	—
87	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
88	C₄²×C₉	C₂²×C₃	1	2	yes	—
89	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
90	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
91	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
92	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
93	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
94	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
95	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
96	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
97	C₂×AGL(1,ℤ/9)	—	2	2	no	—
98	C₂×AGL(1,ℤ/9)	—	2	2	no	—
99	C₂×AGL(1,ℤ/9)	C₂×Q₈	1	4	yes	—
100	C₄×3₋¹⁺²	—	2	2	no	—
101	C₄×3₋¹⁺²	—	2	1	no	—
102	C₄×3₋¹⁺²	—	2	2	no	—
103	C₄×3₋¹⁺²	C₂×Q₈	1	2	yes	—
104	C₄×3₋¹⁺²	#41	1	2	yes	—
105	3₋¹⁺²⋊C₄	—	2	2	no	—
106	3₋¹⁺²⋊C₄	—	2	4	no	—
107	C₃×C₄⋊Q₈	—	9	1	no	—
108	C₃×#125	—	9	2	no	—
109	C₃×C₂²⋊Q₈	—	9	4	no	—
110	C₃×C₂²⋊Q₈	—	9	2	no	—
111	C₃×C₄×Q₈	—	3	1	no	—
112	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
113	C₃×C₄×D₄	—	9	2	no	—
114	C₃×C₄×D₄	—	9	1	no	—
115	C₂×C₃×C₄⋊C₄	—	9	2	no	—
116	#946	—	3	2	no	—
117	#896	—	3	4	no	—
118	D₃×C₄⋊C₄	—	3	2	no	—
119	C₄×D₁₂	—	3	2	no	—
120	C₄×D₁₂	—	3	1	no	—
121	#870	—	3	2	no	—
122	#869	—	3	1	no	—
123	C₂²×C₃×D₃	—	3	2	no	—
124	C₃²×Q₈	—	2	2	no	—
125	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
126	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
127	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
130	C₂×C₃×Dic₃	—	3	2	no	—
131	C₂×C₃×Dic₃	—	3	4	no	—
132	C₃×D₁₂	—	3	4	no	—
133	C₃×C₄×D₃	—	6	4	no	—
134	C₃×C₄×D₃	—	12	4	no	—
135	C₃×Dic₆	—	12	2	no	—
136	C₂²×D₉	C₂³×C₃	1	2	yes	—
137	Q₈×C₉	—	2	4	no	—
138	Q₈×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	2	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
145	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
146	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
149	C₂×Dic₉	C₂³×C₃	1	2	yes	—
150	C₂×Dic₉	C₂³×C₃	1	4	yes	—
151	D₃₆	C₃×Q₈	1	4	yes	complemented
152	C₄×D₉	—	2	4	no	—
153	C₄×D₉	—	4	4	no	—
154	Dic₁₈	—	4	2	no	—
155	#554	—	9	1	no	Sylow
156	C₂×3₋¹⁺²	C₂²×Q₈	1	1	yes	characteristic
157	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
158	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
159	AGL(1,ℤ/9)	—	2	4	no	—
160	C₂×C₃×Q₈	—	3	1	no	—
161	C₂×C₃×Q₈	—	9	2	no	—
162	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
163	C₂×C₃×D₄	—	9	1	no	—
164	C₂²×C₃×C₄	—	9	2	no	—
165	C₂²×C₃×C₄	—	9	4	no	—
166	C₂×D₁₂	—	3	1	no	—
167	C₂×C₄×D₃	—	3	2	no	—
168	C₂×C₄×D₃	—	3	4	no	—
169	C₂×Dic₆	—	3	2	no	—
170	C₃×C₄⋊C₄	—	3	1	no	—
171	C₃×C₄⋊C₄	—	3	2	no	—
172	C₃×C₄⋊C₄	—	9	4	no	—
173	C₃×C₄⋊C₄	—	9	4	no	—
174	C₃×C₄⋊C₄	—	9	2	no	—
175	C₃×C₄⋊C₄	—	9	1	no	—
176	C₃×C₄⋊C₄	—	9	2	no	—
177	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
178	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
179	C₃×C₂²⋊C₄	—	9	2	no	—
180	C₃×C₂²⋊C₄	—	9	4	no	—
181	C₃×C₄²	—	3	2	no	—
182	C₃×C₄²	—	3	1	no	—
183	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
184	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
185	(C₂×D₃)⋊C₄	—	3	2	no	—
186	(C₂×D₃)⋊C₄	—	3	4	no	—
187	C₄⋊Dic₃	—	3	2	no	—
188	C₄⋊Dic₃	—	3	2	no	—
189	C₄⋊Dic₃	—	3	1	no	—
190	Dic₃⋊C₄	—	3	4	no	—
191	Dic₃⋊C₄	—	3	4	no	—
192	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
193	C₂×C₃×D₃	—	3	4	no	—
194	C₂×C₃×D₃	—	6	2	no	—
195	C₂×C₃×D₃	—	6	2	no	—
196	C₃²×C₄	—	2	2	no	—
197	C₃²×C₄	—	2	1	no	—
198	C₃²×C₄	—	2	2	no	—
199	C₃²×C₄	#235	1	2	yes	—
200	C₃²×C₄	D₃×Q₈	1	2	yes	—
201	C₃×Dic₃	—	6	2	no	—
202	C₃×Dic₃	—	6	4	no	—
203	C₂²×C₉	—	2	1	no	—
204	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
205	C₂×D₉	—	2	2	no	—
206	C₂×D₉	—	2	2	no	—
207	C₂×D₉	C₂×C₃×Q₈	1	4	yes	—
208	C₄×C₉	—	2	4	no	—
209	C₄×C₉	—	2	2	no	—
210	C₄×C₉	—	2	1	no	—
211	C₄×C₉	—	2	2	no	—
212	C₄×C₉	—	2	2	no	—
213	C₄×C₉	—	2	2	no	—
214	C₄×C₉	—	4	1	no	—
215	C₄×C₉	—	4	2	no	—
216	C₄×C₉	C₂×C₃×Q₈	1	2	yes	—
217	C₄×C₉	C₃×#41	1	2	yes	—
218	Dic₉	—	2	2	no	—
219	Dic₉	—	2	4	no	—
220	C₄⋊Q₈	—	9	1	no	—
221	#125	—	9	2	no	—
222	C₂²⋊Q₈	—	9	2	no	—
223	C₂²⋊Q₈	—	9	4	no	—
224	C₄×Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
225	C₄×D₄	—	9	2	no	—
226	C₄×D₄	—	9	1	no	—
227	C₂×C₄⋊C₄	—	9	2	no	—
228	3₋¹⁺²	#554	1	1	yes	characteristic, complemented, Sylow
229	C₂³×C₃	—	9	2	no	—
230	C₂²×D₃	—	3	2	no	—
231	C₃×Q₈	—	2	2	no	—
232	C₃×Q₈	—	6	2	no	—
233	C₃×Q₈	—	36	2	no	—
234	C₃×D₄	—	9	4	no	—
235	C₂×C₃×C₄	—	3	1	no	—
236	C₂×C₃×C₄	—	3	1	no	—
237	C₂×C₃×C₄	—	3	1	no	—
238	C₂×C₃×C₄	—	3	2	no	—
239	C₂×C₃×C₄	—	3	2	no	—
240	C₂×C₃×C₄	—	9	2	no	—
241	C₂×C₃×C₄	—	9	4	no	—
242	C₂×C₃×C₄	—	18	4	no	—
243	C₂×C₃×C₄	—	36	4	no	—
244	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
245	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
246	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
249	C₂×Dic₃	—	3	2	no	—
250	C₂×Dic₃	—	3	4	no	—
251	D₁₂	—	3	4	no	—
252	C₄×D₃	—	6	4	no	—
253	C₄×D₃	—	12	4	no	—
254	Dic₆	—	12	2	no	—
255	C₂×C₃²	C₂×#235	1	1	yes	characteristic
256	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
257	C₂×C₃²	#1009	1	1	yes	characteristic
258	C₃×D₃	—	6	4	no	—
259	C₂×C₉	—	2	1	no	—
260	C₂×C₉	—	2	1	no	—
261	C₂×C₉	—	2	1	no	—
262	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
263	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
264	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
265	D₉	—	2	4	no	—
266	C₂×Q₈	—	9	2	no	—
267	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
268	C₂×D₄	—	9	1	no	—
269	C₂²×C₄	—	9	2	no	—
270	C₂²×C₄	—	9	4	no	—
271	C₄⋊C₄	—	9	4	no	—
272	C₄⋊C₄	—	9	2	no	—
273	C₄⋊C₄	—	9	1	no	—
274	C₄⋊C₄	—	9	2	no	—
275	C₄⋊C₄	—	9	4	no	—
276	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
277	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
278	C₂²⋊C₄	—	9	2	no	—
279	C₂²⋊C₄	—	9	4	no	—
280	C₄²	C₂×AGL(1,ℤ/9)	1	2	yes	—
281	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
282	C₂²×C₃	—	3	1	no	—
283	C₂²×C₃	—	9	4	no	—
284	C₂²×C₃	—	18	2	no	—
285	C₂²×C₃	—	18	2	no	—
286	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
287	C₂×D₃	—	3	4	no	—
288	C₂×D₃	—	6	2	no	—
289	C₂×D₃	—	6	2	no	—
290	C₃×C₄	—	2	2	no	—
291	C₃×C₄	—	2	1	no	—
292	C₃×C₄	—	2	2	no	—
293	C₃×C₄	—	3	2	no	—
294	C₃×C₄	—	3	2	no	—
295	C₃×C₄	—	6	2	no	—
296	C₃×C₄	—	6	2	no	—
297	C₃×C₄	—	6	1	no	—
298	C₃×C₄	—	18	2	no	—
299	C₃×C₄	—	18	4	no	—
300	C₃×C₄	C₃×#235	1	2	yes	—
301	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
302	Dic₃	—	6	2	no	—
303	Dic₃	—	6	4	no	—
304	C₃²	#5579	1	1	yes	characteristic
305	C₉	—	2	1	no	—
306	C₉	C₃×#554	1	1	yes	characteristic, complemented
307	C₂³	—	9	2	no	—
308	Q₈	—	2	2	no	—
309	Q₈	—	36	2	no	—
310	D₄	—	9	4	no	—
311	C₂×C₄	—	9	2	no	—
312	C₂×C₄	—	9	4	no	—
313	C₂×C₄	—	18	4	no	—
314	C₂×C₄	—	36	4	no	—
315	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
316	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
317	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
318	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
319	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
320	C₂×C₃	—	3	1	no	—
321	C₂×C₃	—	3	1	no	—
322	C₂×C₃	—	3	1	no	—
323	C₂×C₃	—	18	4	no	—
324	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
325	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
326	C₂×C₃	C₃×#1009	1	1	yes	characteristic
327	D₃	—	6	4	no	—
328	C₂²	—	9	4	no	—
329	C₂²	—	18	2	no	—
330	C₂²	—	18	2	no	—
331	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
332	C₄	—	2	2	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	1	no	—
335	C₄	—	18	2	no	—
336	C₄	—	18	4	no	—
337	C₄	#3697⋊C₃	1	2	yes	—
338	C₄	Q₈×AGL(1,ℤ/9)	1	2	yes	—
339	C₃	—	3	1	no	—
340	C₃	C₃×#5579	1	1	yes	characteristic
341	C₂	—	18	4	no	—
342	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
343	C₂	C₂×Q₈×AGL(1,ℤ/9)	1	1	yes	characteristic
344	C₂	#11722641	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	C₄×Q₈×3₋¹⁺²	C₂
prime radical	C₂×C₄⋊AGL(1,ℤ/9)	C₂²
hypercenter	C₄×Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#554
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. C₄×Q₈×3₋¹⁺²	C₂	semidirect
2. #63508⋊C₃	C₂	semidirect
3. #63458⋊C₃	C₂	semidirect
4. C₄⋊C₄×AGL(1,ℤ/9)	C₂	semidirect
7. #63432⋊C₃	C₂	semidirect
8. #63431⋊C₃	C₂	semidirect
10. #10589681	C₃	semidirect
36. C₄×Q₈×C₉	C₂×C₃	semidirect
37. #63508	C₂×C₃	semidirect
38. #63458	C₂×C₃	semidirect
39. C₄⋊C₄×D₉	C₂×C₃	semidirect
42. #63432	C₂×C₃	semidirect
43. #63431	C₂×C₃	semidirect
53. C₄⋊AGL(1,ℤ/9)	Q₈	semidirect
151. D₃₆	C₃×Q₈	semidirect
224. C₄×Q₈	AGL(1,ℤ/9)	semidirect
228. 3₋¹⁺²	#554	semidirect
306. C₉	C₃×#554	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×3₋¹⁺²	2
#63508⋊C₃	2
#63458⋊C₃	2
C₄⋊C₄×AGL(1,ℤ/9)	2
C₄×C₄⋊AGL(1,ℤ/9)	2
#63432⋊C₃	2
#63431⋊C₃	2
C₃×#5579	3
#10589681	3

Subgroups — #10589681⋊C3 #13152740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589681⋊C₃ #13152740