Subgroups — C₂×#10624908 #13090394

Order 1458.

618 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	#10624908	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×#6900	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#6899	C₃	1	2	yes	maximal, complemented
4	C₂×#6899	C₃	1	2	yes	maximal, complemented
5	C₂×#6899	C₃	1	2	yes	maximal, complemented
6	C₂×#6899	C₃	1	2	yes	maximal, complemented
7	C₂×#6898	C₃	1	1	yes	maximal, characteristic, complemented
8	C₂×#6898	C₃	1	2	yes	maximal, complemented
9	C₂×#6897	C₃	1	2	yes	maximal, complemented
10	C₂×#6897	C₃	1	2	yes	maximal, complemented
11	C₂×#6897	C₃	1	2	yes	maximal, complemented
12	C₂×#6896	C₃	1	1	yes	maximal, characteristic, complemented
13	C₂×#6896	C₃	1	2	yes	maximal, complemented
14	C₂×#6896	C₃	1	2	yes	maximal, complemented
15	C₂×#6896	C₃	1	1	yes	maximal, characteristic, complemented
16	C₂×#6895	C₃	1	1	yes	maximal, characteristic, complemented
17	C₂×#6894	C₃	1	1	yes	maximal, characteristic, complemented
18	C₂×#6894	C₃	1	2	yes	maximal, complemented
19	C₂×#6893	C₃	1	1	yes	maximal, characteristic
20	C₂×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
21	C₂×C₉⋊H(3,𝔽₃)	C₃	1	2	yes	maximal
22	C₂×C₉×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
23	C₂×C₉×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
24	C₂×C₉×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
25	C₂×#6887	C₃	1	2	yes	maximal, complemented
26	#6900	C₂×C₃	1	1	yes	characteristic, complemented
27	#6899	C₂×C₃	1	2	yes	complemented
28	#6899	C₂×C₃	1	2	yes	complemented
29	#6899	C₂×C₃	1	2	yes	complemented
30	#6899	C₂×C₃	1	2	yes	complemented
31	#6898	C₂×C₃	1	1	yes	characteristic, complemented
32	#6898	C₂×C₃	1	2	yes	complemented
33	#6897	C₂×C₃	1	2	yes	complemented
34	#6897	C₂×C₃	1	2	yes	complemented
35	#6897	C₂×C₃	1	2	yes	complemented
36	#6896	C₂×C₃	1	1	yes	characteristic, complemented
37	#6896	C₂×C₃	1	2	yes	complemented
38	#6896	C₂×C₃	1	2	yes	complemented
39	#6896	C₂×C₃	1	1	yes	characteristic, complemented
40	#6895	C₂×C₃	1	1	yes	characteristic, complemented
41	#6894	C₂×C₃	1	1	yes	characteristic, complemented
42	#6894	C₂×C₃	1	2	yes	complemented
43	#6893	C₂×C₃	1	1	yes	characteristic
44	C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
45	C₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	—
46	C₉×3₋¹⁺²	C₂×C₃	1	2	yes	complemented
47	C₉×3₋¹⁺²	C₂×C₃	1	2	yes	complemented
48	C₉×3₋¹⁺²	C₂×C₃	1	2	yes	complemented
49	#6887	C₂×C₃	1	2	yes	complemented
50	C₂×C₃×3₋¹⁺²	C₃²	1	2	yes	—
51	C₂×C₃×3₋¹⁺²	C₃²	1	2	yes	—
52	C₂×C₃×3₋¹⁺²	C₃²	1	2	yes	—
53	C₂×C₃×3₋¹⁺²	C₃²	1	2	yes	—
54	C₂×C₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
55	C₂×C₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
56	C₂×C₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
57	C₂×C₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
58	C₂×C₃²×C₉	C₃²	1	2	yes	—
59	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
60	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
61	C₂×C₉⋊C₉	C₃²	1	2	yes	—
62	C₂×C₉⋊C₉	C₃²	1	2	yes	—
63	C₂×C₉⋊C₉	C₃²	1	2	yes	—
64	C₂×C₉⋊C₉	C₃²	1	2	yes	—
65	C₂×C₉⋊C₉	C₃²	1	2	yes	—
66	C₂×C₉⋊C₉	C₃²	1	2	yes	—
67	C₂×C₉⋊C₉	C₃²	1	2	yes	—
68	C₂×C₉⋊C₉	C₃²	1	2	yes	—
69	C₂×C₉⋊C₉	C₃²	1	2	yes	—
70	C₂×C₉⋊C₉	C₃²	1	2	yes	—
71	C₂×C₉⋊C₉	C₃²	1	2	yes	—
72	C₂×C₉⋊C₉	C₃²	1	2	yes	—
73	C₂×C₉⋊C₉	C₃²	1	2	yes	—
74	C₂×C₉⋊C₉	C₃²	1	2	yes	—
75	C₂×C₉⋊C₉	C₃²	1	2	yes	—
76	C₂×C₉⋊C₉	C₃²	1	2	yes	—
77	C₂×C₉⋊C₉	C₃²	1	2	yes	—
78	C₂×C₉⋊C₉	C₃²	1	2	yes	—
79	C₂×C₉⋊C₉	C₃²	1	2	yes	—
80	C₂×C₉⋊C₉	C₃²	1	2	yes	—
81	C₂×C₉⋊C₉	C₃²	1	2	yes	—
82	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
83	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
84	C₂×C₉⋊C₉	C₃²	1	2	yes	—
85	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
86	C₂×C₉⋊C₉	C₃²	1	2	yes	—
87	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
88	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
89	C₂×C₉⋊C₉	C₃²	1	2	yes	—
90	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
91	C₂×C₉⋊C₉	C₃²	1	2	yes	—
92	C₂×C₉⋊C₉	C₃²	1	2	yes	—
93	C₂×C₉⋊C₉	C₃²	1	2	yes	—
94	C₂×C₉⋊C₉	C₃²	1	2	yes	—
95	C₂×C₉⋊C₉	C₃²	1	2	yes	—
96	C₂×C₉⋊C₉	C₃²	1	2	yes	—
97	C₂×C₉⋊C₉	C₃²	1	2	yes	—
98	C₂×C₉⋊C₉	C₃²	1	1	yes	characteristic
99	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
100	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
101	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
102	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
103	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
104	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
105	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
106	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
107	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
108	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
109	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
110	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
111	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
112	C₂×C₃²⋊C₉	C₃²	1	1	yes	characteristic
113	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
114	C₂×C₃²⋊C₉	C₃²	1	1	yes	characteristic
115	C₂×C₃²⋊C₉	C₃²	1	2	yes	—
116	C₂×C₃²⋊C₉	C₃²	1	1	yes	characteristic
117	C₂×C₉²	C₃²	1	1	yes	characteristic
118	C₂×C₉²	C₃²	1	2	yes	—
119	C₂×C₉²	C₃²	1	2	yes	—
120	C₂×C₉²	C₃²	1	2	yes	—
121	C₂×C₉²	C₃²	1	2	yes	—
122	C₂×C₉²	C₃²	1	1	yes	characteristic
123	C₂×C₉²	C₃²	1	2	yes	—
124	C₃×3₋¹⁺²	C₂×C₃²	1	2	yes	—
125	C₃×3₋¹⁺²	C₂×C₃²	1	2	yes	—
126	C₃×3₋¹⁺²	C₂×C₃²	1	2	yes	—
127	C₃×3₋¹⁺²	C₂×C₃²	1	2	yes	—
128	C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
129	C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
130	C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
131	C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
132	C₃²×C₉	C₂×C₃²	1	2	yes	—
133	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
134	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
135	C₉⋊C₉	C₂×C₃²	1	2	yes	—
136	C₉⋊C₉	C₂×C₃²	1	2	yes	—
137	C₉⋊C₉	C₂×C₃²	1	2	yes	—
138	C₉⋊C₉	C₂×C₃²	1	2	yes	—
139	C₉⋊C₉	C₂×C₃²	1	2	yes	—
140	C₉⋊C₉	C₂×C₃²	1	2	yes	—
141	C₉⋊C₉	C₂×C₃²	1	2	yes	—
142	C₉⋊C₉	C₂×C₃²	1	2	yes	—
143	C₉⋊C₉	C₂×C₃²	1	2	yes	—
144	C₉⋊C₉	C₂×C₃²	1	2	yes	—
145	C₉⋊C₉	C₂×C₃²	1	2	yes	—
146	C₉⋊C₉	C₂×C₃²	1	2	yes	—
147	C₉⋊C₉	C₂×C₃²	1	2	yes	—
148	C₉⋊C₉	C₂×C₃²	1	2	yes	—
149	C₉⋊C₉	C₂×C₃²	1	2	yes	—
150	C₉⋊C₉	C₂×C₃²	1	2	yes	—
151	C₉⋊C₉	C₂×C₃²	1	2	yes	—
152	C₉⋊C₉	C₂×C₃²	1	2	yes	—
153	C₉⋊C₉	C₂×C₃²	1	2	yes	—
154	C₉⋊C₉	C₂×C₃²	1	2	yes	—
155	C₉⋊C₉	C₂×C₃²	1	2	yes	—
156	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
157	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
158	C₉⋊C₉	C₂×C₃²	1	2	yes	—
159	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
160	C₉⋊C₉	C₂×C₃²	1	2	yes	—
161	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
162	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
163	C₉⋊C₉	C₂×C₃²	1	2	yes	—
164	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
165	C₉⋊C₉	C₂×C₃²	1	2	yes	—
166	C₉⋊C₉	C₂×C₃²	1	2	yes	—
167	C₉⋊C₉	C₂×C₃²	1	2	yes	—
168	C₉⋊C₉	C₂×C₃²	1	2	yes	—
169	C₉⋊C₉	C₂×C₃²	1	2	yes	—
170	C₉⋊C₉	C₂×C₃²	1	2	yes	—
171	C₉⋊C₉	C₂×C₃²	1	2	yes	—
172	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
173	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
174	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
175	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
176	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
177	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
178	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
179	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
180	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
181	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
182	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
183	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
184	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
185	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
186	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
187	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
188	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
189	C₃²⋊C₉	C₂×C₃²	1	2	yes	—
190	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
191	C₉²	C₂×C₃²	1	1	yes	characteristic
192	C₉²	C₂×C₃²	1	2	yes	—
193	C₉²	C₂×C₃²	1	2	yes	—
194	C₉²	C₂×C₃²	1	2	yes	—
195	C₉²	C₂×C₃²	1	2	yes	—
196	C₉²	C₂×C₃²	1	1	yes	characteristic
197	C₉²	C₂×C₃²	1	2	yes	—
198	C₂×C₃³	C₃³	1	2	yes	—
199	C₂×C₃³	C₃³	1	1	yes	characteristic
200	C₂×C₃³	C₃³	1	1	yes	characteristic
201	C₂×3₋¹⁺²	—	3	6	no	—
202	C₂×3₋¹⁺²	—	3	6	no	—
203	C₂×3₋¹⁺²	—	3	6	no	—
204	C₂×3₋¹⁺²	—	9	2	no	—
205	C₂×3₋¹⁺²	—	9	1	no	—
206	C₂×3₋¹⁺²	—	9	1	no	—
207	C₂×3₋¹⁺²	—	9	1	no	—
208	C₂×H(3,𝔽₃)	—	9	1	no	—
209	C₂×C₃×C₉	—	3	6	no	—
210	C₂×C₃×C₉	—	9	1	no	—
211	C₂×C₃×C₉	—	9	1	no	—
212	C₂×C₃×C₉	C₃³	1	2	yes	—
213	C₂×C₃×C₉	C₃³	1	2	yes	—
214	C₂×C₃×C₉	C₃³	1	2	yes	—
215	C₂×C₃×C₉	C₃³	1	2	yes	—
216	C₂×C₃×C₉	C₃³	1	2	yes	—
217	C₂×C₃×C₉	C₃³	1	2	yes	—
218	C₂×C₃×C₉	C₃³	1	2	yes	—
219	C₂×C₃×C₉	C₃³	1	2	yes	—
220	C₂×C₃×C₉	C₃³	1	2	yes	—
221	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
222	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
223	C₂×C₃×C₉	C₃³	1	2	yes	—
224	C₂×C₃×C₉	C₃³	1	2	yes	—
225	C₂×C₃×C₉	C₃³	1	2	yes	—
226	C₂×C₃×C₉	C₃³	1	2	yes	—
227	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
228	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
229	C₂×C₃×C₉	C₃³	1	2	yes	—
230	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
231	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
232	C₂×C₃×C₉	C₃³	1	2	yes	—
233	C₃³	C₂×C₃³	1	2	yes	—
234	C₃³	C₂×C₃³	1	1	yes	characteristic
235	C₃³	C₂×C₃³	1	1	yes	characteristic
236	3₋¹⁺²	—	3	6	no	—
237	3₋¹⁺²	—	3	6	no	—
238	3₋¹⁺²	—	3	6	no	—
239	3₋¹⁺²	—	9	2	no	—
240	3₋¹⁺²	—	9	1	no	—
241	3₋¹⁺²	—	9	1	no	—
242	3₋¹⁺²	—	9	1	no	—
243	H(3,𝔽₃)	—	9	1	no	—
244	C₃×C₉	—	3	6	no	—
245	C₃×C₉	—	9	1	no	—
246	C₃×C₉	—	9	1	no	—
247	C₃×C₉	C₂×C₃³	1	2	yes	—
248	C₃×C₉	C₂×C₃³	1	2	yes	—
249	C₃×C₉	C₂×C₃³	1	2	yes	—
250	C₃×C₉	C₂×C₃³	1	2	yes	—
251	C₃×C₉	C₂×C₃³	1	2	yes	—
252	C₃×C₉	C₂×C₃³	1	2	yes	—
253	C₃×C₉	C₂×C₃³	1	2	yes	—
254	C₃×C₉	C₂×C₃³	1	2	yes	—
255	C₃×C₉	C₂×C₃³	1	2	yes	—
256	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
257	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
258	C₃×C₉	C₂×C₃³	1	2	yes	—
259	C₃×C₉	C₂×C₃³	1	2	yes	—
260	C₃×C₉	C₂×C₃³	1	2	yes	—
261	C₃×C₉	C₂×C₃³	1	2	yes	—
262	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
263	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
264	C₃×C₉	C₂×C₃³	1	2	yes	—
265	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
266	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
267	C₃×C₉	C₂×C₃³	1	2	yes	—
268	C₂×C₃²	—	3	2	no	—
269	C₂×C₃²	—	3	2	no	—
270	C₂×C₃²	—	3	2	no	—
271	C₂×C₃²	—	3	2	no	—
272	C₂×C₃²	—	3	1	no	—
273	C₂×C₃²	—	3	1	no	—
274	C₂×C₃²	—	3	2	no	—
275	C₂×C₃²	—	3	1	no	—
276	C₂×C₃²	—	3	2	no	—
277	C₂×C₃²	—	3	1	no	—
278	C₂×C₃²	C₃⁴	1	1	yes	characteristic
279	C₂×C₉	—	3	2	no	—
280	C₂×C₉	—	3	2	no	—
281	C₂×C₉	—	3	2	no	—
282	C₂×C₉	—	3	2	no	—
283	C₂×C₉	—	3	2	no	—
284	C₂×C₉	—	3	2	no	—
285	C₂×C₉	—	3	2	no	—
286	C₂×C₉	—	3	2	no	—
287	C₂×C₉	—	3	2	no	—
288	C₂×C₉	—	3	2	no	—
289	C₂×C₉	—	3	1	no	—
290	C₂×C₉	—	3	1	no	—
291	C₂×C₉	—	3	1	no	—
292	C₂×C₉	—	3	2	no	—
293	C₂×C₉	—	3	2	no	—
294	C₂×C₉	—	3	1	no	—
295	C₂×C₉	—	3	1	no	—
296	C₂×C₉	—	3	2	no	—
297	C₂×C₉	—	3	2	no	—
298	C₂×C₉	—	3	1	no	—
299	C₂×C₉	#737	1	6	yes	—
300	C₃²	—	3	2	no	—
301	C₃²	—	3	2	no	—
302	C₃²	—	3	2	no	—
303	C₃²	—	3	2	no	—
304	C₃²	—	3	1	no	—
305	C₃²	—	3	1	no	—
306	C₃²	—	3	2	no	—
307	C₃²	—	3	1	no	—
308	C₃²	—	3	2	no	—
309	C₃²	—	3	1	no	—
310	C₃²	C₂×C₃⁴	1	1	yes	characteristic
311	C₉	—	3	2	no	—
312	C₉	—	3	2	no	—
313	C₉	—	3	2	no	—
314	C₉	—	3	2	no	—
315	C₉	—	3	2	no	—
316	C₉	—	3	2	no	—
317	C₉	—	3	2	no	—
318	C₉	—	3	2	no	—
319	C₉	—	3	2	no	—
320	C₉	—	3	2	no	—
321	C₉	—	3	1	no	—
322	C₉	—	3	1	no	—
323	C₉	—	3	1	no	—
324	C₉	—	3	2	no	—
325	C₉	—	3	2	no	—
326	C₉	—	3	1	no	—
327	C₉	—	3	1	no	—
328	C₉	—	3	2	no	—
329	C₉	—	3	2	no	—
330	C₉	—	3	1	no	—
331	C₉	C₂×#737	1	6	yes	—
332	C₂×C₃	—	9	2	no	—
333	C₂×C₃	—	9	1	no	—
334	C₂×C₃	—	9	1	no	—
335	C₂×C₃	C₃×#737	1	2	yes	—
336	C₂×C₃	3₋¹⁺⁴	1	1	yes	characteristic
337	C₂×C₃	3₋¹⁺⁴	1	1	yes	characteristic
338	C₃	—	9	2	no	—
339	C₃	—	9	1	no	—
340	C₃	—	9	1	no	—
341	C₃	C₂×C₃×#737	1	2	yes	—
342	C₃	C₂×3₋¹⁺⁴	1	1	yes	characteristic
343	C₃	C₂×3₋¹⁺⁴	1	1	yes	characteristic
344	C₂	#10624908	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃²	C₃⁴
commutator, Frattini, cosocle	C₃²	C₂×C₃⁴
prime radical	C₂×C₃×H(3,𝔽₃)	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. #10624908	C₂	direct (N × H)
2. C₂×#6900	C₃	semidirect
3. C₂×#6899	C₃	semidirect
4. C₂×#6899	C₃	semidirect
5. C₂×#6899	C₃	semidirect
6. C₂×#6899	C₃	semidirect
7. C₂×#6898	C₃	semidirect
8. C₂×#6898	C₃	semidirect
9. C₂×#6897	C₃	semidirect
10. C₂×#6897	C₃	semidirect
11. C₂×#6897	C₃	semidirect
12. C₂×#6896	C₃	semidirect
13. C₂×#6896	C₃	semidirect
14. C₂×#6896	C₃	semidirect
15. C₂×#6896	C₃	semidirect
16. C₂×#6895	C₃	semidirect
17. C₂×#6894	C₃	semidirect
18. C₂×#6894	C₃	semidirect
22. C₂×C₉×3₋¹⁺²	C₃	semidirect
23. C₂×C₉×3₋¹⁺²	C₃	semidirect
24. C₂×C₉×3₋¹⁺²	C₃	semidirect
25. C₂×#6887	C₃	semidirect
26. #6900	C₂×C₃	semidirect
27. #6899	C₂×C₃	semidirect
28. #6899	C₂×C₃	semidirect
29. #6899	C₂×C₃	semidirect
30. #6899	C₂×C₃	semidirect
31. #6898	C₂×C₃	semidirect
32. #6898	C₂×C₃	semidirect
33. #6897	C₂×C₃	semidirect
34. #6897	C₂×C₃	semidirect
35. #6897	C₂×C₃	semidirect
36. #6896	C₂×C₃	semidirect
37. #6896	C₂×C₃	semidirect
38. #6896	C₂×C₃	semidirect
39. #6896	C₂×C₃	semidirect
40. #6895	C₂×C₃	semidirect
41. #6894	C₂×C₃	semidirect
42. #6894	C₂×C₃	semidirect
46. C₉×3₋¹⁺²	C₂×C₃	semidirect
47. C₉×3₋¹⁺²	C₂×C₃	semidirect
48. C₉×3₋¹⁺²	C₂×C₃	semidirect
49. #6887	C₂×C₃	semidirect
344. C₂	#10624908	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624908	2
C₂×#6900	3
C₂×#6899	3
C₂×#6898	3
C₂×#6897	3
C₂×#6896	3
C₂×#6895	3
C₂×#6894	3
C₂×#6893	3
C₂×C₉⋊H(3,𝔽₃)	3
C₂×C₉×3₋¹⁺²	3
C₂×#6887	3

Subgroups — C2×#10624908 #13090394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624908 #13090394