Subgroups — C₃×#10589687 #13152691

Order 1728.

778 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63509	C₂	1	2	yes	maximal, complemented
3	C₃×#63456	C₂	1	4	yes	maximal, complemented
4	C₃×#63455	C₂	1	2	yes	maximal, complemented
5	C₃×#63437	C₂	1	2	yes	maximal, complemented
6	C₃×#63436	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×D₃₆	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5585	—	3	1	no	maximal
10	#10589687	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₃×D₃₆	C₂²	1	2	yes	—
13	C₂×C₃×D₃₆	C₂²	1	2	yes	—
14	C₂×C₃×D₃₆	C₂²	1	2	yes	—
15	C₂×C₃×C₄×D₉	C₂²	1	4	yes	—
16	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
17	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
20	C₃×C₄²×C₉	C₂²	1	2	yes	—
21	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	—
22	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	—
23	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	—
24	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
25	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
26	C₃×C₄×Dic₉	C₂²	1	2	yes	—
27	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic
28	C₃×#947	—	3	2	no	—
29	C₃×#894	—	3	4	no	—
30	C₃×#893	—	3	2	no	—
31	C₃×#875	—	3	2	no	—
32	C₃×#874	—	3	1	no	—
33	C₃×C₄×D₁₂	—	3	2	no	—
34	C₃×C₄×Dic₆	—	3	1	no	—
35	C₄×Q₈×C₉	—	2	1	no	—
36	C₄×Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
37	#63509	C₂×C₃	1	2	yes	complemented
38	#63456	C₂×C₃	1	4	yes	complemented
39	#63455	C₂×C₃	1	2	yes	complemented
40	#63437	C₂×C₃	1	2	yes	complemented
41	#63436	C₂×C₃	1	1	yes	characteristic
42	C₄×D₃₆	C₂×C₃	1	2	yes	complemented
43	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₃×D₉	C₂³	1	4	yes	—
45	C₃×Q₈×C₉	—	2	2	no	—
46	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₃×Dic₉	C₂³	1	2	yes	—
52	C₂×C₃×Dic₉	C₂³	1	2	yes	—
53	C₃×D₃₆	—	2	4	no	—
54	C₃×D₃₆	—	2	4	no	—
55	C₃×D₃₆	—	4	2	no	—
56	C₃×C₄×D₉	—	4	4	no	—
57	C₃×Dic₁₈	—	2	2	no	—
58	C₃×#559	—	9	1	no	—
59	#5585	—	3	1	no	—
60	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
61	C₂×C₃×D₁₂	—	3	2	no	—
62	C₂×C₃×D₁₂	—	3	2	no	—
63	C₂×C₃×D₁₂	—	3	2	no	—
64	C₂×C₃×C₄×D₃	—	3	4	no	—
65	C₂×C₃×Dic₆	—	3	1	no	—
66	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
67	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
68	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
69	C₃²×C₄²	C₂×D₃	1	2	yes	—
70	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
71	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
72	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
73	C₃×C₄⋊Dic₃	—	3	1	no	—
74	C₃×Dic₃⋊C₄	—	3	2	no	—
75	C₃×C₄×Dic₃	—	3	2	no	—
76	C₂×Q₈×C₉	—	2	1	no	—
77	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
78	C₂×D₃₆	C₂²×C₃	1	2	yes	—
79	C₂×D₃₆	C₂²×C₃	1	2	yes	—
80	C₂×D₃₆	C₂²×C₃	1	2	yes	—
81	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
82	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
83	C₉×C₄⋊C₄	—	2	1	no	—
84	C₉×C₄⋊C₄	—	2	2	no	—
85	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₄²×C₉	—	2	1	no	—
88	C₄²×C₉	—	2	2	no	—
89	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
90	C₄²×C₉	C₂²×C₃	1	2	yes	—
91	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
92	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
93	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
94	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
95	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
96	C₄×Dic₉	C₂²×C₃	1	2	yes	—
97	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
98	C₂×C₃×D₉	—	2	4	no	—
99	C₂×C₃×D₉	—	2	4	no	—
100	C₂×C₃×D₉	—	2	4	no	—
101	C₃×C₄×C₉	—	2	2	no	—
102	C₃×C₄×C₉	—	2	2	no	—
103	C₃×C₄×C₉	—	2	1	no	—
104	C₃×C₄×C₉	#41	1	2	yes	—
105	C₃×C₄×C₉	#41	1	2	yes	—
106	C₃×Dic₉	—	2	2	no	—
107	C₃×Dic₉	—	2	2	no	—
108	C₃×#127	—	9	1	no	—
109	C₃×#124	—	9	2	no	—
110	C₃×#124	—	9	2	no	—
111	C₃×#123	—	9	4	no	—
112	C₃×C₄×Q₈	—	2	1	no	—
113	C₃×C₄×Q₈	—	9	1	no	—
114	C₃×C₄×Q₈	D₉	1	1	yes	characteristic, complemented
115	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
116	C₃×C₄×D₄	—	9	2	no	—
117	C₃×C₄×D₄	—	9	2	no	—
118	#947	—	3	2	no	—
119	#894	—	3	4	no	—
120	#893	—	3	2	no	—
121	#875	—	3	2	no	—
122	#874	—	3	1	no	—
123	C₄×D₁₂	—	3	2	no	—
124	C₄×Dic₆	—	3	1	no	—
125	C₂²×C₃×D₃	—	3	4	no	—
126	C₃²×Q₈	—	2	2	no	—
127	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
129	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
130	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
132	C₂×C₃×Dic₃	—	3	2	no	—
133	C₂×C₃×Dic₃	—	3	2	no	—
134	C₃×D₁₂	—	6	4	no	—
135	C₃×D₁₂	—	6	4	no	—
136	C₃×D₁₂	—	12	2	no	—
137	C₃×C₄×D₃	—	12	4	no	—
138	C₃×Dic₆	—	6	2	no	—
139	C₂²×D₉	C₂³×C₃	1	4	yes	—
140	Q₈×C₉	—	2	4	no	—
141	Q₈×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	2	no	—
147	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
149	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
150	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
151	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
152	C₂×Dic₉	C₂³×C₃	1	2	yes	—
153	C₂×Dic₉	C₂³×C₃	1	2	yes	—
154	D₃₆	—	2	4	no	—
155	D₃₆	—	2	4	no	—
156	D₃₆	—	4	2	no	—
157	C₄×D₉	—	4	4	no	—
158	Dic₁₈	—	2	2	no	—
159	#559	—	9	1	no	Sylow
160	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
161	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
162	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
163	C₃×D₉	—	4	4	no	—
164	C₂×C₃×Q₈	—	2	1	no	—
165	C₂×C₃×Q₈	—	9	1	no	—
166	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
167	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
168	C₂×C₃×D₄	—	9	2	no	—
169	C₂×C₃×D₄	—	9	2	no	—
170	C₂×C₃×D₄	—	9	2	no	—
171	C₂²×C₃×C₄	—	9	4	no	—
172	C₂×D₁₂	—	3	2	no	—
173	C₂×D₁₂	—	3	2	no	—
174	C₂×D₁₂	—	3	2	no	—
175	C₂×C₄×D₃	—	3	4	no	—
176	C₂×Dic₆	—	3	1	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	—	2	2	no	—
179	C₃×C₄⋊C₄	—	9	2	no	—
180	C₃×C₄⋊C₄	—	9	1	no	—
181	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
183	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
185	C₃×C₂²⋊C₄	—	9	4	no	—
186	C₃×C₂²⋊C₄	—	9	4	no	—
187	C₃×C₂²⋊C₄	—	9	4	no	—
188	C₃×C₄²	—	2	2	no	—
189	C₃×C₄²	—	2	1	no	—
190	C₃×C₄²	—	9	2	no	—
191	C₃×C₄²	C₂×D₉	1	2	yes	—
192	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
193	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
194	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
195	(C₂×D₃)⋊C₄	—	3	4	no	—
196	(C₂×D₃)⋊C₄	—	3	4	no	—
197	(C₂×D₃)⋊C₄	—	3	4	no	—
198	C₄⋊Dic₃	—	3	1	no	—
199	Dic₃⋊C₄	—	3	2	no	—
200	C₄×Dic₃	—	3	2	no	—
201	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
202	C₂×C₃×D₃	—	6	4	no	—
203	C₂×C₃×D₃	—	6	4	no	—
204	C₂×C₃×D₃	—	6	4	no	—
205	C₃²×C₄	—	2	2	no	—
206	C₃²×C₄	—	2	2	no	—
207	C₃²×C₄	—	2	1	no	—
208	C₃²×C₄	#235	1	2	yes	—
209	C₃²×C₄	#239	1	2	yes	—
210	C₃×Dic₃	—	6	2	no	—
211	C₃×Dic₃	—	6	2	no	—
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
214	C₂×D₉	—	2	4	no	—
215	C₂×D₉	—	2	4	no	—
216	C₂×D₉	—	2	4	no	—
217	C₄×C₉	—	2	4	no	—
218	C₄×C₉	—	2	2	no	—
219	C₄×C₉	—	2	2	no	—
220	C₄×C₉	—	2	1	no	—
221	C₄×C₉	—	2	2	no	—
222	C₄×C₉	—	2	2	no	—
223	C₄×C₉	—	4	2	no	—
224	C₄×C₉	—	4	1	no	—
225	C₄×C₉	C₃×#41	1	2	yes	—
226	C₄×C₉	C₃×#41	1	2	yes	—
227	Dic₉	—	2	2	no	—
228	Dic₉	—	2	2	no	—
229	#127	—	9	1	no	—
230	#124	—	9	2	no	—
231	#124	—	9	2	no	—
232	#123	—	9	4	no	—
233	C₄×Q₈	—	9	1	no	—
234	C₄×Q₈	C₃×D₉	1	1	yes	characteristic, complemented
235	C₄×D₄	—	9	2	no	—
236	C₄×D₄	—	9	2	no	—
237	C₃×C₉	#559	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₃	—	9	4	no	—
239	C₂²×D₃	—	3	4	no	—
240	C₃×Q₈	—	2	4	no	—
241	C₃×Q₈	—	2	2	no	—
242	C₃×Q₈	—	2	2	no	—
243	C₃×Q₈	—	18	2	no	—
244	C₃×D₄	—	18	4	no	—
245	C₃×D₄	—	18	4	no	—
246	C₃×D₄	—	36	2	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	9	2	no	—
253	C₂×C₃×C₄	—	9	2	no	—
254	C₂×C₃×C₄	—	36	4	no	—
255	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
256	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
257	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
262	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
263	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
265	C₂×Dic₃	—	3	2	no	—
266	C₂×Dic₃	—	3	2	no	—
267	D₁₂	—	6	4	no	—
268	D₁₂	—	6	4	no	—
269	D₁₂	—	12	2	no	—
270	C₄×D₃	—	12	4	no	—
271	Dic₆	—	6	2	no	—
272	C₂×C₃²	C₂×#235	1	1	yes	characteristic
273	C₂×C₃²	C₂×#239	1	1	yes	characteristic
274	C₂×C₃²	#1009	1	1	yes	characteristic
275	C₃×D₃	—	12	4	no	—
276	C₂×C₉	—	2	1	no	—
277	C₂×C₉	—	2	1	no	—
278	C₂×C₉	—	2	1	no	—
279	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
280	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
281	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
282	D₉	—	4	4	no	—
283	C₂×Q₈	—	9	1	no	—
284	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
285	C₂×D₄	—	9	2	no	—
286	C₂×D₄	—	9	2	no	—
287	C₂×D₄	—	9	2	no	—
288	C₂²×C₄	—	9	4	no	—
289	C₄⋊C₄	—	9	1	no	—
290	C₄⋊C₄	—	9	2	no	—
291	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
292	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
293	C₂²⋊C₄	—	9	4	no	—
294	C₂²⋊C₄	—	9	4	no	—
295	C₂²⋊C₄	—	9	4	no	—
296	C₄²	—	9	2	no	—
297	C₄²	C₂×C₃×D₉	1	2	yes	—
298	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	18	4	no	—
301	C₂²×C₃	—	18	4	no	—
302	C₂²×C₃	—	18	4	no	—
303	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
304	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
305	C₂×D₃	—	6	4	no	—
306	C₂×D₃	—	6	4	no	—
307	C₂×D₃	—	6	4	no	—
308	C₃×C₄	—	2	4	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	18	2	no	—
320	C₃×C₄	—	18	2	no	—
321	C₃×C₄	#3697	1	2	yes	—
322	C₃×C₄	#3701	1	2	yes	—
323	C₃×C₄	C₃×#235	1	2	yes	—
324	C₃×C₄	C₃×#239	1	2	yes	—
325	Dic₃	—	6	2	no	—
326	Dic₃	—	6	2	no	—
327	C₃²	#5585	1	1	yes	characteristic
328	C₉	—	2	1	no	—
329	C₉	C₃×#559	1	1	yes	characteristic, complemented
330	C₂³	—	9	4	no	—
331	Q₈	—	2	2	no	—
332	Q₈	—	18	2	no	—
333	D₄	—	18	4	no	—
334	D₄	—	18	4	no	—
335	D₄	—	36	2	no	—
336	C₂×C₄	—	9	2	no	—
337	C₂×C₄	—	9	2	no	—
338	C₂×C₄	—	36	4	no	—
339	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
340	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
341	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	36	4	no	—
348	C₂×C₃	C₂×#3697	1	1	yes	characteristic
349	C₂×C₃	C₂×#3701	1	1	yes	characteristic
350	C₂×C₃	#63715	1	1	yes	characteristic
351	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
352	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
353	C₂×C₃	C₃×#1009	1	1	yes	characteristic
354	D₃	—	12	4	no	—
355	C₂²	—	18	4	no	—
356	C₂²	—	18	4	no	—
357	C₂²	—	18	4	no	—
358	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	1	no	—
362	C₄	—	18	2	no	—
363	C₄	—	18	2	no	—
364	C₄	C₃×#3697	1	2	yes	—
365	C₄	C₃×#3701	1	2	yes	—
366	C₃	—	2	1	no	—
367	C₃	#10589687	1	1	yes	characteristic, direct product factor
368	C₃	C₃×#5585	1	1	yes	characteristic
369	C₂	—	36	4	no	—
370	C₂	C₂×C₃×#3697	1	1	yes	characteristic
371	C₂	C₂×C₃×#3701	1	1	yes	characteristic
372	C₂	C₃×#63715	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₄×Q₈×C₉	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₃×#63436	C₂
hypercenter	C₃×C₄×Q₈	D₉
hypocenter	C₉	C₃×#559
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×Q₈×C₉	C₂	semidirect
2. C₃×#63509	C₂	semidirect
3. C₃×#63456	C₂	semidirect
4. C₃×#63455	C₂	semidirect
5. C₃×#63437	C₂	semidirect
7. C₃×C₄×D₃₆	C₂	semidirect
8. C₃×C₄×Dic₁₈	C₂	semidirect
10. #10589687	C₃	direct (N × H)
36. C₄×Q₈×C₉	C₂×C₃	semidirect
37. #63509	C₂×C₃	semidirect
38. #63456	C₂×C₃	semidirect
39. #63455	C₂×C₃	semidirect
40. #63437	C₂×C₃	semidirect
42. C₄×D₃₆	C₂×C₃	semidirect
43. C₄×Dic₁₈	C₂×C₃	semidirect
114. C₃×C₄×Q₈	D₉	semidirect
234. C₄×Q₈	C₃×D₉	semidirect
237. C₃×C₉	#559	semidirect
329. C₉	C₃×#559	semidirect
367. C₃	#10589687	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×Q₈×C₉	2
C₃×#63509	2
C₃×#63456	2
C₃×#63455	2
C₃×#63437	2
C₃×#63436	2
C₃×C₄×D₃₆	2
C₃×C₄×Dic₁₈	2
C₃×#5585	3
#10589687	3

Subgroups — C3×#10589687 #13152691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589687 #13152691