Subgroups — C₃×#10589681 #13152685

Order 1728.

754 conjugacy classes of subgroups.

The subgroup lattice has 368 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×#63508	C₂	1	2	yes	maximal, complemented
3	C₃×#63458	C₂	1	4	yes	maximal, complemented
4	C₃×C₄⋊C₄×D₉	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×D₃₆	C₂	1	1	yes	maximal, characteristic
6	C₃×C₄×D₃₆	C₂	1	2	yes	maximal
7	C₃×#63432	C₂	1	2	yes	maximal, complemented
8	C₃×#63431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5579	—	3	1	no	maximal
10	#10589681	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	1	yes	characteristic
13	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
14	C₂×C₃×C₄×D₉	C₂²	1	4	yes	—
15	C₂×C₃×Dic₁₈	C₂²	1	2	yes	—
16	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
19	C₃×C₄²×C₉	C₂²	1	2	yes	—
20	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	—
21	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
22	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
23	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
24	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
25	C₃×Dic₉⋊C₄	C₂²	1	4	yes	—
26	C₃×Dic₉⋊C₄	C₂²	1	4	yes	—
27	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic
28	C₃×#946	—	3	2	no	—
29	C₃×#896	—	3	4	no	—
30	C₃×D₃×C₄⋊C₄	—	3	2	no	—
31	C₃×C₄×D₁₂	—	3	2	no	—
32	C₃×C₄×D₁₂	—	3	1	no	—
33	C₃×#870	—	3	2	no	—
34	C₃×#869	—	3	1	no	—
35	C₄×Q₈×C₉	—	2	1	no	—
36	C₄×Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
37	#63508	C₂×C₃	1	2	yes	complemented
38	#63458	C₂×C₃	1	4	yes	complemented
39	C₄⋊C₄×D₉	C₂×C₃	1	2	yes	complemented
40	C₄×D₃₆	C₂×C₃	1	2	yes	—
41	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic
42	#63432	C₂×C₃	1	2	yes	complemented
43	#63431	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₃×D₉	C₂³	1	2	yes	—
45	C₃×Q₈×C₉	—	2	2	no	—
46	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
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	4	yes	—
52	C₂×C₃×Dic₉	C₂³	1	2	yes	—
53	C₃×D₃₆	Q₈	1	4	yes	complemented
54	C₃×C₄×D₉	—	2	4	no	—
55	C₃×C₄×D₉	—	4	4	no	—
56	C₃×Dic₁₈	—	4	2	no	—
57	C₃×#554	—	9	1	no	—
58	#5579	—	3	1	no	—
59	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
60	C₂×C₃×D₁₂	—	3	1	no	—
61	C₂×C₃×C₄×D₃	—	3	2	no	—
62	C₂×C₃×C₄×D₃	—	3	4	no	—
63	C₂×C₃×Dic₆	—	3	2	no	—
64	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
65	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
66	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
67	C₃²×C₄²	C₂×D₃	1	2	yes	—
68	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
69	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
70	C₃×C₄⋊Dic₃	—	3	2	no	—
71	C₃×C₄⋊Dic₃	—	3	2	no	—
72	C₃×C₄⋊Dic₃	—	3	1	no	—
73	C₃×Dic₃⋊C₄	—	3	4	no	—
74	C₃×Dic₃⋊C₄	—	3	4	no	—
75	C₂×Q₈×C₉	—	2	1	no	—
76	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
77	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
79	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
80	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
81	C₉×C₄⋊C₄	—	2	1	no	—
82	C₉×C₄⋊C₄	—	2	2	no	—
83	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₄²×C₉	—	2	1	no	—
86	C₄²×C₉	—	2	2	no	—
87	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
88	C₄²×C₉	C₂²×C₃	1	2	yes	—
89	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
90	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
91	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
92	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
93	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
94	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
95	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
96	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
97	C₂×C₃×D₉	—	2	2	no	—
98	C₂×C₃×D₉	—	2	2	no	—
99	C₂×C₃×D₉	C₂×Q₈	1	4	yes	—
100	C₃×C₄×C₉	—	2	2	no	—
101	C₃×C₄×C₉	—	2	1	no	—
102	C₃×C₄×C₉	—	2	2	no	—
103	C₃×C₄×C₉	C₂×Q₈	1	2	yes	—
104	C₃×C₄×C₉	#41	1	2	yes	—
105	C₃×Dic₉	—	2	2	no	—
106	C₃×Dic₉	—	2	4	no	—
107	C₃×C₄⋊Q₈	—	9	1	no	—
108	C₃×#125	—	9	2	no	—
109	C₃×C₂²⋊Q₈	—	9	2	no	—
110	C₃×C₂²⋊Q₈	—	9	4	no	—
111	C₃×C₄×Q₈	—	2	1	no	—
112	C₃×C₄×Q₈	D₉	1	1	yes	characteristic, complemented
113	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
114	C₃×C₄×D₄	—	9	2	no	—
115	C₃×C₄×D₄	—	9	1	no	—
116	C₂×C₃×C₄⋊C₄	—	9	2	no	—
117	#946	—	3	2	no	—
118	#896	—	3	4	no	—
119	D₃×C₄⋊C₄	—	3	2	no	—
120	C₄×D₁₂	—	3	2	no	—
121	C₄×D₁₂	—	3	1	no	—
122	#870	—	3	2	no	—
123	#869	—	3	1	no	—
124	C₂²×C₃×D₃	—	3	2	no	—
125	C₃²×Q₈	—	2	2	no	—
126	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
127	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
128	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
131	C₂×C₃×Dic₃	—	3	2	no	—
132	C₂×C₃×Dic₃	—	3	4	no	—
133	C₃×D₁₂	—	3	4	no	—
134	C₃×C₄×D₃	—	6	4	no	—
135	C₃×C₄×D₃	—	12	4	no	—
136	C₃×Dic₆	—	12	2	no	—
137	C₂²×D₉	C₂³×C₃	1	2	yes	—
138	Q₈×C₉	—	2	4	no	—
139	Q₈×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×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	C₂³×C₃	1	2	yes	—
146	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
147	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
150	C₂×Dic₉	C₂³×C₃	1	2	yes	—
151	C₂×Dic₉	C₂³×C₃	1	4	yes	—
152	D₃₆	C₃×Q₈	1	4	yes	complemented
153	C₄×D₉	—	2	4	no	—
154	C₄×D₉	—	4	4	no	—
155	Dic₁₈	—	4	2	no	—
156	#554	—	9	1	no	Sylow
157	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
159	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
160	C₃×D₉	—	2	4	no	—
161	C₂×C₃×Q₈	—	2	1	no	—
162	C₂×C₃×Q₈	—	9	2	no	—
163	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
164	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
165	C₂×C₃×D₄	—	9	1	no	—
166	C₂²×C₃×C₄	—	9	2	no	—
167	C₂²×C₃×C₄	—	9	4	no	—
168	C₂×D₁₂	—	3	1	no	—
169	C₂×C₄×D₃	—	3	2	no	—
170	C₂×C₄×D₃	—	3	4	no	—
171	C₂×Dic₆	—	3	2	no	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	—	9	4	no	—
175	C₃×C₄⋊C₄	—	9	4	no	—
176	C₃×C₄⋊C₄	—	9	2	no	—
177	C₃×C₄⋊C₄	—	9	1	no	—
178	C₃×C₄⋊C₄	—	9	2	no	—
179	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
181	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
183	C₃×C₂²⋊C₄	—	9	2	no	—
184	C₃×C₂²⋊C₄	—	9	4	no	—
185	C₃×C₄²	—	2	2	no	—
186	C₃×C₄²	—	2	1	no	—
187	C₃×C₄²	C₂×D₉	1	2	yes	—
188	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
189	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
190	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
191	(C₂×D₃)⋊C₄	—	3	2	no	—
192	(C₂×D₃)⋊C₄	—	3	4	no	—
193	C₄⋊Dic₃	—	3	2	no	—
194	C₄⋊Dic₃	—	3	2	no	—
195	C₄⋊Dic₃	—	3	1	no	—
196	Dic₃⋊C₄	—	3	4	no	—
197	Dic₃⋊C₄	—	3	4	no	—
198	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
199	C₂×C₃×D₃	—	3	4	no	—
200	C₂×C₃×D₃	—	6	2	no	—
201	C₂×C₃×D₃	—	6	2	no	—
202	C₃²×C₄	—	2	2	no	—
203	C₃²×C₄	—	2	1	no	—
204	C₃²×C₄	—	2	2	no	—
205	C₃²×C₄	#235	1	2	yes	—
206	C₃²×C₄	D₃×Q₈	1	2	yes	—
207	C₃×Dic₃	—	6	2	no	—
208	C₃×Dic₃	—	6	4	no	—
209	C₂²×C₉	—	2	1	no	—
210	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
211	C₂×D₉	—	2	2	no	—
212	C₂×D₉	—	2	2	no	—
213	C₂×D₉	C₂×C₃×Q₈	1	4	yes	—
214	C₄×C₉	—	2	4	no	—
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	2	1	no	—
217	C₄×C₉	—	2	2	no	—
218	C₄×C₉	—	2	2	no	—
219	C₄×C₉	—	2	2	no	—
220	C₄×C₉	—	4	1	no	—
221	C₄×C₉	—	4	2	no	—
222	C₄×C₉	C₂×C₃×Q₈	1	2	yes	—
223	C₄×C₉	C₃×#41	1	2	yes	—
224	Dic₉	—	2	2	no	—
225	Dic₉	—	2	4	no	—
226	C₄⋊Q₈	—	9	1	no	—
227	#125	—	9	2	no	—
228	C₂²⋊Q₈	—	9	2	no	—
229	C₂²⋊Q₈	—	9	4	no	—
230	C₄×Q₈	C₃×D₉	1	1	yes	characteristic, complemented
231	C₄×D₄	—	9	2	no	—
232	C₄×D₄	—	9	1	no	—
233	C₂×C₄⋊C₄	—	9	2	no	—
234	C₃×C₉	#554	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₃	—	9	2	no	—
236	C₂²×D₃	—	3	2	no	—
237	C₃×Q₈	—	2	4	no	—
238	C₃×Q₈	—	2	2	no	—
239	C₃×Q₈	—	2	2	no	—
240	C₃×Q₈	—	36	2	no	—
241	C₃×D₄	—	9	4	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	9	2	no	—
248	C₂×C₃×C₄	—	9	4	no	—
249	C₂×C₃×C₄	—	18	4	no	—
250	C₂×C₃×C₄	—	36	4	no	—
251	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
252	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
254	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
257	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
258	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
261	C₂×Dic₃	—	3	2	no	—
262	C₂×Dic₃	—	3	4	no	—
263	D₁₂	—	3	4	no	—
264	C₄×D₃	—	6	4	no	—
265	C₄×D₃	—	12	4	no	—
266	Dic₆	—	12	2	no	—
267	C₂×C₃²	C₂×#235	1	1	yes	characteristic
268	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
269	C₂×C₃²	#1009	1	1	yes	characteristic
270	C₃×D₃	—	6	4	no	—
271	C₂×C₉	—	2	1	no	—
272	C₂×C₉	—	2	1	no	—
273	C₂×C₉	—	2	1	no	—
274	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
275	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
276	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
277	D₉	—	2	4	no	—
278	C₂×Q₈	—	9	2	no	—
279	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
280	C₂×D₄	—	9	1	no	—
281	C₂²×C₄	—	9	2	no	—
282	C₂²×C₄	—	9	4	no	—
283	C₄⋊C₄	—	9	4	no	—
284	C₄⋊C₄	—	9	2	no	—
285	C₄⋊C₄	—	9	1	no	—
286	C₄⋊C₄	—	9	2	no	—
287	C₄⋊C₄	—	9	4	no	—
288	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
289	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
290	C₂²⋊C₄	—	9	2	no	—
291	C₂²⋊C₄	—	9	4	no	—
292	C₄²	C₂×C₃×D₉	1	2	yes	—
293	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	9	4	no	—
296	C₂²×C₃	—	18	2	no	—
297	C₂²×C₃	—	18	2	no	—
298	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
299	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
300	C₂×D₃	—	3	4	no	—
301	C₂×D₃	—	6	2	no	—
302	C₂×D₃	—	6	2	no	—
303	C₃×C₄	—	2	4	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	2	2	no	—
312	C₃×C₄	—	4	2	no	—
313	C₃×C₄	—	4	1	no	—
314	C₃×C₄	—	18	2	no	—
315	C₃×C₄	—	18	4	no	—
316	C₃×C₄	#3697	1	2	yes	—
317	C₃×C₄	Q₈×D₉	1	2	yes	—
318	C₃×C₄	C₃×#235	1	2	yes	—
319	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
320	Dic₃	—	6	2	no	—
321	Dic₃	—	6	4	no	—
322	C₃²	#5579	1	1	yes	characteristic
323	C₉	—	2	1	no	—
324	C₉	C₃×#554	1	1	yes	characteristic, complemented
325	C₂³	—	9	2	no	—
326	Q₈	—	2	2	no	—
327	Q₈	—	36	2	no	—
328	D₄	—	9	4	no	—
329	C₂×C₄	—	9	2	no	—
330	C₂×C₄	—	9	4	no	—
331	C₂×C₄	—	18	4	no	—
332	C₂×C₄	—	36	4	no	—
333	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
334	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
335	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
336	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
338	C₂×C₃	—	2	1	no	—
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	2	1	no	—
341	C₂×C₃	—	18	4	no	—
342	C₂×C₃	C₂×#3697	1	1	yes	characteristic
343	C₂×C₃	C₂×Q₈×D₉	1	1	yes	characteristic
344	C₂×C₃	#63715	1	1	yes	characteristic
345	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
346	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
347	C₂×C₃	C₃×#1009	1	1	yes	characteristic
348	D₃	—	6	4	no	—
349	C₂²	—	9	4	no	—
350	C₂²	—	18	2	no	—
351	C₂²	—	18	2	no	—
352	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	18	2	no	—
357	C₄	—	18	4	no	—
358	C₄	C₃×#3697	1	2	yes	—
359	C₄	C₃×Q₈×D₉	1	2	yes	—
360	C₃	—	2	1	no	—
361	C₃	#10589681	1	1	yes	characteristic, direct product factor
362	C₃	C₃×#5579	1	1	yes	characteristic
363	C₂	—	18	4	no	—
364	C₂	C₂×C₃×#3697	1	1	yes	characteristic
365	C₂	C₂×C₃×Q₈×D₉	1	1	yes	characteristic
366	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	C₂×C₃×D₃₆	C₂²
hypercenter	C₃×C₄×Q₈	D₉
hypocenter	C₉	C₃×#554
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×#63508	C₂	semidirect
3. C₃×#63458	C₂	semidirect
4. C₃×C₄⋊C₄×D₉	C₂	semidirect
7. C₃×#63432	C₂	semidirect
8. C₃×#63431	C₂	semidirect
10. #10589681	C₃	direct (N × H)
36. C₄×Q₈×C₉	C₂×C₃	semidirect
37. #63508	C₂×C₃	semidirect
38. #63458	C₂×C₃	semidirect
39. C₄⋊C₄×D₉	C₂×C₃	semidirect
42. #63432	C₂×C₃	semidirect
43. #63431	C₂×C₃	semidirect
53. C₃×D₃₆	Q₈	semidirect
112. C₃×C₄×Q₈	D₉	semidirect
152. D₃₆	C₃×Q₈	semidirect
230. C₄×Q₈	C₃×D₉	semidirect
234. C₃×C₉	#554	semidirect
324. C₉	C₃×#554	semidirect
361. C₃	#10589681	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×#63508	2
C₃×#63458	2
C₃×C₄⋊C₄×D₉	2
C₃×C₄×D₃₆	2
C₃×#63432	2
C₃×#63431	2
C₃×#5579	3
#10589681	3

Subgroups — C3×#10589681 #13152685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589681 #13152685