Subgroups — #10589687⋊C₃ #13152746

Order 1728.

743 conjugacy classes of subgroups.

The subgroup lattice has 352 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	#63509⋊C₃	C₂	1	2	yes	maximal, complemented
3	#63456⋊C₃	C₂	1	4	yes	maximal, complemented
4	#63455⋊C₃	C₂	1	2	yes	maximal, complemented
5	#63437⋊C₃	C₂	1	2	yes	maximal, complemented
6	#11721394	C₂	1	1	yes	maximal, characteristic
7	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	2	yes	maximal, complemented
8	C₄×3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5585	—	3	1	no	maximal
10	#10589687	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	2	yes	—
13	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	2	yes	—
14	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	2	yes	—
15	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	4	yes	—
16	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
19	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
20	C₄²×3₋¹⁺²	C₂²	1	2	yes	—
21	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	4	yes	—
22	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	4	yes	—
23	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	4	yes	—
24	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
25	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
26	C₄×3₋¹⁺²⋊C₄	C₂²	1	2	yes	—
27	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic
28	C₃×#947	—	3	2	no	—
29	C₃×#894	—	3	4	no	—
30	C₃×#893	—	3	2	no	—
31	C₃×#875	—	3	2	no	—
32	C₃×#874	—	3	1	no	—
33	C₃×C₄×D₁₂	—	3	2	no	—
34	C₃×C₄×Dic₆	—	3	1	no	—
35	C₄×Q₈×C₉	—	2	1	no	—
36	C₄×Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
37	#63509	C₂×C₃	1	2	yes	complemented
38	#63456	C₂×C₃	1	4	yes	complemented
39	#63455	C₂×C₃	1	2	yes	complemented
40	#63437	C₂×C₃	1	2	yes	complemented
41	#63436	C₂×C₃	1	1	yes	characteristic
42	C₄×D₃₆	C₂×C₃	1	2	yes	complemented
43	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×AGL(1,ℤ/9)	C₂³	1	4	yes	—
45	Q₈×3₋¹⁺²	—	2	2	no	—
46	C₂×C₄×3₋¹⁺²	C₂³	1	2	yes	—
47	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
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	2	yes	—
52	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
53	C₄⋊AGL(1,ℤ/9)	—	2	4	no	—
54	C₄⋊AGL(1,ℤ/9)	—	2	4	no	—
55	C₄⋊AGL(1,ℤ/9)	—	4	2	no	—
56	C₄×AGL(1,ℤ/9)	—	4	4	no	—
57	3₋¹⁺²⋊Q₈	—	2	2	no	—
58	C₃×#559	—	9	1	no	—
59	#5585	—	3	1	no	—
60	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
61	C₂×C₃×D₁₂	—	3	2	no	—
62	C₂×C₃×D₁₂	—	3	2	no	—
63	C₂×C₃×D₁₂	—	3	2	no	—
64	C₂×C₃×C₄×D₃	—	3	4	no	—
65	C₂×C₃×Dic₆	—	3	1	no	—
66	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
67	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
68	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
69	C₃²×C₄²	C₂×D₃	1	2	yes	—
70	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
71	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
72	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
73	C₃×C₄⋊Dic₃	—	3	1	no	—
74	C₃×Dic₃⋊C₄	—	3	2	no	—
75	C₃×C₄×Dic₃	—	3	2	no	—
76	C₂×Q₈×C₉	—	2	1	no	—
77	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
78	C₂×D₃₆	C₂²×C₃	1	2	yes	—
79	C₂×D₃₆	C₂²×C₃	1	2	yes	—
80	C₂×D₃₆	C₂²×C₃	1	2	yes	—
81	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
82	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
83	C₉×C₄⋊C₄	—	2	1	no	—
84	C₉×C₄⋊C₄	—	2	2	no	—
85	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₄²×C₉	—	2	1	no	—
88	C₄²×C₉	—	2	2	no	—
89	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
90	C₄²×C₉	C₂²×C₃	1	2	yes	—
91	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
92	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
93	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
94	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
95	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
96	C₄×Dic₉	C₂²×C₃	1	2	yes	—
97	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
98	C₂×AGL(1,ℤ/9)	—	2	4	no	—
99	C₂×AGL(1,ℤ/9)	—	2	4	no	—
100	C₂×AGL(1,ℤ/9)	—	2	4	no	—
101	C₄×3₋¹⁺²	—	2	2	no	—
102	C₄×3₋¹⁺²	—	2	2	no	—
103	C₄×3₋¹⁺²	—	2	1	no	—
104	C₄×3₋¹⁺²	#41	1	2	yes	—
105	C₄×3₋¹⁺²	#41	1	2	yes	—
106	3₋¹⁺²⋊C₄	—	2	2	no	—
107	3₋¹⁺²⋊C₄	—	2	2	no	—
108	C₃×#127	—	9	1	no	—
109	C₃×#124	—	9	2	no	—
110	C₃×#124	—	9	2	no	—
111	C₃×#123	—	9	4	no	—
112	C₃×C₄×Q₈	—	3	1	no	—
113	C₃×C₄×Q₈	—	9	1	no	—
114	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
115	C₃×C₄×D₄	—	9	2	no	—
116	C₃×C₄×D₄	—	9	2	no	—
117	#947	—	3	2	no	—
118	#894	—	3	4	no	—
119	#893	—	3	2	no	—
120	#875	—	3	2	no	—
121	#874	—	3	1	no	—
122	C₄×D₁₂	—	3	2	no	—
123	C₄×Dic₆	—	3	1	no	—
124	C₂²×C₃×D₃	—	3	4	no	—
125	C₃²×Q₈	—	2	2	no	—
126	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
128	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
129	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
131	C₂×C₃×Dic₃	—	3	2	no	—
132	C₂×C₃×Dic₃	—	3	2	no	—
133	C₃×D₁₂	—	6	4	no	—
134	C₃×D₁₂	—	6	4	no	—
135	C₃×D₁₂	—	12	2	no	—
136	C₃×C₄×D₃	—	12	4	no	—
137	C₃×Dic₆	—	6	2	no	—
138	C₂²×D₉	C₂³×C₃	1	4	yes	—
139	Q₈×C₉	—	2	4	no	—
140	Q₈×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	—	2	1	no	—
145	C₂×C₄×C₉	—	2	2	no	—
146	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
148	C₂×C₄×C₉	C₂³×C₃	1	2	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	D₃₆	—	2	4	no	—
154	D₃₆	—	2	4	no	—
155	D₃₆	—	4	2	no	—
156	C₄×D₉	—	4	4	no	—
157	Dic₁₈	—	2	2	no	—
158	#559	—	9	1	no	Sylow
159	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
160	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
161	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
162	AGL(1,ℤ/9)	—	4	4	no	—
163	C₂×C₃×Q₈	—	3	1	no	—
164	C₂×C₃×Q₈	—	9	1	no	—
165	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
166	C₂×C₃×D₄	—	9	2	no	—
167	C₂×C₃×D₄	—	9	2	no	—
168	C₂×C₃×D₄	—	9	2	no	—
169	C₂²×C₃×C₄	—	9	4	no	—
170	C₂×D₁₂	—	3	2	no	—
171	C₂×D₁₂	—	3	2	no	—
172	C₂×D₁₂	—	3	2	no	—
173	C₂×C₄×D₃	—	3	4	no	—
174	C₂×Dic₆	—	3	1	no	—
175	C₃×C₄⋊C₄	—	3	1	no	—
176	C₃×C₄⋊C₄	—	3	2	no	—
177	C₃×C₄⋊C₄	—	9	2	no	—
178	C₃×C₄⋊C₄	—	9	1	no	—
179	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
181	C₃×C₂²⋊C₄	—	9	4	no	—
182	C₃×C₂²⋊C₄	—	9	4	no	—
183	C₃×C₂²⋊C₄	—	9	4	no	—
184	C₃×C₄²	—	3	2	no	—
185	C₃×C₄²	—	3	1	no	—
186	C₃×C₄²	—	9	2	no	—
187	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
188	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
189	(C₂×D₃)⋊C₄	—	3	4	no	—
190	(C₂×D₃)⋊C₄	—	3	4	no	—
191	(C₂×D₃)⋊C₄	—	3	4	no	—
192	C₄⋊Dic₃	—	3	1	no	—
193	Dic₃⋊C₄	—	3	2	no	—
194	C₄×Dic₃	—	3	2	no	—
195	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
196	C₂×C₃×D₃	—	6	4	no	—
197	C₂×C₃×D₃	—	6	4	no	—
198	C₂×C₃×D₃	—	6	4	no	—
199	C₃²×C₄	—	2	2	no	—
200	C₃²×C₄	—	2	2	no	—
201	C₃²×C₄	—	2	1	no	—
202	C₃²×C₄	#235	1	2	yes	—
203	C₃²×C₄	#239	1	2	yes	—
204	C₃×Dic₃	—	6	2	no	—
205	C₃×Dic₃	—	6	2	no	—
206	C₂²×C₉	—	2	1	no	—
207	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
208	C₂×D₉	—	2	4	no	—
209	C₂×D₉	—	2	4	no	—
210	C₂×D₉	—	2	4	no	—
211	C₄×C₉	—	2	4	no	—
212	C₄×C₉	—	2	2	no	—
213	C₄×C₉	—	2	2	no	—
214	C₄×C₉	—	2	1	no	—
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	2	2	no	—
217	C₄×C₉	—	4	2	no	—
218	C₄×C₉	—	4	1	no	—
219	C₄×C₉	C₃×#41	1	2	yes	—
220	C₄×C₉	C₃×#41	1	2	yes	—
221	Dic₉	—	2	2	no	—
222	Dic₉	—	2	2	no	—
223	#127	—	9	1	no	—
224	#124	—	9	2	no	—
225	#124	—	9	2	no	—
226	#123	—	9	4	no	—
227	C₄×Q₈	—	9	1	no	—
228	C₄×Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
229	C₄×D₄	—	9	2	no	—
230	C₄×D₄	—	9	2	no	—
231	3₋¹⁺²	#559	1	1	yes	characteristic, complemented, Sylow
232	C₂³×C₃	—	9	4	no	—
233	C₂²×D₃	—	3	4	no	—
234	C₃×Q₈	—	2	2	no	—
235	C₃×Q₈	—	6	2	no	—
236	C₃×Q₈	—	18	2	no	—
237	C₃×D₄	—	18	4	no	—
238	C₃×D₄	—	18	4	no	—
239	C₃×D₄	—	36	2	no	—
240	C₂×C₃×C₄	—	3	1	no	—
241	C₂×C₃×C₄	—	3	1	no	—
242	C₂×C₃×C₄	—	3	2	no	—
243	C₂×C₃×C₄	—	3	2	no	—
244	C₂×C₃×C₄	—	3	1	no	—
245	C₂×C₃×C₄	—	9	2	no	—
246	C₂×C₃×C₄	—	9	2	no	—
247	C₂×C₃×C₄	—	36	4	no	—
248	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
250	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
253	C₂×Dic₃	—	3	2	no	—
254	C₂×Dic₃	—	3	2	no	—
255	D₁₂	—	6	4	no	—
256	D₁₂	—	6	4	no	—
257	D₁₂	—	12	2	no	—
258	C₄×D₃	—	12	4	no	—
259	Dic₆	—	6	2	no	—
260	C₂×C₃²	C₂×#235	1	1	yes	characteristic
261	C₂×C₃²	C₂×#239	1	1	yes	characteristic
262	C₂×C₃²	#1009	1	1	yes	characteristic
263	C₃×D₃	—	12	4	no	—
264	C₂×C₉	—	2	1	no	—
265	C₂×C₉	—	2	1	no	—
266	C₂×C₉	—	2	1	no	—
267	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
268	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
269	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
270	D₉	—	4	4	no	—
271	C₂×Q₈	—	9	1	no	—
272	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
273	C₂×D₄	—	9	2	no	—
274	C₂×D₄	—	9	2	no	—
275	C₂×D₄	—	9	2	no	—
276	C₂²×C₄	—	9	4	no	—
277	C₄⋊C₄	—	9	1	no	—
278	C₄⋊C₄	—	9	2	no	—
279	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
280	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
281	C₂²⋊C₄	—	9	4	no	—
282	C₂²⋊C₄	—	9	4	no	—
283	C₂²⋊C₄	—	9	4	no	—
284	C₄²	—	9	2	no	—
285	C₄²	C₂×AGL(1,ℤ/9)	1	2	yes	—
286	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
287	C₂²×C₃	—	3	1	no	—
288	C₂²×C₃	—	18	4	no	—
289	C₂²×C₃	—	18	4	no	—
290	C₂²×C₃	—	18	4	no	—
291	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
292	C₂×D₃	—	6	4	no	—
293	C₂×D₃	—	6	4	no	—
294	C₂×D₃	—	6	4	no	—
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	—	2	2	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	3	2	no	—
299	C₃×C₄	—	3	2	no	—
300	C₃×C₄	—	6	2	no	—
301	C₃×C₄	—	6	1	no	—
302	C₃×C₄	—	6	2	no	—
303	C₃×C₄	—	18	2	no	—
304	C₃×C₄	—	18	2	no	—
305	C₃×C₄	C₃×#235	1	2	yes	—
306	C₃×C₄	C₃×#239	1	2	yes	—
307	Dic₃	—	6	2	no	—
308	Dic₃	—	6	2	no	—
309	C₃²	#5585	1	1	yes	characteristic
310	C₉	—	2	1	no	—
311	C₉	C₃×#559	1	1	yes	characteristic, complemented
312	C₂³	—	9	4	no	—
313	Q₈	—	2	2	no	—
314	Q₈	—	18	2	no	—
315	D₄	—	18	4	no	—
316	D₄	—	18	4	no	—
317	D₄	—	36	2	no	—
318	C₂×C₄	—	9	2	no	—
319	C₂×C₄	—	9	2	no	—
320	C₂×C₄	—	36	4	no	—
321	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
322	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
323	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
324	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
325	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
326	C₂×C₃	—	3	1	no	—
327	C₂×C₃	—	3	1	no	—
328	C₂×C₃	—	3	1	no	—
329	C₂×C₃	—	36	4	no	—
330	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
331	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
332	C₂×C₃	C₃×#1009	1	1	yes	characteristic
333	D₃	—	12	4	no	—
334	C₂²	—	18	4	no	—
335	C₂²	—	18	4	no	—
336	C₂²	—	18	4	no	—
337	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
338	C₄	—	2	2	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	1	no	—
341	C₄	—	18	2	no	—
342	C₄	—	18	2	no	—
343	C₄	#3697⋊C₃	1	2	yes	—
344	C₄	#88724	1	2	yes	—
345	C₃	—	3	1	no	—
346	C₃	C₃×#5585	1	1	yes	characteristic
347	C₂	—	36	4	no	—
348	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
349	C₂	C₂×#88724	1	1	yes	characteristic
350	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	#11721394	C₂
hypercenter	C₄×Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#559
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. #63509⋊C₃	C₂	semidirect
3. #63456⋊C₃	C₂	semidirect
4. #63455⋊C₃	C₂	semidirect
5. #63437⋊C₃	C₂	semidirect
7. C₄×C₄⋊AGL(1,ℤ/9)	C₂	semidirect
8. C₄×3₋¹⁺²⋊Q₈	C₂	semidirect
10. #10589687	C₃	semidirect
36. C₄×Q₈×C₉	C₂×C₃	semidirect
37. #63509	C₂×C₃	semidirect
38. #63456	C₂×C₃	semidirect
39. #63455	C₂×C₃	semidirect
40. #63437	C₂×C₃	semidirect
42. C₄×D₃₆	C₂×C₃	semidirect
43. C₄×Dic₁₈	C₂×C₃	semidirect
228. C₄×Q₈	AGL(1,ℤ/9)	semidirect
231. 3₋¹⁺²	#559	semidirect
311. C₉	C₃×#559	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
#63509⋊C₃	2
#63456⋊C₃	2
#63455⋊C₃	2
#63437⋊C₃	2
#11721394	2
C₄×C₄⋊AGL(1,ℤ/9)	2
C₄×3₋¹⁺²⋊Q₈	2
C₃×#5585	3
#10589687	3

Subgroups — #10589687⋊C3 #13152746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589687⋊C₃ #13152746