Subgroups — #13139490

Order 1728.

422 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#611	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88413	C₂	1	1	yes	maximal, characteristic, complemented
4	#11720571	C₂	1	1	yes	maximal, characteristic, complemented
5	(C₂×D₉)⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#11720274	C₂	1	1	yes	maximal, characteristic, complemented
7	Dic₉⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	#10591155	—	3	1	no	maximal
9	#10588792	—	3	1	no	maximal
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₃×#611	C₄	1	1	yes	characteristic
12	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
13	C₂×C₃⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₃⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₃×#3676	C₄	1	1	yes	characteristic
16	C₃×(C₂×D₉)⋊C₄	C₄	1	1	yes	characteristic
17	C₃×Dic₉⋊C₄	C₄	1	1	yes	characteristic
18	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
19	C₂×C₉×C₃⋊C₈	—	2	2	no	—
20	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	#88413	—	2	2	no	—
23	C₃×C₄×#67	—	3	1	no	—
24	C₂²×C₃×C₃⋊C₈	D₃	1	1	yes	characteristic
25	C₂×#3711	—	3	1	no	—
26	#63657	—	3	1	no	—
27	Dic₃⋊(C₃⋊C₈)	—	3	1	no	—
28	(C₂×D₃)⋊(C₃⋊C₈)	—	3	1	no	—
29	#63554	—	3	1	no	—
30	C₂²×C₈×C₉	—	3	1	no	—
31	C₄×#611	D₃	1	1	yes	characteristic
32	C₂×#3663	—	3	1	no	—
33	#63389	—	3	1	no	—
34	#63389	—	6	1	no	—
35	(C₂×D₉)⋊C₈	—	3	1	no	—
36	#63375	—	3	1	no	—
37	Dic₉⋊C₈	—	3	1	no	—
38	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×D₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	—	2	1	no	—
41	C₂×C₃×C₄×C₉	—	2	1	no	—
42	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
44	C₃×#611	—	2	2	no	—
45	C₂×C₃×Dic₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×Dic₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×Dic₉	C₂×C₄	1	1	yes	characteristic
48	C₃×C₄×D₉	—	2	1	no	—
49	C₃×C₄×D₉	—	2	1	no	—
50	C₃⋊(C₉⋊C₈)	—	2	1	no	—
51	C₃⋊(C₉⋊C₈)	—	2	1	no	—
52	C₉×C₃⋊C₈	—	2	1	no	—
53	C₉×C₃⋊C₈	D₄	1	2	yes	complemented
54	#5111	—	9	1	no	—
55	#5011	—	9	1	no	—
56	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
57	C₂×C₃×#67	—	3	1	no	—
58	C₂×C₃×C₄×D₃	—	3	1	no	—
59	C₂×C₃⋊(C₃⋊C₈)	—	3	1	no	—
60	C₂×C₃⋊(C₃⋊C₈)	—	3	1	no	—
61	C₃×#217	—	3	1	no	—
62	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
63	C₃×Dic₃⋊C₄	—	3	1	no	—
64	C₃×C₄×Dic₃	—	3	1	no	—
65	C₂×C₃×C₃⋊C₈	—	2	2	no	—
66	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
67	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
68	#3711	—	6	2	no	—
69	C₂²×C₄×C₉	—	2	1	no	—
70	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
71	C₂×#611	Dic₃	1	1	yes	characteristic
72	C₂×C₄×D₉	C₂×D₃	1	1	yes	characteristic
73	C₂×C₈×C₉	—	3	1	no	—
74	C₂×C₈×C₉	—	3	1	no	—
75	C₂×C₈×C₉	—	6	2	no	—
76	#3676	Dic₃	1	1	yes	characteristic
77	(C₂×D₉)⋊C₄	Dic₃	1	1	yes	characteristic
78	Dic₉⋊C₄	Dic₃	1	1	yes	characteristic
79	C₄×Dic₉	C₂×D₃	1	1	yes	characteristic
80	C₂×C₉⋊C₈	—	3	1	no	—
81	C₂×C₉⋊C₈	—	3	1	no	—
82	C₂×C₉⋊C₈	—	6	1	no	—
83	C₂×C₉⋊C₈	—	6	1	no	—
84	#3663	—	6	2	no	—
85	C₂²×C₃×C₉	—	2	1	no	—
86	C₂²×C₃×C₉	—	2	1	no	—
87	C₂²×C₃×C₉	M₁₆	1	2	yes	complemented
88	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×D₉	—	2	1	no	—
90	C₂×C₃×D₉	—	2	1	no	—
91	C₂×C₃×D₉	—	2	1	no	—
92	C₃×C₄×C₉	—	2	1	no	—
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	C₃×Dic₉	—	2	1	no	—
97	C₃×Dic₉	—	2	1	no	—
98	C₂²×C₃×C₈	—	3	1	no	—
99	C₃×C₄×D₄	—	9	1	no	—
100	C₄×#67	—	3	1	no	—
101	C₂×#208	—	9	1	no	—
102	C₂²×C₃⋊C₈	D₉	1	1	yes	characteristic, complemented
103	C₂×ΓL(1,𝔽₂₅)	—	9	1	no	—
104	#830	—	9	1	no	—
105	#830	—	9	1	no	—
106	#830	—	9	1	no	—
107	#830	—	18	1	no	—
108	(C₂×D₃)⋊C₈	—	9	1	no	—
109	#815	—	9	1	no	—
110	Dic₃⋊C₈	—	9	1	no	—
111	C₄⋊(C₃⋊C₈)	—	9	1	no	—
112	#803	—	9	1	no	—
113	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
114	C₂²×C₃×D₃	—	3	1	no	—
115	C₂×C₃²×C₄	—	2	1	no	—
116	C₂×C₃²×C₄	—	2	1	no	—
117	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
119	C₃×#67	—	6	2	no	—
120	C₂×C₃×Dic₃	—	3	1	no	—
121	C₂×C₃×Dic₃	—	3	1	no	—
122	C₂×C₃×Dic₃	—	3	1	no	—
123	C₃×C₄×D₃	—	6	1	no	—
124	C₃×C₄×D₃	—	6	1	no	—
125	C₂³×C₉	—	2	1	no	—
126	C₂³×C₉	C₂×Dic₃	1	1	yes	characteristic
127	C₂²×D₉	C₂×Dic₃	1	1	yes	characteristic
128	C₃⋊(C₃⋊C₈)	—	6	1	no	—
129	C₃⋊(C₃⋊C₈)	—	6	1	no	—
130	C₃×C₃⋊C₈	—	2	1	no	—
131	C₃×C₃⋊C₈	#67	1	2	yes	—
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	—	4	1	no	—
137	C₂×C₄×C₉	—	4	1	no	—
138	C₂×C₄×C₉	C₂×Dic₃	1	1	yes	characteristic
139	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
140	#611	—	2	2	no	—
141	C₂×Dic₉	C₂×Dic₃	1	1	yes	characteristic
142	C₂×Dic₉	C₂×Dic₃	1	1	yes	characteristic
143	C₂×Dic₉	C₂×Dic₃	1	1	yes	characteristic
144	C₄×D₉	—	2	1	no	—
145	C₄×D₉	—	2	1	no	—
146	C₈×C₉	—	3	2	no	—
147	C₈×C₉	—	6	1	no	—
148	C₉⋊C₈	—	6	1	no	—
149	C₉⋊C₈	—	6	1	no	—
150	C₉⋊C₈	—	12	1	no	—
151	C₉⋊C₈	—	12	1	no	—
152	#435	—	27	1	no	Sylow
153	C₂×C₃×C₉	—	2	2	no	—
154	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₃×C₉	C₂×M₁₆	1	1	yes	characteristic
156	C₂×C₃×C₉	#131	1	1	yes	characteristic
157	C₃×D₉	—	4	1	no	—
158	C₂×C₃×D₄	—	9	1	no	—
159	C₂²×C₃×C₄	—	2	1	no	—
160	C₂²×C₃×C₄	—	9	1	no	—
161	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
162	C₂²×C₃×C₄	D₃²	1	1	yes	characteristic
163	C₂×#67	—	3	1	no	—
164	C₂×C₄×D₃	—	3	1	no	—
165	C₂×C₃×C₈	—	3	1	no	—
166	C₂×C₃×C₈	—	3	1	no	—
167	C₂×C₃×C₈	—	6	2	no	—
168	C₃×C₄⋊C₄	—	9	1	no	—
169	C₃×C₂²⋊C₄	—	9	1	no	—
170	C₃×C₂²⋊C₄	—	9	1	no	—
171	C₃×C₄²	—	9	1	no	—
172	#217	—	3	1	no	—
173	(C₂×D₃)⋊C₄	—	3	1	no	—
174	Dic₃⋊C₄	—	3	1	no	—
175	C₄×Dic₃	—	3	1	no	—
176	#208	—	18	2	no	—
177	C₂×C₃⋊C₈	—	2	2	no	—
178	C₂×C₃⋊C₈	—	9	1	no	—
179	C₂×C₃⋊C₈	—	9	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	1	no	—
184	C₂×C₃⋊C₈	C₂×D₉	1	1	yes	characteristic
185	C₂×C₃⋊C₈	C₂×D₉	1	1	yes	characteristic
186	ΓL(1,𝔽₂₅)	—	18	2	no	—
187	C₂²×C₃²	—	2	1	no	—
188	C₂²×C₃²	—	2	1	no	—
189	C₂²×C₃²	ΓL(1,𝔽₂₅)	1	2	yes	—
190	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
191	C₂×C₃×D₃	—	6	1	no	—
192	C₂×C₃×D₃	—	6	1	no	—
193	C₂×C₃×D₃	—	6	1	no	—
194	C₃²×C₄	—	2	1	no	—
195	C₃²×C₄	#235	1	1	yes	characteristic
196	C₃²×C₄	C₂×#67	1	1	yes	characteristic
197	C₃×Dic₃	—	6	1	no	—
198	C₃×Dic₃	—	6	1	no	—
199	C₃×Dic₃	—	6	1	no	—
200	C₂²×C₉	—	2	1	no	—
201	C₂²×C₉	—	2	1	no	—
202	C₂²×C₉	—	2	2	no	—
203	C₂²×C₉	—	2	1	no	—
204	C₂²×C₉	—	4	1	no	—
205	C₂²×C₉	—	4	1	no	—
206	C₂²×C₉	#208	1	2	yes	complemented
207	C₂²×C₉	C₂²×Dic₃	1	1	yes	characteristic
208	C₂×D₉	—	2	1	no	—
209	C₂×D₉	—	2	1	no	—
210	C₂×D₉	—	2	1	no	—
211	C₄×C₉	—	2	1	no	—
212	C₄×C₉	—	2	1	no	—
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	4	1	no	—
215	C₄×C₉	D₃×D₄	1	1	yes	characteristic
216	C₄×C₉	#237	1	1	yes	characteristic
217	Dic₉	—	2	1	no	—
218	Dic₉	—	2	1	no	—
219	Dic₉	—	2	1	no	—
220	C₂×M₁₆	—	27	1	no	—
221	C₂²×C₈	—	3	1	no	—
222	C₄×D₄	—	9	1	no	—
223	C₄⋊C₈	—	27	1	no	—
224	C₂²⋊C₈	—	27	1	no	—
225	C₂²⋊C₈	—	27	1	no	—
226	#97	—	27	1	no	—
227	C₃×C₉	#435	1	1	yes	characteristic, complemented, Sylow
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	9	1	no	—
230	C₂³×C₃	C₄×D₉	1	1	yes	characteristic
231	C₂³×C₃	D₃×Dic₃	1	1	yes	characteristic
232	C₂²×D₃	—	3	1	no	—
233	C₃×D₄	—	18	2	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	4	1	no	—
241	C₂×C₃×C₄	—	4	1	no	—
242	C₂×C₃×C₄	—	9	1	no	—
243	C₂×C₃×C₄	—	9	1	no	—
244	C₂×C₃×C₄	—	9	1	no	—
245	C₂×C₃×C₄	—	18	1	no	—
246	C₂×C₃×C₄	—	18	1	no	—
247	C₂×C₃×C₄	C₄×D₉	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
249	C₂×C₃×C₄	D₃×Dic₃	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
251	#67	—	6	2	no	—
252	C₂×Dic₃	—	3	1	no	—
253	C₂×Dic₃	—	3	1	no	—
254	C₂×Dic₃	—	3	1	no	—
255	C₄×D₃	—	6	1	no	—
256	C₄×D₃	—	6	1	no	—
257	C₃×C₈	—	3	2	no	—
258	C₃×C₈	—	6	1	no	—
259	C₃⋊C₈	—	2	1	no	—
260	C₃⋊C₈	—	18	1	no	—
261	C₃⋊C₈	—	18	1	no	—
262	C₃⋊C₈	—	18	1	no	—
263	C₃⋊C₈	—	18	1	no	—
264	C₃⋊C₈	—	36	1	no	—
265	C₃⋊C₈	—	36	1	no	—
266	C₃⋊C₈	#611	1	2	yes	complemented
267	C₂×C₃²	—	2	2	no	—
268	C₂×C₃²	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
269	C₂×C₃²	#901	1	1	yes	characteristic
270	C₂×C₃²	C₄×#67	1	1	yes	characteristic
271	C₃×D₃	—	12	1	no	—
272	C₂×C₉	—	2	2	no	—
273	C₂×C₉	—	2	1	no	—
274	C₂×C₉	—	2	1	no	—
275	C₂×C₉	—	2	1	no	—
276	C₂×C₉	—	4	2	no	—
277	C₂×C₉	C₂×#208	1	1	yes	characteristic
278	C₂×C₉	D₄×Dic₃	1	1	yes	characteristic
279	C₂×C₉	#948	1	1	yes	characteristic
280	D₉	—	4	1	no	—
281	C₂×D₄	—	9	1	no	—
282	C₂²×C₄	—	9	1	no	—
283	C₂²×C₄	D₃×D₉	1	1	yes	characteristic
284	M₁₆	—	54	2	no	—
285	C₂×C₈	—	3	1	no	—
286	C₂×C₈	—	3	1	no	—
287	C₂×C₈	—	6	2	no	—
288	C₂×C₈	—	27	1	no	—
289	C₂×C₈	—	27	1	no	—
290	C₄⋊C₄	—	9	1	no	—
291	C₂²⋊C₄	—	9	1	no	—
292	C₂²⋊C₄	—	9	1	no	—
293	C₄²	—	9	1	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	4	1	no	—
302	C₂²×C₃	—	18	1	no	—
303	C₂²×C₃	—	18	1	no	—
304	C₂²×C₃	—	18	1	no	—
305	C₂²×C₃	#3663	1	2	yes	complemented
306	C₂²×C₃	C₂×C₄×D₉	1	1	yes	characteristic
307	C₂²×C₃	#3711	1	2	yes	—
308	C₂²×C₃	C₂×D₃×Dic₃	1	1	yes	characteristic
309	C₂×D₃	—	6	1	no	—
310	C₂×D₃	—	6	1	no	—
311	C₂×D₃	—	6	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	4	1	no	—
317	C₃×C₄	—	18	1	no	—
318	C₃×C₄	—	18	1	no	—
319	C₃×C₄	—	18	1	no	—
320	C₃×C₄	#3697	1	1	yes	characteristic
321	C₃×C₄	C₂×#611	1	1	yes	characteristic
322	C₃×C₄	#3804	1	1	yes	characteristic
323	C₃×C₄	D₃×#67	1	1	yes	characteristic
324	Dic₃	—	6	1	no	—
325	Dic₃	—	6	1	no	—
326	Dic₃	—	6	1	no	—
327	C₃²	#5111	1	1	yes	characteristic
328	C₉	—	2	1	no	—
329	C₉	#5011	1	1	yes	characteristic, complemented
330	C₂³	—	9	1	no	—
331	C₂³	Dic₃×D₉	1	1	yes	characteristic
332	D₄	—	18	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	9	1	no	—
336	C₂×C₄	—	9	1	no	—
337	C₂×C₄	—	9	1	no	—
338	C₂×C₄	—	18	1	no	—
339	C₂×C₄	—	18	1	no	—
340	C₂×C₄	Dic₃×D₉	1	1	yes	characteristic
341	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
342	C₈	—	3	2	no	—
343	C₈	—	6	1	no	—
344	C₈	—	54	1	no	—
345	C₈	—	54	1	no	—
346	C₂×C₃	—	2	2	no	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	2	1	no	—
351	C₂×C₃	—	4	2	no	—
352	C₂×C₃	—	36	1	no	—
353	C₂×C₃	C₂×#3663	1	1	yes	characteristic
354	C₂×C₃	#63464	1	1	yes	characteristic
355	C₂×C₃	C₄×#611	1	1	yes	characteristic
356	C₂×C₃	#63814	1	1	yes	characteristic
357	C₂×C₃	C₂×#3711	1	1	yes	characteristic
358	C₂×C₃	Dic₃×#67	1	1	yes	characteristic
359	D₃	—	12	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	18	1	no	—
363	C₂²	—	18	1	no	—
364	C₂²	—	18	1	no	—
365	C₂²	#88413	1	2	yes	complemented
366	C₂²	C₂×Dic₃×D₉	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	18	1	no	—
369	C₄	—	18	1	no	—
370	C₄	—	18	1	no	—
371	C₄	#88658	1	1	yes	characteristic
372	C₄	D₃×#611	1	1	yes	characteristic
373	C₃	—	2	1	no	—
374	C₃	#10588792	1	1	yes	characteristic, complemented
375	C₃	#10591155	1	1	yes	characteristic
376	C₂	—	2	2	no	—
377	C₂	—	36	1	no	—
378	C₂	#11720858	1	1	yes	characteristic
379	C₂	C₂×#88413	1	1	yes	characteristic
380	C₂	Dic₃×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₉
commutator	C₂²×C₃×C₉	C₂²×C₄
Frattini	C₂×C₃×C₄	C₂×D₃²
Fitting	C₂²×C₃×C₄×C₉	C₂²
socle	C₂²×C₃²	C₂×C₄×D₃
prime radical	C₂×C₃×#611	C₄
cosocle	C₂×C₃×C₄×C₉	C₂³
hypercenter	C₂²×C₄	D₃×D₉
hypocenter	C₃×C₉	#435
LCS	G ▷ C₂²×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₉×C₃⋊C₈	C₂	semidirect
3. C₂×#88413	C₂	semidirect
4. #11720571	C₂	semidirect
5. (C₂×D₉)⋊(C₃⋊C₈)	C₂	semidirect
6. #11720274	C₂	semidirect
7. Dic₉⋊(C₃⋊C₈)	C₂	semidirect
53. C₉×C₃⋊C₈	D₄	semidirect
87. C₂²×C₃×C₉	M₁₆	semidirect
102. C₂²×C₃⋊C₈	D₉	semidirect
206. C₂²×C₉	#208	semidirect
227. C₃×C₉	#435	semidirect
266. C₃⋊C₈	#611	semidirect
305. C₂²×C₃	#3663	semidirect
329. C₉	#5011	semidirect
365. C₂²	#88413	semidirect
374. C₃	#10588792	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#611	2
C₂²×C₉×C₃⋊C₈	2
C₂×#88413	2
#11720571	2
(C₂×D₉)⋊(C₃⋊C₈)	2
#11720274	2
Dic₉⋊(C₃⋊C₈)	2
#10591155	3
#10588792	3