Subgroups — C₂×C₉×#556 #11768195

Order 1152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#556	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#126	C₂	1	4	yes	maximal, complemented
4	C₂×C₉×#124	C₂	1	2	yes	maximal
5	C₂×C₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×Q₈×C₉	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
9	C₂×C₉×#117	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#556	C₃	1	1	yes	maximal, characteristic
11	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
12	C₂²×Q₈×C₉	C₂²	1	2	yes	—
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₉	C₂²	1	2	yes	—
15	C₉×C₄⋊Q₈	C₂²	1	8	yes	complemented
16	C₉×#126	C₂²	1	32	yes	complemented
17	C₉×#124	C₂²	1	16	yes	—
18	C₉×C₂²⋊Q₈	C₂²	1	16	yes	complemented
19	C₄×Q₈×C₉	C₂²	1	16	yes	complemented
20	C₄×Q₈×C₉	C₂²	1	8	yes	complemented
21	C₄×D₄×C₉	C₂²	1	8	yes	—
22	C₉×#117	C₂²	1	16	yes	complemented
23	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
24	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
30	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
31	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₄²×C₉	C₂²	1	2	yes	—
33	C₂×C₄²×C₉	C₂²	1	4	yes	—
34	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
35	C₃×#556	C₂×C₃	1	16	yes	—
36	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
37	C₂×C₃×#126	C₂×C₃	1	4	yes	—
38	C₂×C₃×#124	C₂×C₃	1	2	yes	—
39	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
40	C₂×C₃×C₄×Q₈	C₂×C₃	1	2	yes	—
41	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
42	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
43	C₂×C₃×#117	C₂×C₃	1	2	yes	—
44	C₂⁴×C₉	C₂³	1	2	yes	—
45	C₂×Q₈×C₉	—	2	4	no	—
46	C₂×Q₈×C₉	—	2	8	no	—
47	C₂×Q₈×C₉	C₂³	1	4	yes	—
48	C₂×Q₈×C₉	C₂³	1	8	yes	—
49	C₂×D₄×C₉	—	2	4	no	—
50	C₂×D₄×C₉	C₂³	1	4	yes	—
51	C₂²×C₄×C₉	—	2	8	no	—
52	C₂²×C₄×C₉	C₂³	1	8	yes	—
53	C₂²×C₄×C₉	C₂³	1	2	yes	—
54	C₂²×C₄×C₉	C₂³	1	2	yes	—
55	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₉	C₂³	1	2	yes	—
57	C₂²×C₄×C₉	C₂³	1	4	yes	—
58	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₉×C₄⋊C₄	C₂³	1	4	yes	—
61	C₉×C₄⋊C₄	C₂³	1	8	yes	—
62	C₉×C₄⋊C₄	C₂³	1	4	yes	—
63	C₉×C₄⋊C₄	C₂³	1	16	yes	—
64	C₉×C₄⋊C₄	C₂³	1	8	yes	—
65	C₉×C₄⋊C₄	C₂³	1	8	yes	—
66	C₉×C₂²⋊C₄	C₂³	1	16	yes	—
67	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
68	C₉×C₂²⋊C₄	C₂³	1	16	yes	—
69	C₄²×C₉	C₂³	1	16	yes	—
70	C₄²×C₉	C₂³	1	4	yes	—
71	C₄²×C₉	C₂³	1	8	yes	—
72	C₂×#556	C₉	1	1	yes	characteristic, direct product factor, Sylow
73	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
75	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
76	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
77	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
78	C₃×#126	C₂²×C₃	1	32	yes	—
79	C₃×#124	C₂²×C₃	1	16	yes	—
80	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
81	C₃×C₄×Q₈	C₂²×C₃	1	16	yes	—
82	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
83	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
84	C₃×#117	C₂²×C₃	1	16	yes	—
85	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
92	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
94	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
95	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
97	C₂³×C₉	—	2	4	no	—
98	C₂³×C₉	—	2	4	no	—
99	C₂³×C₉	—	2	4	no	—
100	C₂³×C₉	C₂⁴	1	4	yes	—
101	C₂³×C₉	C₂⁴	1	1	yes	characteristic
102	Q₈×C₉	—	2	8	no	—
103	Q₈×C₉	—	2	16	no	—
104	D₄×C₉	—	2	8	no	—
105	C₂×C₄×C₉	—	2	4	no	—
106	C₂×C₄×C₉	—	2	4	no	—
107	C₂×C₄×C₉	—	2	8	no	—
108	C₂×C₄×C₉	—	2	4	no	—
109	C₂×C₄×C₉	—	2	2	no	—
110	C₂×C₄×C₉	—	2	16	no	—
111	C₂×C₄×C₉	#41	1	4	yes	—
112	C₂×C₄×C₉	#41	1	4	yes	—
113	C₂×C₄×C₉	C₂⁴	1	4	yes	—
114	C₂×C₄×C₉	C₂⁴	1	4	yes	—
115	C₂×C₄×C₉	C₂⁴	1	2	yes	—
116	C₂×C₄×C₉	C₂⁴	1	8	yes	—
117	C₂×C₄×C₉	C₂⁴	1	4	yes	—
118	C₂×C₄×C₉	C₂⁴	1	2	yes	—
119	C₂×C₄×C₉	C₂⁴	1	2	yes	—
120	#556	C₂×C₉	1	16	yes	direct product factor
121	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
122	C₂×#126	C₂×C₉	1	4	yes	complemented
123	C₂×#124	C₂×C₉	1	2	yes	—
124	C₂×C₂²⋊Q₈	C₂×C₉	1	2	yes	complemented
125	C₂×C₄×Q₈	C₂×C₉	1	2	yes	complemented
126	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
127	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
128	C₂×#117	C₂×C₉	1	2	yes	complemented
129	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
130	C₂×C₃×Q₈	—	2	4	no	—
131	C₂×C₃×Q₈	—	2	8	no	—
132	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
133	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
134	C₂×C₃×D₄	—	2	4	no	—
135	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
136	C₂²×C₃×C₄	—	2	8	no	—
137	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
138	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
139	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
141	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
142	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
143	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
145	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
146	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
147	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
148	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
149	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
150	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
151	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
152	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
153	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
154	C₃×C₄²	C₂³×C₃	1	16	yes	—
155	C₃×C₄²	C₂³×C₃	1	4	yes	—
156	C₃×C₄²	C₂³×C₃	1	8	yes	—
157	C₂²×C₉	—	2	4	no	—
158	C₂²×C₉	—	2	4	no	—
159	C₂²×C₉	—	2	4	no	—
160	C₂²×C₉	—	4	8	no	—
161	C₂²×C₉	C₂×#41	1	2	yes	—
162	C₂²×C₉	C₂×#41	1	2	yes	—
163	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
164	C₂²×C₉	C₂⁵	1	1	yes	characteristic
165	C₄×C₉	—	2	4	no	—
166	C₄×C₉	—	2	4	no	—
167	C₄×C₉	—	2	8	no	—
168	C₄×C₉	—	2	4	no	—
169	C₄×C₉	—	2	2	no	—
170	C₄×C₉	C₂×#41	1	4	yes	—
171	C₄×C₉	C₂×#41	1	4	yes	—
172	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
173	C₂²×Q₈	C₂²×C₉	1	2	yes	—
174	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
175	C₂³×C₄	C₂²×C₉	1	2	yes	—
176	C₄⋊Q₈	C₂²×C₉	1	8	yes	complemented
177	#126	C₂²×C₉	1	32	yes	complemented
178	#124	C₂²×C₉	1	16	yes	—
179	C₂²⋊Q₈	C₂²×C₉	1	16	yes	complemented
180	C₄×Q₈	C₂²×C₉	1	16	yes	complemented
181	C₄×Q₈	C₂²×C₉	1	8	yes	complemented
182	C₄×D₄	C₂²×C₉	1	8	yes	—
183	#117	C₂²×C₉	1	16	yes	complemented
184	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
185	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
186	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
187	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
188	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
189	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
190	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
191	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
192	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
193	C₂×C₄²	C₂²×C₉	1	4	yes	—
194	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
195	C₂×C₄²	C₂²×C₉	1	2	yes	—
196	C₂³×C₃	—	2	4	no	—
197	C₂³×C₃	—	2	4	no	—
198	C₂³×C₃	—	2	4	no	—
199	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
200	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
201	C₃×Q₈	—	2	8	no	—
202	C₃×Q₈	—	2	16	no	—
203	C₃×D₄	—	2	8	no	—
204	C₂×C₃×C₄	—	2	4	no	—
205	C₂×C₃×C₄	—	2	4	no	—
206	C₂×C₃×C₄	—	2	8	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	2	2	no	—
209	C₂×C₃×C₄	—	2	16	no	—
210	C₂×C₃×C₄	C₃×#41	1	4	yes	—
211	C₂×C₃×C₄	C₃×#41	1	4	yes	—
212	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
213	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
214	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
215	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
216	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
217	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
218	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
219	C₂×C₉	—	4	4	no	—
220	C₂×C₉	#556	1	4	yes	direct product factor
221	C₂×C₉	C₂²×#41	1	1	yes	characteristic
222	C₂×C₉	C₂²×#41	1	1	yes	characteristic
223	C₂×C₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
224	C₂⁴	C₂³×C₉	1	2	yes	—
225	C₂×Q₈	—	2	4	no	—
226	C₂×Q₈	—	2	8	no	—
227	C₂×Q₈	C₂³×C₉	1	4	yes	—
228	C₂×Q₈	C₂³×C₉	1	8	yes	—
229	C₂×D₄	—	2	4	no	—
230	C₂×D₄	C₂³×C₉	1	4	yes	—
231	C₂²×C₄	—	2	8	no	—
232	C₂²×C₄	C₂³×C₉	1	2	yes	—
233	C₂²×C₄	C₂³×C₉	1	2	yes	—
234	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
235	C₂²×C₄	C₂³×C₉	1	4	yes	—
236	C₂²×C₄	C₂³×C₉	1	2	yes	—
237	C₂²×C₄	C₂³×C₉	1	8	yes	—
238	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
239	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
240	C₄⋊C₄	C₂³×C₉	1	4	yes	—
241	C₄⋊C₄	C₂³×C₉	1	8	yes	—
242	C₄⋊C₄	C₂³×C₉	1	4	yes	—
243	C₄⋊C₄	C₂³×C₉	1	16	yes	—
244	C₄⋊C₄	C₂³×C₉	1	8	yes	—
245	C₄⋊C₄	C₂³×C₉	1	8	yes	—
246	C₂²⋊C₄	C₂³×C₉	1	16	yes	—
247	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
248	C₂²⋊C₄	C₂³×C₉	1	16	yes	—
249	C₄²	C₂³×C₉	1	16	yes	—
250	C₄²	C₂³×C₉	1	4	yes	—
251	C₄²	C₂³×C₉	1	8	yes	—
252	C₂²×C₃	—	2	4	no	—
253	C₂²×C₃	—	2	4	no	—
254	C₂²×C₃	—	2	4	no	—
255	C₂²×C₃	—	4	8	no	—
256	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
257	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
258	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
259	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
260	C₃×C₄	—	2	4	no	—
261	C₃×C₄	—	2	4	no	—
262	C₃×C₄	—	2	8	no	—
263	C₃×C₄	—	2	4	no	—
264	C₃×C₄	—	2	2	no	—
265	C₃×C₄	C₂×C₃×#41	1	4	yes	—
266	C₃×C₄	C₂×C₃×#41	1	4	yes	—
267	C₉	C₂×#556	1	1	yes	characteristic, direct product factor, Sylow
268	C₂³	—	2	4	no	—
269	C₂³	—	2	4	no	—
270	C₂³	—	2	4	no	—
271	C₂³	C₂⁴×C₉	1	4	yes	—
272	C₂³	C₂⁴×C₉	1	1	yes	characteristic
273	Q₈	—	2	8	no	—
274	Q₈	—	2	16	no	—
275	D₄	—	2	8	no	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	16	no	—
282	C₂×C₄	C₉×#41	1	4	yes	—
283	C₂×C₄	C₉×#41	1	4	yes	—
284	C₂×C₄	C₂⁴×C₉	1	4	yes	—
285	C₂×C₄	C₂⁴×C₉	1	4	yes	—
286	C₂×C₄	C₂⁴×C₉	1	2	yes	—
287	C₂×C₄	C₂⁴×C₉	1	8	yes	—
288	C₂×C₄	C₂⁴×C₉	1	4	yes	—
289	C₂×C₄	C₂⁴×C₉	1	2	yes	—
290	C₂×C₄	C₂⁴×C₉	1	2	yes	—
291	C₂×C₃	—	4	4	no	—
292	C₂×C₃	C₃×#556	1	4	yes	—
293	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
294	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
295	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
296	C₂²	—	2	4	no	—
297	C₂²	—	2	4	no	—
298	C₂²	—	2	4	no	—
299	C₂²	—	4	8	no	—
300	C₂²	C₂×C₉×#41	1	2	yes	—
301	C₂²	C₂×C₉×#41	1	2	yes	—
302	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
303	C₂²	C₂⁵×C₉	1	1	yes	characteristic
304	C₄	—	2	4	no	—
305	C₄	—	2	4	no	—
306	C₄	—	2	8	no	—
307	C₄	—	2	4	no	—
308	C₄	—	2	2	no	—
309	C₄	C₂×C₉×#41	1	4	yes	—
310	C₄	C₂×C₉×#41	1	4	yes	—
311	C₃	C₂×C₃×#556	1	1	yes	characteristic
312	C₂	—	4	4	no	—
313	C₂	C₉×#556	1	4	yes	direct product factor
314	C₂	C₂²×C₉×#41	1	1	yes	characteristic
315	C₂	C₂²×C₉×#41	1	1	yes	characteristic
316	C₂	C₂×C₉×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂⁵×C₉
Frattini, cosocle	C₂²×C₃	C₂⁵×C₃
socle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#556	C₂	direct (N × H)
2. C₂×C₉×C₄⋊Q₈	C₂	semidirect
3. C₂×C₉×#126	C₂	semidirect
5. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
6. C₂×C₄×Q₈×C₉	C₂	semidirect
7. C₂×C₄×Q₈×C₉	C₂	semidirect
9. C₂×C₉×#117	C₂	semidirect
15. C₉×C₄⋊Q₈	C₂²	semidirect
16. C₉×#126	C₂²	semidirect
18. C₉×C₂²⋊Q₈	C₂²	semidirect
19. C₄×Q₈×C₉	C₂²	semidirect
20. C₄×Q₈×C₉	C₂²	semidirect
22. C₉×#117	C₂²	semidirect
72. C₂×#556	C₉	direct (N × H)
120. #556	C₂×C₉	direct (N × H)
121. C₂×C₄⋊Q₈	C₂×C₉	semidirect
122. C₂×#126	C₂×C₉	semidirect
124. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
125. C₂×C₄×Q₈	C₂×C₉	semidirect
126. C₂×C₄×Q₈	C₂×C₉	semidirect
128. C₂×#117	C₂×C₉	semidirect
176. C₄⋊Q₈	C₂²×C₉	semidirect
177. #126	C₂²×C₉	semidirect
179. C₂²⋊Q₈	C₂²×C₉	semidirect
180. C₄×Q₈	C₂²×C₉	semidirect
181. C₄×Q₈	C₂²×C₉	semidirect
183. #117	C₂²×C₉	semidirect
220. C₂×C₉	#556	direct (N × H)
267. C₉	C₂×#556	direct (N × H)
313. C₂	C₉×#556	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#556	2
C₂×C₉×C₄⋊Q₈	2
C₂×C₉×#126	2
C₂×C₉×#124	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₄×Q₈×C₉	2
C₂×C₄×D₄×C₉	2
C₂×C₉×#117	2
C₂×C₃×#556	3

Subgroups — C2×C9×#556 #11768195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#556 #11768195