Subgroups — C₃²×#5051 #13162482

Order 1728.

980 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×#216	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#924	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₃²×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₃²×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#810	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#807	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#467	—	3	1	no	maximal
9	C₃×#5051	C₃	1	4	yes	maximal, direct product factor
10	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
13	C₃³×C₄⋊C₄	—	2	1	no	—
14	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃³×C₂²⋊C₄	—	2	1	no	—
16	C₃²×#217	—	2	1	no	—
17	C₃²×#216	—	2	2	no	—
18	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₃²×Dic₃⋊C₄	—	2	1	no	—
20	C₂×C₃²×C₃⋊C₈	—	2	2	no	—
21	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₃²×Q₁₆	—	3	1	no	—
24	C₂²×C₃²×C₈	—	3	1	no	—
25	C₃²×C₂²⋊Q₈	—	2	4	no	—
26	C₃²×C₂²⋊Q₈	—	3	1	no	—
27	C₃²×C₂²⋊Q₈	D₃	1	1	yes	characteristic
28	C₃²×C₂²⋊Q₈	C₂×C₃	1	4	yes	—
29	C₂×C₃×#216	C₂×C₃	1	4	yes	complemented
30	C₃×#924	C₂×C₃	1	4	yes	—
31	C₂²×C₃×C₃⋊C₈	C₂×C₃	1	4	yes	—
32	C₃²×#107	—	3	1	no	—
33	C₃²×#103	—	3	1	no	—
34	C₃²×#103	—	3	1	no	—
35	C₃×#835	C₂×C₃	1	4	yes	complemented
36	C₃×#810	C₂×C₃	1	4	yes	complemented
37	C₃×#807	C₂×C₃	1	4	yes	complemented
38	C₂³×C₃³	D₄	1	1	yes	characteristic
39	C₃³×Q₈	—	2	1	no	—
40	C₃³×Q₈	—	2	1	no	—
41	C₂×C₃³×C₄	—	2	1	no	—
42	C₂×C₃³×C₄	—	2	1	no	—
43	C₂×C₃³×C₄	—	2	1	no	—
44	C₂×C₃³×C₄	—	2	1	no	—
45	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
46	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
47	C₂×C₃²×Dic₃	—	2	1	no	—
48	C₂×C₃²×Dic₃	—	2	1	no	—
49	C₃²×Dic₆	—	2	1	no	—
50	C₃²×Dic₆	—	2	1	no	—
51	C₃²×C₃⋊C₈	—	2	1	no	—
52	C₃²×C₃⋊C₈	D₄	1	2	yes	—
53	C₃×#467	—	3	4	no	—
54	#5051	C₃²	1	1	yes	characteristic, direct product factor
55	C₂×C₃²×Q₈	—	2	4	no	—
56	C₂×C₃²×Q₈	—	3	1	no	—
57	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
58	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
59	C₂²×C₃²×C₄	—	2	4	no	—
60	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
62	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
63	C₃²×Q₁₆	—	6	2	no	—
64	C₂×C₃²×C₈	—	3	1	no	—
65	C₂×C₃²×C₈	—	3	1	no	—
66	C₂×C₃²×C₈	—	6	2	no	—
67	C₃²×C₄⋊C₄	—	2	8	no	—
68	C₃²×C₄⋊C₄	—	2	4	no	—
69	C₃²×C₄⋊C₄	—	2	1	no	—
70	C₃²×C₄⋊C₄	—	2	4	no	—
71	C₃²×C₄⋊C₄	—	3	1	no	—
72	C₃²×C₄⋊C₄	—	6	1	no	—
73	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
74	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
75	C₃²×C₂²⋊C₄	—	2	8	no	—
76	C₃²×C₂²⋊C₄	—	2	1	no	—
77	C₃²×C₂²⋊C₄	—	2	4	no	—
78	C₃²×C₂²⋊C₄	—	6	1	no	—
79	C₃×#217	—	2	4	no	—
80	C₃×#216	—	2	8	no	—
81	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
82	C₃×Dic₃⋊C₄	—	2	4	no	—
83	C₂×C₃×C₃⋊C₈	—	2	8	no	—
84	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
85	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
86	C₂²×C₃³	—	2	1	no	—
87	C₂²×C₃³	—	2	1	no	—
88	C₂²×C₃³	Q₁₆	1	2	yes	complemented
89	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
90	C₃³×C₄	—	2	1	no	—
91	C₃³×C₄	—	4	1	no	—
92	C₃³×C₄	—	4	1	no	—
93	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
94	C₃³×C₄	#41	1	1	yes	characteristic
95	C₃²×Dic₃	—	4	1	no	—
96	C₃²×Dic₃	—	4	1	no	—
97	C₂×C₃×Q₁₆	—	3	4	no	—
98	C₂²×C₃×C₈	—	3	4	no	—
99	C₃×C₂²⋊Q₈	—	2	4	no	—
100	C₃×C₂²⋊Q₈	—	3	4	no	—
101	C₃×C₂²⋊Q₈	C₃×D₃	1	4	yes	—
102	C₃×C₂²⋊Q₈	C₂×C₃²	1	1	yes	characteristic
103	C₂×#216	C₂×C₃²	1	1	yes	characteristic, complemented
104	#924	C₂×C₃²	1	1	yes	characteristic
105	C₂²×C₃⋊C₈	C₂×C₃²	1	1	yes	characteristic
106	C₃×#107	—	3	4	no	—
107	C₃×#103	—	3	4	no	—
108	C₃×#103	—	3	4	no	—
109	#835	C₂×C₃²	1	1	yes	characteristic, complemented
110	#810	C₂×C₃²	1	1	yes	characteristic, complemented
111	#807	C₂×C₃²	1	1	yes	characteristic, complemented
112	C₂³×C₃²	—	2	4	no	—
113	C₂³×C₃²	#67	1	1	yes	characteristic
114	C₂³×C₃²	C₃×D₄	1	4	yes	—
115	C₃²×Q₈	—	2	1	no	—
116	C₃²×Q₈	—	2	1	no	—
117	C₃²×Q₈	—	2	4	no	—
118	C₃²×Q₈	—	2	4	no	—
119	C₃²×Q₈	—	4	4	no	—
120	C₃²×Q₈	—	4	4	no	—
121	C₃²×Q₈	—	6	1	no	—
122	C₃²×Q₈	—	6	1	no	—
123	C₂×C₃²×C₄	—	2	1	no	—
124	C₂×C₃²×C₄	—	2	1	no	—
125	C₂×C₃²×C₄	—	2	8	no	—
126	C₂×C₃²×C₄	—	2	8	no	—
127	C₂×C₃²×C₄	—	2	1	no	—
128	C₂×C₃²×C₄	—	2	1	no	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	2	4	no	—
133	C₂×C₃²×C₄	—	2	4	no	—
134	C₂×C₃²×C₄	—	2	4	no	—
135	C₂×C₃²×C₄	—	4	4	no	—
136	C₂×C₃²×C₄	—	4	4	no	—
137	C₂×C₃²×C₄	—	6	1	no	—
138	C₂×C₃²×C₄	—	6	1	no	—
139	C₂×C₃²×C₄	#67	1	1	yes	characteristic
140	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
141	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
143	C₂×C₃×Dic₃	—	2	4	no	—
144	C₂×C₃×Dic₃	—	2	4	no	—
145	C₃×Dic₆	—	2	4	no	—
146	C₃×Dic₆	—	2	4	no	—
147	C₃²×C₈	—	3	2	no	—
148	C₃²×C₈	—	6	1	no	—
149	C₃×C₃⋊C₈	—	2	4	no	—
150	C₃×C₃⋊C₈	C₃×D₄	1	8	yes	—
151	#467	—	3	1	no	Sylow
152	C₂×C₃³	—	2	2	no	—
153	C₂×C₃³	#121	1	1	yes	characteristic
154	C₂×C₃³	C₂×Q₁₆	1	1	yes	characteristic
155	C₂×C₃³	#135	1	1	yes	characteristic
156	C₂×C₃×Q₈	—	2	4	no	—
157	C₂×C₃×Q₈	—	3	4	no	—
158	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
159	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
162	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
163	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
164	C₃×Q₁₆	—	6	8	no	—
165	C₂×C₃×C₈	—	3	4	no	—
166	C₂×C₃×C₈	—	3	4	no	—
167	C₂×C₃×C₈	—	6	8	no	—
168	C₃×C₄⋊C₄	—	2	8	no	—
169	C₃×C₄⋊C₄	—	2	4	no	—
170	C₃×C₄⋊C₄	—	2	1	no	—
171	C₃×C₄⋊C₄	—	2	4	no	—
172	C₃×C₄⋊C₄	—	3	4	no	—
173	C₃×C₄⋊C₄	—	6	4	no	—
174	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
175	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
176	C₃×C₂²⋊C₄	—	2	8	no	—
177	C₃×C₂²⋊C₄	—	2	4	no	—
178	C₃×C₂²⋊C₄	—	2	1	no	—
179	C₃×C₂²⋊C₄	—	6	4	no	—
180	#217	—	2	1	no	—
181	#216	—	2	2	no	—
182	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
183	Dic₃⋊C₄	—	2	1	no	—
184	C₂×C₃⋊C₈	—	2	2	no	—
185	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
186	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
187	C₂²×C₃²	—	2	1	no	—
188	C₂²×C₃²	—	2	1	no	—
189	C₂²×C₃²	—	2	8	no	—
190	C₂²×C₃²	—	2	4	no	—
191	C₂²×C₃²	—	2	4	no	—
192	C₂²×C₃²	—	2	4	no	—
193	C₂²×C₃²	—	4	4	no	—
194	C₂²×C₃²	—	4	4	no	—
195	C₂²×C₃²	#216	1	2	yes	complemented
196	C₂²×C₃²	C₃×Q₁₆	1	8	yes	complemented
197	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
198	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
199	C₃²×C₄	—	2	1	no	—
200	C₃²×C₄	—	2	4	no	—
201	C₃²×C₄	—	2	4	no	—
202	C₃²×C₄	—	2	4	no	—
203	C₃²×C₄	—	4	4	no	—
204	C₃²×C₄	—	4	8	no	—
205	C₃²×C₄	—	4	8	no	—
206	C₃²×C₄	—	4	1	no	—
207	C₃²×C₄	—	4	1	no	—
208	C₃²×C₄	—	4	4	no	—
209	C₃²×C₄	—	4	4	no	—
210	C₃²×C₄	—	12	1	no	—
211	C₃²×C₄	—	12	1	no	—
212	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
213	C₃²×C₄	#237	1	1	yes	characteristic
214	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
215	C₃²×C₄	C₃×#41	1	4	yes	—
216	C₃×Dic₃	—	4	4	no	—
217	C₃×Dic₃	—	4	4	no	—
218	C₂×Q₁₆	—	3	1	no	—
219	C₂²×C₈	—	3	1	no	—
220	C₂²⋊Q₈	—	3	1	no	—
221	C₂²⋊Q₈	C₃²×D₃	1	1	yes	characteristic
222	#107	—	3	1	no	—
223	#103	—	3	1	no	—
224	#103	—	3	1	no	—
225	C₃³	#467	1	1	yes	characteristic, complemented, Sylow
226	C₂³×C₃	—	2	4	no	—
227	C₂³×C₃	C₃×#67	1	4	yes	—
228	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
229	C₃×Q₈	—	2	4	no	—
230	C₃×Q₈	—	2	4	no	—
231	C₃×Q₈	—	2	1	no	—
232	C₃×Q₈	—	2	1	no	—
233	C₃×Q₈	—	4	4	no	—
234	C₃×Q₈	—	4	4	no	—
235	C₃×Q₈	—	6	4	no	—
236	C₃×Q₈	—	6	4	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	8	no	—
242	C₂×C₃×C₄	—	2	8	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	4	4	no	—
250	C₂×C₃×C₄	—	4	4	no	—
251	C₂×C₃×C₄	—	6	4	no	—
252	C₂×C₃×C₄	—	6	4	no	—
253	C₂×C₃×C₄	C₃×#67	1	4	yes	—
254	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
256	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
257	C₂×Dic₃	—	2	1	no	—
258	C₂×Dic₃	—	2	1	no	—
259	Dic₆	—	2	1	no	—
260	Dic₆	—	2	1	no	—
261	C₃×C₈	—	3	8	no	—
262	C₃×C₈	—	6	4	no	—
263	C₃⋊C₈	—	2	1	no	—
264	C₃⋊C₈	C₃²×D₄	1	2	yes	—
265	C₂×C₃²	—	2	2	no	—
266	C₂×C₃²	—	2	4	no	—
267	C₂×C₃²	—	2	4	no	—
268	C₂×C₃²	—	2	4	no	—
269	C₂×C₃²	—	2	8	no	—
270	C₂×C₃²	—	4	8	no	—
271	C₂×C₃²	#939	1	1	yes	characteristic
272	C₂×C₃²	C₂×#216	1	1	yes	characteristic
273	C₂×C₃²	#950	1	1	yes	characteristic
274	C₂×C₃²	C₃×#121	1	4	yes	—
275	C₂×C₃²	C₂×C₃×Q₁₆	1	4	yes	—
276	C₂×C₃²	C₃×#135	1	4	yes	—
277	C₂×Q₈	—	3	1	no	—
278	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
280	Q₁₆	—	6	2	no	—
281	C₂×C₈	—	3	1	no	—
282	C₂×C₈	—	3	1	no	—
283	C₂×C₈	—	6	2	no	—
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	—	3	1	no	—
286	C₄⋊C₄	—	6	1	no	—
287	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
288	C₂²⋊C₄	—	2	1	no	—
289	C₂²⋊C₄	—	6	1	no	—
290	C₂²×C₃	—	2	4	no	—
291	C₂²×C₃	—	2	4	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	2	4	no	—
295	C₂²×C₃	—	2	8	no	—
296	C₂²×C₃	—	4	4	no	—
297	C₂²×C₃	—	4	4	no	—
298	C₂²×C₃	C₃×#216	1	8	yes	complemented
299	C₂²×C₃	C₃²×Q₁₆	1	2	yes	complemented
300	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
301	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
302	C₃×C₄	—	2	4	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	4	no	—
305	C₃×C₄	—	2	4	no	—
306	C₃×C₄	—	4	4	no	—
307	C₃×C₄	—	4	8	no	—
308	C₃×C₄	—	4	8	no	—
309	C₃×C₄	—	4	4	no	—
310	C₃×C₄	—	4	4	no	—
311	C₃×C₄	—	4	1	no	—
312	C₃×C₄	—	4	1	no	—
313	C₃×C₄	—	12	4	no	—
314	C₃×C₄	—	12	4	no	—
315	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
316	C₃×C₄	C₃×#237	1	4	yes	—
317	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
318	C₃×C₄	C₃²×#41	1	1	yes	characteristic
319	Dic₃	—	4	1	no	—
320	Dic₃	—	4	1	no	—
321	C₃²	—	2	4	no	—
322	C₃²	#5051	1	1	yes	characteristic, direct product factor
323	C₃²	C₃×#467	1	4	yes	complemented
324	C₂³	C₃²×#67	1	1	yes	characteristic
325	Q₈	—	2	1	no	—
326	Q₈	—	2	1	no	—
327	Q₈	—	6	1	no	—
328	Q₈	—	6	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	6	1	no	—
334	C₂×C₄	—	6	1	no	—
335	C₂×C₄	C₃²×#67	1	1	yes	characteristic
336	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
337	C₈	—	3	2	no	—
338	C₈	—	6	1	no	—
339	C₂×C₃	—	2	2	no	—
340	C₂×C₃	—	2	8	no	—
341	C₂×C₃	—	2	4	no	—
342	C₂×C₃	—	2	4	no	—
343	C₂×C₃	—	2	4	no	—
344	C₂×C₃	—	4	8	no	—
345	C₂×C₃	C₃×#939	1	4	yes	—
346	C₂×C₃	C₂×C₃×#216	1	4	yes	—
347	C₂×C₃	C₃×#950	1	4	yes	—
348	C₂×C₃	C₃²×#121	1	1	yes	characteristic
349	C₂×C₃	C₂×C₃²×Q₁₆	1	1	yes	characteristic
350	C₂×C₃	C₃²×#135	1	1	yes	characteristic
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	C₃²×#216	1	2	yes	complemented
354	C₂²	C₂×C₃²×#67	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	4	1	no	—
357	C₄	—	4	1	no	—
358	C₄	—	12	1	no	—
359	C₄	—	12	1	no	—
360	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
361	C₄	C₃²×#237	1	1	yes	characteristic
362	C₃	—	2	4	no	—
363	C₃	C₃×#5051	1	4	yes	direct product factor
364	C₃	C₃²×#467	1	1	yes	characteristic, complemented
365	C₂	—	2	2	no	—
366	C₂	C₃²×#939	1	1	yes	characteristic
367	C₂	C₂×C₃²×#216	1	1	yes	characteristic
368	C₂	C₃²×#950	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂³×C₃²
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₃³×C₂²⋊Q₈	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂³×C₃³	D₄
hypercenter	C₃²×C₂²⋊Q₈	D₃
hypocenter	C₃	C₃²×#467
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃²×C₄ ◁ C₃²×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×#216	C₂	semidirect
5. C₃²×#835	C₂	semidirect
6. C₃²×#810	C₂	semidirect
7. C₃²×#807	C₂	semidirect
9. C₃×#5051	C₃	direct (N × H)
29. C₂×C₃×#216	C₂×C₃	semidirect
35. C₃×#835	C₂×C₃	semidirect
36. C₃×#810	C₂×C₃	semidirect
37. C₃×#807	C₂×C₃	semidirect
54. #5051	C₃²	direct (N × H)
88. C₂²×C₃³	Q₁₆	semidirect
103. C₂×#216	C₂×C₃²	semidirect
109. #835	C₂×C₃²	semidirect
110. #810	C₂×C₃²	semidirect
111. #807	C₂×C₃²	semidirect
195. C₂²×C₃²	#216	semidirect
196. C₂²×C₃²	C₃×Q₁₆	semidirect
225. C₃³	#467	semidirect
298. C₂²×C₃	C₃×#216	semidirect
299. C₂²×C₃	C₃²×Q₁₆	semidirect
322. C₃²	#5051	direct (N × H)
323. C₃²	C₃×#467	semidirect
353. C₂²	C₃²×#216	semidirect
363. C₃	C₃×#5051	direct (N × H)
364. C₃	C₃²×#467	semidirect

Maximal subgroups

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

subgroup	index
C₃³×C₂²⋊Q₈	2
C₂×C₃²×#216	2
C₃²×#924	2
C₂²×C₃²×C₃⋊C₈	2
C₃²×#835	2
C₃²×#810	2
C₃²×#807	2
C₃²×#467	3
C₃×#5051	3

Subgroups — C32×#5051 #13162482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5051 #13162482