Subgroups — #13138197

Order 1728.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₃⋊D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#6192	C₂	1	1	yes	maximal, characteristic
3	C₂×D₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×(C₂×D₉)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11720282	C₂	1	1	yes	maximal, characteristic, complemented
7	Dic₃×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#10590906	—	3	1	no	maximal
9	#10588518	—	3	1	no	maximal
10	C₂×C₄×C₃⋊D₉	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
12	C₂×#6192	C₄	1	1	yes	characteristic
13	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₃⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₈×C₃⋊D₉	—	2	2	no	—
16	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
19	#88445	C₄	1	1	yes	characteristic
20	(C₂×D₉)⋊Dic₃	C₄	1	1	yes	characteristic
21	Dic₃⋊Dic₉	C₄	1	1	yes	characteristic
22	D₉×C₃⋊C₈	—	2	2	no	—
23	C₂×C₈×C₃⋊D₃	—	3	1	no	—
24	C₄×#626	—	3	1	no	—
25	C₂×D₃×C₃⋊C₈	—	3	1	no	—
26	C₃×(C₂×D₃)⋊C₈	—	3	1	no	—
27	C₃×Dic₃⋊C₈	D₃	1	1	yes	characteristic
28	#63557	—	3	1	no	—
29	Dic₃×C₃⋊C₈	—	3	1	no	—
30	C₂×C₈×D₉	—	3	1	no	—
31	C₂×C₈×D₉	—	3	1	no	—
32	C₂×C₈×D₉	—	6	1	no	—
33	C₄×D₃₆	—	3	1	no	—
34	C₉×C₄⋊C₈	—	3	1	no	—
35	(C₂×D₉)⋊C₈	—	3	1	no	—
36	(C₂×D₉)⋊C₈	D₃	1	1	yes	characteristic, complemented
37	C₄×C₉⋊C₈	—	3	1	no	—
38	C₂²×C₃⋊D₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×D₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
41	C₂×C₃⋊Dic₉	C₂×C₄	1	1	yes	characteristic
42	C₄×C₃⋊D₉	—	2	1	no	—
43	C₄×C₃⋊D₉	—	2	1	no	—
44	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×Dic₉	C₂×C₄	1	1	yes	characteristic
47	C₃×C₄×D₉	—	2	1	no	—
48	C₃×C₄×D₉	—	2	1	no	—
49	#6192	C₈	1	4	yes	complemented
50	C₃×C₈×C₉	—	2	1	no	—
51	C₃⋊(C₉⋊C₈)	D₄	1	2	yes	complemented
52	C₉×C₃⋊C₈	—	2	1	no	—
53	C₃×C₉⋊C₈	—	2	1	no	—
54	#4834	—	9	1	no	—
55	#67⋊C₈	—	9	1	no	—
56	C₂×C₄×C₃⋊D₃	—	3	1	no	—
57	C₂×C₃×C₄×D₃	—	3	1	no	—
58	C₂×#626	—	3	1	no	—
59	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
60	C₂×C₃⋊(C₃⋊C₈)	—	3	1	no	—
61	C₈×C₃⋊D₃	—	6	2	no	—
62	C₃×C₄×Dic₃	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃×C₃⋊C₈	—	3	1	no	—
64	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
65	Dic₃⋊Dic₃	—	3	1	no	—
66	#3722	—	3	1	no	—
67	(C₂×D₃)⋊Dic₃	—	3	1	no	—
68	D₃×C₃⋊C₈	—	6	2	no	—
69	C₂×D₃₆	—	3	1	no	—
70	C₂×C₄×D₉	—	3	1	no	—
71	C₂×C₄×D₉	—	6	1	no	—
72	C₂×C₄×D₉	C₂×D₃	1	1	yes	characteristic
73	C₂×C₈×C₉	—	2	1	no	—
74	C₂×C₈×C₉	—	3	1	no	—
75	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
76	C₄²×C₉	—	3	1	no	—
77	(C₂×D₉)⋊C₄	—	3	1	no	—
78	(C₂×D₉)⋊C₄	—	3	1	no	—
79	C₄⋊Dic₉	—	3	1	no	—
80	C₂×C₉⋊C₈	—	3	1	no	—
81	C₂×C₉⋊C₈	—	6	1	no	—
82	C₂×C₉⋊C₈	C₂×D₃	1	1	yes	characteristic
83	C₈×D₉	—	6	2	no	—
84	C₈×D₉	—	6	2	no	—
85	C₈×D₉	—	6	4	no	—
86	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃⋊D₉	—	2	1	no	—
88	C₂×C₃⋊D₉	—	2	1	no	—
89	C₂×C₃⋊D₉	C₂×C₈	1	2	yes	complemented
90	C₂×C₃×D₉	—	2	1	no	—
91	C₂×C₃×D₉	—	2	1	no	—
92	C₂×C₃×D₉	C₂×C₈	1	2	yes	complemented
93	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
94	C₃×C₄×C₉	#41	1	1	yes	characteristic
95	C₃⋊Dic₉	—	2	1	no	—
96	C₉×Dic₃	—	2	1	no	—
97	C₉×Dic₃	C₂×C₈	1	2	yes	complemented
98	C₃×Dic₉	—	2	1	no	—
99	C₄×#67	—	9	1	no	—
100	C₂²×C₃⋊C₈	—	9	1	no	—
101	C₂×D₃×C₈	—	9	1	no	—
102	C₂×D₃×C₈	—	9	1	no	—
103	C₂×D₃×C₈	—	9	1	no	—
104	C₂×D₃×C₈	—	18	1	no	—
105	C₄×D₁₂	—	9	1	no	—
106	C₃×C₄⋊C₈	—	3	1	no	—
107	C₃×C₂²⋊C₈	—	9	1	no	—
108	(C₂×D₃)⋊C₈	—	3	1	no	—
109	(C₂×D₃)⋊C₈	—	9	1	no	—
110	(C₂×D₃)⋊C₈	—	9	1	no	—
111	Dic₃⋊C₈	D₉	1	1	yes	characteristic, complemented
112	C₈×Dic₃	—	9	1	no	—
113	C₄×C₃⋊C₈	—	9	1	no	—
114	C₂²×C₃⋊D₃	—	3	1	no	—
115	C₂²×C₃×D₃	—	3	1	no	—
116	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
117	C₂×C₃⋊Dic₃	—	3	1	no	—
118	C₄×C₃⋊D₃	—	6	1	no	—
119	C₄×C₃⋊D₃	—	6	1	no	—
120	C₂×C₃×Dic₃	—	3	1	no	—
121	C₂×C₃×Dic₃	C₄×D₃	1	1	yes	characteristic
122	C₂×C₃×Dic₃	C₄×D₃	1	1	yes	characteristic
123	C₃×C₄×D₃	—	6	1	no	—
124	C₃×C₄×D₃	—	6	1	no	—
125	#626	—	3	4	no	—
126	C₂²×D₉	—	3	1	no	—
127	C₂²×D₉	—	6	1	no	—
128	C₂²×D₉	C₄×D₃	1	1	yes	characteristic
129	C₃²×C₈	—	2	1	no	—
130	C₃⋊(C₃⋊C₈)	—	3	2	no	—
131	C₃×C₃⋊C₈	—	2	1	no	—
132	C₃×C₃⋊C₈	—	6	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	3	1	no	—
135	C₂×C₄×C₉	—	3	1	no	—
136	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
137	C₂×Dic₉	—	3	1	no	—
138	C₂×Dic₉	—	6	1	no	—
139	C₂×Dic₉	C₄×D₃	1	1	yes	characteristic
140	D₃₆	—	3	4	no	—
141	C₄×D₉	—	2	1	no	—
142	C₄×D₉	—	2	1	no	—
143	C₄×D₉	—	6	2	no	—
144	C₄×D₉	—	6	2	no	—
145	C₄×D₉	—	6	1	no	—
146	C₄×D₉	—	6	1	no	—
147	C₈×C₉	—	2	2	no	—
148	C₈×C₉	—	2	1	no	—
149	C₈×C₉	—	6	1	no	—
150	C₉⋊C₈	—	2	1	no	—
151	C₉⋊C₈	—	3	2	no	—
152	C₉⋊C₈	—	6	2	no	—
153	C₈×D₄	—	27	1	no	Sylow
154	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₃×C₉	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₃×C₉	#131	1	1	yes	characteristic
157	C₃⋊D₉	—	2	2	no	—
158	C₃×D₉	—	2	2	no	—
159	C₂²×C₃×C₄	—	9	1	no	—
160	C₂×#67	—	9	1	no	—
161	C₂×D₁₂	—	9	1	no	—
162	C₂×C₄×D₃	—	3	1	no	—
163	C₂×C₄×D₃	—	9	1	no	—
164	C₂×C₄×D₃	—	9	1	no	—
165	C₂×C₄×D₃	—	18	1	no	—
166	C₂×C₃×C₈	—	2	1	no	—
167	C₂×C₃×C₈	—	3	1	no	—
168	C₂×C₃×C₈	—	9	1	no	—
169	C₂×C₃×C₈	C₂×D₉	1	1	yes	characteristic
170	C₂×C₃×C₈	D₃²	1	1	yes	characteristic
171	C₃×C₄²	—	3	1	no	—
172	#217	—	9	1	no	—
173	(C₂×D₃)⋊C₄	—	9	1	no	—
174	(C₂×D₃)⋊C₄	—	9	1	no	—
175	(C₂×D₃)⋊C₄	—	9	1	no	—
176	C₄⋊Dic₃	—	9	1	no	—
177	Dic₃⋊C₄	—	9	1	no	—
178	C₄×Dic₃	C₂×D₉	1	1	yes	characteristic
179	C₂×C₃⋊C₈	—	3	1	no	—
180	C₂×C₃⋊C₈	—	9	1	no	—
181	C₂×C₃⋊C₈	—	9	1	no	—
182	C₂×C₃⋊C₈	—	18	1	no	—
183	C₂×C₃⋊C₈	—	18	2	no	—
184	C₂×C₃⋊C₈	C₂×D₉	1	1	yes	characteristic
185	D₃×C₈	—	18	2	no	—
186	D₃×C₈	—	18	2	no	—
187	D₃×C₈	—	18	2	no	—
188	D₃×C₈	—	18	4	no	—
189	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
190	C₂×C₃⋊D₃	—	3	2	no	—
191	C₂×C₃⋊D₃	—	6	1	no	—
192	C₂×C₃⋊D₃	—	6	1	no	—
193	C₂×C₃×D₃	—	3	2	no	—
194	C₂×C₃×D₃	—	6	1	no	—
195	C₂×C₃×D₃	—	6	1	no	—
196	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
197	C₃²×C₄	#239	1	1	yes	characteristic
198	C₃⋊Dic₃	—	6	1	no	—
199	C₃×Dic₃	—	2	1	no	—
200	C₃×Dic₃	—	6	1	no	—
201	C₃×Dic₃	D₃×C₈	1	2	yes	—
202	C₂²×C₉	—	2	1	no	—
203	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
204	C₂×D₉	—	2	1	no	—
205	C₂×D₉	—	2	1	no	—
206	C₂×D₉	—	3	2	no	—
207	C₂×D₉	—	6	2	no	—
208	C₂×D₉	—	6	2	no	—
209	C₂×D₉	—	6	2	no	—
210	C₂×D₉	—	6	1	no	—
211	C₂×D₉	—	6	1	no	—
212	C₂×D₉	D₃×C₈	1	2	yes	complemented
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	2	1	no	—
215	C₄×C₉	—	3	2	no	—
216	C₄×C₉	—	6	1	no	—
217	C₄×C₉	D₃×D₄	1	1	yes	characteristic
218	C₄×C₉	#237	1	1	yes	characteristic
219	Dic₉	—	2	1	no	—
220	Dic₉	—	6	2	no	—
221	Dic₉	—	6	1	no	—
222	C₂²×C₈	—	27	1	no	—
223	C₂²×C₈	—	27	1	no	—
224	C₄×D₄	—	27	1	no	—
225	C₄⋊C₈	—	3	1	no	—
226	C₂²⋊C₈	—	9	1	no	—
227	C₂²⋊C₈	—	27	1	no	—
228	C₄×C₈	—	27	1	no	—
229	C₃×C₉	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₃	—	9	1	no	—
231	C₂²×D₃	—	3	1	no	—
232	C₂²×D₃	—	9	1	no	—
233	C₂²×D₃	—	9	1	no	—
234	C₂²×D₃	—	18	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	3	1	no	—
237	C₂×C₃×C₄	—	3	1	no	—
238	C₂×C₃×C₄	—	9	1	no	—
239	C₂×C₃×C₄	—	18	1	no	—
240	C₂×C₃×C₄	—	18	1	no	—
241	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
243	#67	—	9	4	no	—
244	C₂×Dic₃	—	3	1	no	—
245	C₂×Dic₃	—	9	1	no	—
246	C₂×Dic₃	—	9	1	no	—
247	C₂×Dic₃	—	18	1	no	—
248	C₂×Dic₃	C₄×D₉	1	1	yes	characteristic
249	C₂×Dic₃	C₄×D₉	1	1	yes	characteristic
250	D₁₂	—	9	4	no	—
251	C₄×D₃	—	6	1	no	—
252	C₄×D₃	—	6	1	no	—
253	C₄×D₃	—	18	2	no	—
254	C₄×D₃	—	18	2	no	—
255	C₄×D₃	—	18	1	no	—
256	C₄×D₃	—	18	1	no	—
257	C₄×D₃	—	18	1	no	—
258	C₄×D₃	—	18	1	no	—
259	C₃×C₈	—	2	2	no	—
260	C₃×C₈	—	2	1	no	—
261	C₃×C₈	—	2	1	no	—
262	C₃×C₈	—	6	1	no	—
263	C₃×C₈	—	18	1	no	—
264	C₃⋊C₈	—	2	1	no	—
265	C₃⋊C₈	—	6	1	no	—
266	C₃⋊C₈	—	9	2	no	—
267	C₃⋊C₈	—	9	2	no	—
268	C₃⋊C₈	—	18	2	no	—
269	C₂×C₃²	#893	1	1	yes	characteristic
270	C₂×C₃²	C₂×D₃×C₈	1	1	yes	characteristic
271	C₂×C₃²	#907	1	1	yes	characteristic
272	C₃⋊D₃	—	6	2	no	—
273	C₃×D₃	—	6	2	no	—
274	C₂×C₉	—	2	1	no	—
275	C₂×C₉	—	2	1	no	—
276	C₂×C₉	—	2	1	no	—
277	C₂×C₉	#67⋊C₄	1	1	yes	characteristic
278	C₂×C₉	C₂×D₃×C₈	1	1	yes	characteristic
279	C₂×C₉	#907	1	1	yes	characteristic
280	D₉	—	2	2	no	—
281	D₉	—	6	4	no	—
282	D₉	—	6	2	no	—
283	C₂×D₄	—	27	1	no	—
284	C₂²×C₄	—	9	1	no	—
285	C₂²×C₄	—	27	1	no	—
286	C₂×C₈	—	3	1	no	—
287	C₂×C₈	—	9	1	no	—
288	C₂×C₈	—	27	1	no	—
289	C₂×C₈	—	54	2	no	—
290	C₂×C₈	—	54	2	no	—
291	C₂×C₈	D₃×D₉	1	1	yes	characteristic
292	C₄⋊C₄	—	27	1	no	—
293	C₂²⋊C₄	—	27	1	no	—
294	C₂²⋊C₄	—	27	1	no	—
295	C₄²	—	3	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	9	2	no	—
298	C₂²×C₃	—	18	1	no	—
299	C₂²×C₃	—	18	1	no	—
300	C₂²×C₃	C₂×C₄×D₉	1	1	yes	characteristic
301	C₂²×C₃	C₄×D₃²	1	1	yes	characteristic
302	C₂×D₃	—	3	2	no	—
303	C₂×D₃	—	6	1	no	—
304	C₂×D₃	—	6	1	no	—
305	C₂×D₃	—	9	2	no	—
306	C₂×D₃	—	9	2	no	—
307	C₂×D₃	—	18	2	no	—
308	C₂×D₃	—	18	2	no	—
309	C₂×D₃	—	18	2	no	—
310	C₂×D₃	—	18	1	no	—
311	C₂×D₃	—	18	1	no	—
312	C₂×D₃	—	18	1	no	—
313	C₂×D₃	—	18	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	3	2	no	—
317	C₃×C₄	—	6	1	no	—
318	C₃×C₄	—	18	1	no	—
319	C₃×C₄	D₄×D₉	1	1	yes	characteristic
320	C₃×C₄	#3701	1	1	yes	characteristic
321	C₃×C₄	#3796	1	1	yes	characteristic
322	C₃×C₄	#3811	1	1	yes	characteristic
323	Dic₃	—	2	1	no	—
324	Dic₃	—	6	1	no	—
325	Dic₃	—	18	2	no	—
326	Dic₃	—	18	1	no	—
327	Dic₃	—	18	1	no	—
328	Dic₃	C₈×D₉	1	2	yes	complemented
329	C₃²	#4834	1	1	yes	characteristic
330	C₉	—	2	1	no	—
331	C₉	#67⋊C₈	1	1	yes	characteristic, complemented
332	C₂³	—	9	1	no	—
333	C₂³	—	27	1	no	—
334	D₄	—	27	4	no	—
335	C₂×C₄	—	3	1	no	—
336	C₂×C₄	—	3	1	no	—
337	C₂×C₄	—	9	1	no	—
338	C₂×C₄	—	18	1	no	—
339	C₂×C₄	—	18	1	no	—
340	C₂×C₄	—	27	1	no	—
341	C₂×C₄	—	54	1	no	—
342	C₂×C₄	—	54	1	no	—
343	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
344	C₈	—	2	1	no	—
345	C₈	—	6	1	no	—
346	C₈	—	18	1	no	—
347	C₈	—	27	2	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	2	1	no	—
351	C₂×C₃	—	18	2	no	—
352	C₂×C₃	#63455	1	1	yes	characteristic
353	C₂×C₃	C₂×C₈×D₉	1	1	yes	characteristic
354	C₂×C₃	#63469	1	1	yes	characteristic
355	C₂×C₃	D₃²×C₈	1	1	yes	characteristic
356	C₂×C₃	#63805	1	1	yes	characteristic
357	C₂×C₃	#63881	1	1	yes	characteristic
358	D₃	—	6	2	no	—
359	D₃	—	18	4	no	—
360	D₃	—	18	2	no	—
361	D₃	—	18	2	no	—
362	C₂²	—	9	2	no	—
363	C₂²	—	18	1	no	—
364	C₂²	—	18	1	no	—
365	C₂²	—	27	2	no	—
366	C₂²	—	54	1	no	—
367	C₂²	—	54	1	no	—
368	C₂²	C₄×D₃×D₉	1	1	yes	characteristic
369	C₄	—	3	2	no	—
370	C₄	—	6	1	no	—
371	C₄	—	18	1	no	—
372	C₄	—	54	1	no	—
373	C₄	#88634	1	1	yes	characteristic
374	C₄	#88668	1	1	yes	characteristic
375	C₃	—	2	1	no	—
376	C₃	#10588518	1	1	yes	characteristic, complemented
377	C₃	#10590906	1	1	yes	characteristic
378	C₂	—	18	2	no	—
379	C₂	—	54	2	no	—
380	C₂	D₃×C₈×D₉	1	1	yes	characteristic
381	C₂	#11720809	1	1	yes	characteristic
382	C₂	#11720978	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₉
commutator	C₂×C₃×C₉	C₂²×C₈
Frattini	C₂×C₃×C₄	C₂×D₃²
Fitting	C₂×C₃×C₈×C₉	C₂²
socle	C₂²×C₃²	C₂×C₄×D₃
prime radical	C₂×#6192	C₄
cosocle	C₂×C₃×C₄×C₉	C₂³
hypercenter	C₂×C₈	D₃×D₉
hypocenter	C₃×C₉	C₈×D₄
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×C₃⋊D₉	C₂	semidirect
3. C₂×D₉×C₃⋊C₈	C₂	semidirect
4. C₃×(C₂×D₉)⋊C₈	C₂	semidirect
5. C₉×Dic₃⋊C₈	C₂	semidirect
6. #11720282	C₂	semidirect
7. Dic₃×C₉⋊C₈	C₂	semidirect
36. (C₂×D₉)⋊C₈	D₃	semidirect
49. #6192	C₈	semidirect
51. C₃⋊(C₉⋊C₈)	D₄	semidirect
89. C₂×C₃⋊D₉	C₂×C₈	semidirect
92. C₂×C₃×D₉	C₂×C₈	semidirect
97. C₉×Dic₃	C₂×C₈	semidirect
111. Dic₃⋊C₈	D₉	semidirect
212. C₂×D₉	D₃×C₈	semidirect
229. C₃×C₉	C₈×D₄	semidirect
328. Dic₃	C₈×D₉	semidirect
331. C₉	#67⋊C₈	semidirect
376. C₃	#10588518	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₃⋊D₉	2
C₄×#6192	2
C₂×D₉×C₃⋊C₈	2
C₃×(C₂×D₉)⋊C₈	2
C₉×Dic₃⋊C₈	2
#11720282	2
Dic₃×C₉⋊C₈	2
#10590906	3
#10588518	3