Subgroups — #10588814⋊C₃ #13143238

Order 1728.

484 conjugacy classes of subgroups.

The subgroup lattice has 368 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	C₂×M₁₆×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#3667⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63383⋊C₃	C₂	1	2	yes	maximal, complemented
5	#63382⋊C₃	C₂	1	2	yes	maximal, complemented
6	C₃×#5132	—	3	1	no	maximal
7	#10588814	C₃	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
9	C₂×#611⋊C₃	C₄	1	2	yes	—
10	#3697⋊C₃	—	2	1	no	—
11	#3697⋊C₃	—	2	1	no	—
12	#3697⋊C₃	—	2	1	no	—
13	#3697⋊C₃	—	2	1	no	—
14	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
15	C₂×C₄×AGL(1,ℤ/9)	C₄	1	2	yes	—
16	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
17	M₁₆×3₋¹⁺²	—	2	1	no	—
18	M₁₆×3₋¹⁺²	C₂²	1	2	yes	—
19	C₂×C₈×3₋¹⁺²	—	2	1	no	—
20	#3667⋊C₃	—	2	1	no	—
21	#3667⋊C₃	C₂²	1	2	yes	—
22	C₂×3₋¹⁺²⋊C₈	—	2	1	no	—
23	C₂×C₃×#235	—	3	1	no	—
24	C₂×C₃²×M₁₆	D₃	1	1	yes	characteristic
25	C₂×C₃×#208	—	3	1	no	—
26	C₂×#3697	C₂×C₃	1	1	yes	characteristic
27	C₃×#824	—	3	2	no	—
28	C₃×#823	—	3	2	no	—
29	C₂×C₉×M₁₆	—	2	1	no	—
30	C₂×C₉×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#3667	C₂×C₃	1	1	yes	characteristic, complemented
32	#63383	C₂×C₃	1	2	yes	complemented
33	#63382	C₂×C₃	1	2	yes	complemented
34	C₂³×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
35	C₂²×AGL(1,ℤ/9)	C₂×C₄	1	2	yes	—
36	C₂×C₄×3₋¹⁺²	C₂×C₄	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	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
41	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
42	#611⋊C₃	—	2	2	no	—
43	#611⋊C₃	—	2	2	no	—
44	C₂×3₋¹⁺²⋊C₄	C₂×C₄	1	2	yes	—
45	C₄⋊AGL(1,ℤ/9)	—	2	1	no	—
46	C₄⋊AGL(1,ℤ/9)	—	2	1	no	—
47	C₄×AGL(1,ℤ/9)	—	2	2	no	—
48	C₄×AGL(1,ℤ/9)	—	2	2	no	—
49	3₋¹⁺²⋊Q₈	—	2	1	no	—
50	3₋¹⁺²⋊Q₈	—	2	1	no	—
51	C₈×3₋¹⁺²	—	2	2	no	—
52	3₋¹⁺²⋊C₈	—	2	2	no	—
53	C₃×#413	—	9	1	no	—
54	#5132	—	3	1	no	—
55	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
56	C₂×C₃×#67	—	3	2	no	—
57	C₃×#235	—	6	1	no	—
58	C₃×#235	—	6	1	no	—
59	C₃×#235	—	6	1	no	—
60	C₃×#235	—	6	1	no	—
61	C₂×C₃×D₁₂	—	3	1	no	—
62	C₂×C₃×C₄×D₃	—	3	2	no	—
63	C₂×C₃×Dic₆	—	3	1	no	—
64	C₃²×M₁₆	—	2	1	no	—
65	C₃²×M₁₆	C₂×D₃	1	2	yes	—
66	C₂×C₃²×C₈	—	2	1	no	—
67	C₃×#208	—	3	2	no	—
68	C₃×#208	—	6	1	no	—
69	C₂×C₃×C₃⋊C₈	—	6	1	no	—
70	C₂²×C₄×C₉	—	2	1	no	—
71	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
72	C₂×#611	C₃×C₄	1	2	yes	—
73	#3697	—	2	1	no	—
74	#3697	—	2	1	no	—
75	#3697	—	2	1	no	—
76	#3697	—	2	1	no	—
77	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₄×D₉	C₃×C₄	1	2	yes	—
79	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
80	C₉×M₁₆	—	2	2	no	—
81	C₉×M₁₆	—	2	2	no	—
82	C₉×M₁₆	—	2	1	no	—
83	C₉×M₁₆	C₂²×C₃	1	2	yes	—
84	C₂×C₈×C₉	—	2	2	no	—
85	C₂×C₈×C₉	—	2	1	no	—
86	#3667	—	2	1	no	—
87	#3667	C₂²×C₃	1	2	yes	—
88	C₂×C₉⋊C₈	—	2	1	no	—
89	C₂²×3₋¹⁺²	—	4	1	no	—
90	C₂²×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
93	C₂×AGL(1,ℤ/9)	—	2	2	no	—
94	C₂×AGL(1,ℤ/9)	—	4	2	no	—
95	C₄×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
96	C₄×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
97	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
98	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
99	3₋¹⁺²⋊C₄	—	2	2	no	—
100	C₂×C₃×#41	—	9	1	no	—
101	C₂×#235	—	3	1	no	—
102	C₂×C₃×M₁₆	—	3	1	no	—
103	C₂×C₃×M₁₆	—	9	1	no	—
104	C₂×C₃×M₁₆	C₃×D₃	1	1	yes	characteristic
105	C₂×#208	—	3	1	no	—
106	C₃×#101	—	9	2	no	—
107	C₃×#100	—	9	2	no	—
108	#824	—	3	2	no	—
109	#823	—	3	2	no	—
110	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
111	C₂²×C₃×D₃	—	3	2	no	—
112	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
113	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
114	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
115	C₂×C₃²×C₄	#67	1	1	yes	characteristic
116	C₂×C₃²×C₄	#67	1	1	yes	characteristic
117	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
118	C₃×#67	—	6	2	no	—
119	C₃×#67	—	6	2	no	—
120	C₂×C₃×Dic₃	—	3	2	no	—
121	C₃×D₁₂	—	6	1	no	—
122	C₃×D₁₂	—	6	1	no	—
123	C₃×C₄×D₃	—	6	2	no	—
124	C₃×C₄×D₃	—	6	2	no	—
125	C₃×Dic₆	—	6	1	no	—
126	C₃×Dic₆	—	6	1	no	—
127	C₂³×C₉	—	2	1	no	—
128	C₂³×C₉	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂²×D₉	C₂×C₃×C₄	1	2	yes	—
130	C₃²×C₈	—	2	2	no	—
131	C₃×C₃⋊C₈	—	6	2	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	—	2	1	no	—
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	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
144	#611	—	2	2	no	—
145	#611	—	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	C₈×C₉	—	2	4	no	—
154	C₈×C₉	—	2	2	no	—
155	C₉⋊C₈	—	2	2	no	—
156	#413	—	9	1	no	Sylow
157	C₂×3₋¹⁺²	—	2	1	no	—
158	C₂×3₋¹⁺²	—	2	1	no	—
159	C₂×3₋¹⁺²	—	2	1	no	—
160	C₂×3₋¹⁺²	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	AGL(1,ℤ/9)	—	4	2	no	—
162	C₃×#41	—	18	1	no	—
163	C₃×#41	—	18	1	no	—
164	C₃×#41	—	18	1	no	—
165	C₃×#41	—	18	1	no	—
166	C₂×C₃×Q₈	—	9	1	no	—
167	C₂×C₃×D₄	—	9	1	no	—
168	C₂×C₃×D₄	—	9	2	no	—
169	C₂²×C₃×C₄	—	3	1	no	—
170	C₂²×C₃×C₄	—	9	2	no	—
171	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
172	C₂×#67	—	3	2	no	—
173	#235	—	6	1	no	—
174	#235	—	6	1	no	—
175	#235	—	6	1	no	—
176	#235	—	6	1	no	—
177	C₂×D₁₂	—	3	1	no	—
178	C₂×C₄×D₃	—	3	2	no	—
179	C₂×Dic₆	—	3	1	no	—
180	C₃×M₁₆	—	2	1	no	—
181	C₃×M₁₆	—	3	2	no	—
182	C₃×M₁₆	—	6	1	no	—
183	C₃×M₁₆	—	9	2	no	—
184	C₃×M₁₆	—	18	1	no	—
185	C₃×M₁₆	C₂×C₃×D₃	1	2	yes	—
186	C₂×C₃×C₈	—	2	1	no	—
187	C₂×C₃×C₈	—	6	1	no	—
188	C₂×C₃×C₈	—	18	1	no	—
189	#208	—	3	2	no	—
190	#208	—	6	1	no	—
191	C₂×C₃⋊C₈	—	6	1	no	—
192	C₂²×C₃²	—	4	1	no	—
193	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
194	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
195	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
196	C₂×C₃×D₃	—	6	2	no	—
197	C₂×C₃×D₃	—	12	2	no	—
198	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
199	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
200	C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
201	C₃²×C₄	C₂×#67	1	1	yes	characteristic
202	C₃×Dic₃	—	6	2	no	—
203	C₂²×C₉	—	2	1	no	—
204	C₂²×C₉	—	2	1	no	—
205	C₂²×C₉	—	2	1	no	—
206	C₂²×C₉	—	4	1	no	—
207	C₂²×C₉	—	4	2	no	—
208	C₂²×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
210	C₂²×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
211	C₂×D₉	—	2	2	no	—
212	C₂×D₉	—	4	2	no	—
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	2	1	no	—
215	C₄×C₉	—	2	1	no	—
216	C₄×C₉	—	2	1	no	—
217	C₄×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
218	C₄×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
219	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
220	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
221	Dic₉	—	2	2	no	—
222	C₂×#41	—	9	1	no	—
223	C₂×M₁₆	—	9	1	no	—
224	C₂×M₁₆	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
225	#101	—	9	2	no	—
226	#100	—	9	2	no	—
227	3₋¹⁺²	#413	1	1	yes	characteristic, complemented, Sylow
228	C₂³×C₃	—	3	1	no	—
229	C₂³×C₃	—	9	2	no	—
230	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
231	C₂²×D₃	—	3	2	no	—
232	C₃×Q₈	—	18	1	no	—
233	C₃×Q₈	—	18	1	no	—
234	C₃×D₄	—	18	1	no	—
235	C₃×D₄	—	18	1	no	—
236	C₃×D₄	—	18	2	no	—
237	C₃×D₄	—	18	2	no	—
238	C₂×C₃×C₄	—	3	1	no	—
239	C₂×C₃×C₄	—	3	1	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	—	9	2	no	—
245	C₂×C₃×C₄	—	18	2	no	—
246	C₂×C₃×C₄	—	18	2	no	—
247	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
248	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
249	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
250	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
251	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
253	#67	—	6	2	no	—
254	#67	—	6	2	no	—
255	C₂×Dic₃	—	3	2	no	—
256	D₁₂	—	6	1	no	—
257	D₁₂	—	6	1	no	—
258	C₄×D₃	—	6	2	no	—
259	C₄×D₃	—	6	2	no	—
260	Dic₆	—	6	1	no	—
261	Dic₆	—	6	1	no	—
262	C₃×C₈	—	2	2	no	—
263	C₃×C₈	—	6	2	no	—
264	C₃×C₈	—	18	2	no	—
265	C₃⋊C₈	—	6	2	no	—
266	C₂×C₃²	—	2	1	no	—
267	C₂×C₃²	—	2	1	no	—
268	C₂×C₃²	—	2	1	no	—
269	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
270	C₃×D₃	—	12	2	no	—
271	C₂×C₉	—	2	2	no	—
272	C₂×C₉	—	2	1	no	—
273	C₂×C₉	—	2	1	no	—
274	C₂×C₉	—	2	1	no	—
275	C₂×C₉	—	2	1	no	—
276	C₂×C₉	—	4	1	no	—
277	C₂×C₉	—	4	1	no	—
278	C₂×C₉	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
279	D₉	—	4	2	no	—
280	#41	—	18	1	no	—
281	#41	—	18	1	no	—
282	#41	—	18	1	no	—
283	#41	—	18	1	no	—
284	C₂×Q₈	—	9	1	no	—
285	C₂×D₄	—	9	2	no	—
286	C₂×D₄	—	9	1	no	—
287	C₂²×C₄	—	9	2	no	—
288	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
289	M₁₆	—	2	1	no	—
290	M₁₆	—	9	2	no	—
291	M₁₆	—	18	1	no	—
292	M₁₆	C₂×AGL(1,ℤ/9)	1	2	yes	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	18	1	no	—
295	C₂²×C₃	—	3	1	no	—
296	C₂²×C₃	—	3	1	no	—
297	C₂²×C₃	—	3	1	no	—
298	C₂²×C₃	—	4	1	no	—
299	C₂²×C₃	—	12	1	no	—
300	C₂²×C₃	—	18	2	no	—
301	C₂²×C₃	—	36	2	no	—
302	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
303	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
304	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
305	C₂×D₃	—	6	2	no	—
306	C₂×D₃	—	12	2	no	—
307	C₃×C₄	—	3	1	no	—
308	C₃×C₄	—	3	1	no	—
309	C₃×C₄	—	3	1	no	—
310	C₃×C₄	—	3	1	no	—
311	C₃×C₄	—	18	2	no	—
312	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
313	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
314	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
315	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
316	Dic₃	—	6	2	no	—
317	C₃²	#5132	1	1	yes	characteristic
318	C₉	—	2	1	no	—
319	C₉	C₃×#413	1	1	yes	characteristic, complemented
320	C₂³	—	9	2	no	—
321	C₂³	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
322	Q₈	—	18	1	no	—
323	Q₈	—	18	1	no	—
324	D₄	—	18	2	no	—
325	D₄	—	18	2	no	—
326	D₄	—	18	1	no	—
327	D₄	—	18	1	no	—
328	C₂×C₄	—	9	2	no	—
329	C₂×C₄	—	18	2	no	—
330	C₂×C₄	—	18	2	no	—
331	C₂×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
332	C₂×C₄	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
333	C₂×C₄	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
334	C₂×C₄	#611⋊C₃	1	1	yes	characteristic
335	C₂×C₄	#611⋊C₃	1	1	yes	characteristic
336	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
337	C₈	—	2	2	no	—
338	C₈	—	18	2	no	—
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	2	1	no	—
341	C₂×C₃	—	2	1	no	—
342	C₂×C₃	—	3	1	no	—
343	C₂×C₃	—	6	1	no	—
344	C₂×C₃	—	6	1	no	—
345	C₂×C₃	—	6	1	no	—
346	C₂×C₃	—	36	2	no	—
347	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
348	D₃	—	12	2	no	—
349	C₂²	—	4	1	no	—
350	C₂²	—	18	2	no	—
351	C₂²	—	36	2	no	—
352	C₂²	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
353	C₂²	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
354	C₂²	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
355	C₄	—	18	2	no	—
356	C₄	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
357	C₄	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
358	C₄	C₂×C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
359	C₄	C₂×#611⋊C₃	1	1	yes	characteristic
360	C₃	—	3	1	no	—
361	C₃	C₃×#5132	1	1	yes	characteristic
362	C₂	—	2	1	no	—
363	C₂	—	2	1	no	—
364	C₂	—	2	1	no	—
365	C₂	—	36	2	no	—
366	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	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×M₁₆×3₋¹⁺²	C₂
socle	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄
prime radical	C₂×#3697⋊C₃	C₂
cosocle	C₂×C₄×C₉	C₂³×C₃
hypercenter	C₂×M₁₆	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#413
LCS	G ▷ C₂²×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×3₋¹⁺²	C₂	semidirect
3. C₂×#3667⋊C₃	C₂	semidirect
4. #63383⋊C₃	C₂	semidirect
5. #63382⋊C₃	C₂	semidirect
7. #10588814	C₃	semidirect
30. C₂×C₉×M₁₆	C₂×C₃	semidirect
31. C₂×#3667	C₂×C₃	semidirect
32. #63383	C₂×C₃	semidirect
33. #63382	C₂×C₃	semidirect
224. C₂×M₁₆	AGL(1,ℤ/9)	semidirect
227. 3₋¹⁺²	#413	semidirect
319. C₉	C₃×#413	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
C₂×M₁₆×3₋¹⁺²	2
C₂×#3667⋊C₃	2
#63383⋊C₃	2
#63382⋊C₃	2
C₃×#5132	3
#10588814	3

Subgroups — #10588814⋊C3 #13143238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588814⋊C₃ #13143238