Subgroups — C₃²×#5748 #13179125

Order 1728.

1844 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#235	C₂	1	2	yes	maximal, complemented
2	C₂×C₃³×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#909	C₂	1	4	yes	maximal, complemented
4	C₃²×#908	C₂	1	4	yes	maximal, complemented
5	C₃²×#904	C₂	1	4	yes	maximal, complemented
6	C₃²×#575	—	3	1	no	maximal
7	C₃×#5748	C₃	1	4	yes	maximal, direct product factor
8	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
9	C₂×C₃²×#67	—	2	2	no	—
10	C₃²×#235	—	2	2	no	—
11	C₃²×#235	—	2	2	no	—
12	C₃²×#235	C₂²	1	4	yes	—
13	C₃²×#235	C₂²	1	4	yes	complemented
14	C₂×C₃²×D₁₂	C₂²	1	2	yes	complemented
15	C₂×C₃²×C₄×D₃	—	2	2	no	—
16	C₂×C₃²×Dic₆	C₂²	1	2	yes	complemented
17	C₃³×M₁₆	C₂²	1	4	yes	complemented
18	C₂×C₃³×C₈	C₂²	1	2	yes	complemented
19	C₃²×Dic₁₂	C₂²	1	4	yes	complemented
20	C₃²×D₂₄	C₂²	1	4	yes	complemented
21	C₃²×#204	C₂²	1	8	yes	complemented
22	C₂×C₃²×#41	—	3	2	no	—
23	C₂×C₃×#235	C₂×C₃	1	8	yes	complemented
24	C₃²×#137	—	3	4	no	—
25	C₃²×AGL(1,ℤ/8)	—	3	4	no	—
26	C₃²×#135	—	3	4	no	—
27	C₂×C₃²×M₁₆	—	2	4	no	—
28	C₂×C₃²×M₁₆	D₃	1	1	yes	characteristic, complemented
29	C₂×C₃²×M₁₆	C₂×C₃	1	4	yes	complemented
30	C₃×#909	C₂×C₃	1	16	yes	complemented
31	C₃×#908	C₂×C₃	1	16	yes	complemented
32	C₃×#904	C₂×C₃	1	16	yes	complemented
33	C₂³×C₃³	D₄	1	1	yes	characteristic
34	C₂²×C₃²×D₃	—	2	2	no	—
35	C₂×C₃³×C₄	D₄	1	2	yes	—
36	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
37	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
38	C₂×C₃³×C₄	C₂³	1	2	yes	—
39	C₃²×#67	—	2	4	no	—
40	C₃²×#67	—	2	4	no	—
41	C₂×C₃²×Dic₃	—	2	2	no	—
42	C₃²×D₁₂	—	2	2	no	—
43	C₃²×D₁₂	C₂³	1	4	yes	—
44	C₃²×C₄×D₃	—	2	4	no	—
45	C₃²×C₄×D₃	—	2	4	no	—
46	C₃²×Dic₆	—	2	2	no	—
47	C₃²×Dic₆	C₂³	1	4	yes	—
48	C₃³×C₈	C₂³	1	4	yes	—
49	C₃×#575	—	3	4	no	—
50	#5748	C₃²	1	1	yes	characteristic, direct product factor
51	C₃²×#41	—	3	4	no	—
52	C₃²×#41	—	3	4	no	—
53	C₃²×#41	—	6	2	no	—
54	C₃²×#41	—	6	2	no	—
55	C₂×C₃²×Q₈	—	3	2	no	—
56	C₂×C₃²×D₄	—	3	2	no	—
57	C₂×C₃²×D₄	—	6	2	no	—
58	C₂²×C₃²×C₄	—	2	4	no	—
59	C₂²×C₃²×C₄	—	6	2	no	—
60	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
62	C₂×C₃×#67	—	2	8	no	—
63	C₃×#235	—	2	8	no	—
64	C₃×#235	—	2	8	no	—
65	C₃×#235	C₂²×C₃	1	16	yes	—
66	C₃×#235	C₂²×C₃	1	16	yes	complemented
67	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	complemented
68	C₂×C₃×C₄×D₃	—	2	8	no	—
69	C₂×C₃×Dic₆	C₂²×C₃	1	8	yes	complemented
70	C₃²×Q₁₆	—	3	4	no	—
71	C₃²×SD₁₆	—	3	8	no	—
72	C₃²×D₈	—	3	4	no	—
73	C₃²×M₁₆	—	2	16	no	—
74	C₃²×M₁₆	C₂×D₃	1	4	yes	complemented
75	C₃²×M₁₆	C₂²×C₃	1	16	yes	complemented
76	C₂×C₃²×C₈	—	2	8	no	—
77	C₂×C₃²×C₈	C₂×D₃	1	2	yes	complemented
78	C₂×C₃²×C₈	C₂²×C₃	1	8	yes	complemented
79	C₃×Dic₁₂	C₂²×C₃	1	16	yes	complemented
80	C₃×D₂₄	C₂²×C₃	1	16	yes	complemented
81	C₃×#204	C₂²×C₃	1	32	yes	complemented
82	C₂²×C₃³	—	4	1	no	—
83	C₂²×C₃³	C₂×D₄	1	2	yes	—
84	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃²×D₃	—	2	4	no	—
86	C₂×C₃²×D₃	—	4	4	no	—
87	C₃³×C₄	C₂×D₄	1	2	yes	—
88	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
89	C₃³×C₄	C₂⁴	1	1	yes	characteristic
90	C₃²×Dic₃	—	2	4	no	—
91	C₂×C₃×#41	—	3	8	no	—
92	C₂×#235	C₂×C₃²	1	2	yes	complemented
93	C₃×#137	—	3	16	no	—
94	C₃×AGL(1,ℤ/8)	—	3	16	no	—
95	C₃×#135	—	3	16	no	—
96	C₂×C₃×M₁₆	—	2	4	no	—
97	C₂×C₃×M₁₆	C₃×D₃	1	4	yes	complemented
98	C₂×C₃×M₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
99	#909	C₂×C₃²	1	4	yes	complemented
100	#908	C₂×C₃²	1	4	yes	complemented
101	#904	C₂×C₃²	1	4	yes	complemented
102	C₂³×C₃²	—	2	4	no	—
103	C₂³×C₃²	—	6	2	no	—
104	C₂³×C₃²	D₁₂	1	1	yes	characteristic
105	C₂³×C₃²	C₃×D₄	1	4	yes	—
106	C₂²×C₃×D₃	—	2	8	no	—
107	C₃²×Q₈	—	3	4	no	—
108	C₃²×Q₈	—	6	2	no	—
109	C₃²×D₄	—	3	4	no	—
110	C₃²×D₄	—	6	4	no	—
111	C₃²×D₄	—	6	4	no	—
112	C₃²×D₄	—	6	2	no	—
113	C₂×C₃²×C₄	—	2	8	no	—
114	C₂×C₃²×C₄	—	2	4	no	—
115	C₂×C₃²×C₄	—	2	4	no	—
116	C₂×C₃²×C₄	—	2	8	no	—
117	C₂×C₃²×C₄	—	6	2	no	—
118	C₂×C₃²×C₄	—	6	4	no	—
119	C₂×C₃²×C₄	—	6	4	no	—
120	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
121	C₂×C₃²×C₄	D₁₂	1	2	yes	—
122	C₂×C₃²×C₄	C₃×D₄	1	8	yes	—
123	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
124	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
125	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
127	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
128	C₃×#67	—	2	16	no	—
129	C₃×#67	—	2	16	no	—
130	C₂×C₃×Dic₃	—	2	8	no	—
131	C₃×D₁₂	—	2	8	no	—
132	C₃×D₁₂	C₂³×C₃	1	16	yes	—
133	C₃×C₄×D₃	—	2	16	no	—
134	C₃×C₄×D₃	—	2	16	no	—
135	C₃×Dic₆	—	2	8	no	—
136	C₃×Dic₆	C₂³×C₃	1	16	yes	—
137	C₃²×C₈	—	2	16	no	—
138	C₃²×C₈	C₂²×D₃	1	4	yes	—
139	C₃²×C₈	C₂³×C₃	1	16	yes	—
140	#575	—	3	1	no	Sylow
141	C₂×C₃³	—	2	1	no	—
142	C₂×C₃³	—	2	2	no	—
143	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
144	C₃²×D₃	—	4	4	no	—
145	C₃×#41	—	3	16	no	—
146	C₃×#41	—	3	16	no	—
147	C₃×#41	—	6	8	no	—
148	C₃×#41	—	6	8	no	—
149	C₂×C₃×Q₈	—	3	8	no	—
150	C₂×C₃×D₄	—	3	8	no	—
151	C₂×C₃×D₄	—	6	8	no	—
152	C₂²×C₃×C₄	—	2	4	no	—
153	C₂²×C₃×C₄	—	6	8	no	—
154	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
155	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
156	C₂×#67	—	2	2	no	—
157	#235	—	2	2	no	—
158	#235	—	2	2	no	—
159	#235	C₂²×C₃²	1	4	yes	—
160	#235	C₂²×C₃²	1	4	yes	complemented
161	C₂×D₁₂	C₂²×C₃²	1	2	yes	complemented
162	C₂×C₄×D₃	—	2	2	no	—
163	C₂×Dic₆	C₂²×C₃²	1	2	yes	complemented
164	C₃×Q₁₆	—	3	16	no	—
165	C₃×SD₁₆	—	3	32	no	—
166	C₃×D₈	—	3	16	no	—
167	C₃×M₁₆	—	2	16	no	—
168	C₃×M₁₆	C₂×C₃×D₃	1	16	yes	complemented
169	C₃×M₁₆	C₂²×C₃²	1	4	yes	complemented
170	C₂×C₃×C₈	—	2	8	no	—
171	C₂×C₃×C₈	C₂×C₃×D₃	1	8	yes	complemented
172	C₂×C₃×C₈	C₂²×C₃²	1	2	yes	complemented
173	Dic₁₂	C₂²×C₃²	1	4	yes	complemented
174	D₂₄	C₂²×C₃²	1	4	yes	complemented
175	#204	C₂²×C₃²	1	8	yes	complemented
176	C₂²×C₃²	—	2	4	no	—
177	C₂²×C₃²	—	2	8	no	—
178	C₂²×C₃²	—	4	1	no	—
179	C₂²×C₃²	—	4	4	no	—
180	C₂²×C₃²	—	4	8	no	—
181	C₂²×C₃²	—	6	4	no	—
182	C₂²×C₃²	—	12	4	no	—
183	C₂²×C₃²	C₂×D₁₂	1	2	yes	—
184	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
185	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
186	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
187	C₂×C₃×D₃	—	2	16	no	—
188	C₂×C₃×D₃	—	4	16	no	—
189	C₃²×C₄	—	2	4	no	—
190	C₃²×C₄	—	2	4	no	—
191	C₃²×C₄	—	2	8	no	—
192	C₃²×C₄	—	6	4	no	—
193	C₃²×C₄	C₂×D₁₂	1	2	yes	—
194	C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
195	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
196	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
197	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
198	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
199	C₃×Dic₃	—	2	16	no	—
200	C₂×#41	—	3	2	no	—
201	#137	—	3	4	no	—
202	AGL(1,ℤ/8)	—	3	4	no	—
203	#135	—	3	4	no	—
204	C₂×M₁₆	C₃²×D₃	1	1	yes	characteristic, complemented
205	C₃³	#575	1	1	yes	characteristic, complemented, Sylow
206	C₂³×C₃	—	2	4	no	—
207	C₂³×C₃	—	6	8	no	—
208	C₂³×C₃	C₃×D₁₂	1	4	yes	—
209	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
210	C₂²×D₃	—	2	2	no	—
211	C₃×Q₈	—	3	16	no	—
212	C₃×Q₈	—	6	8	no	—
213	C₃×D₄	—	3	16	no	—
214	C₃×D₄	—	6	16	no	—
215	C₃×D₄	—	6	16	no	—
216	C₃×D₄	—	6	8	no	—
217	C₂×C₃×C₄	—	2	8	no	—
218	C₂×C₃×C₄	—	2	4	no	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	2	8	no	—
221	C₂×C₃×C₄	—	6	8	no	—
222	C₂×C₃×C₄	—	6	16	no	—
223	C₂×C₃×C₄	—	6	16	no	—
224	C₂×C₃×C₄	C₃×D₁₂	1	8	yes	—
225	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
226	C₂×C₃×C₄	C₃²×D₄	1	2	yes	—
227	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
229	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
230	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
231	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
232	#67	—	2	4	no	—
233	#67	—	2	4	no	—
234	C₂×Dic₃	—	2	2	no	—
235	D₁₂	—	2	2	no	—
236	D₁₂	C₂³×C₃²	1	4	yes	—
237	C₄×D₃	—	2	4	no	—
238	C₄×D₃	—	2	4	no	—
239	Dic₆	—	2	2	no	—
240	Dic₆	C₂³×C₃²	1	4	yes	—
241	C₃×C₈	—	2	16	no	—
242	C₃×C₈	C₂²×C₃×D₃	1	16	yes	—
243	C₃×C₈	C₂³×C₃²	1	4	yes	—
244	C₂×C₃²	—	2	8	no	—
245	C₂×C₃²	—	2	4	no	—
246	C₂×C₃²	—	2	2	no	—
247	C₂×C₃²	—	2	1	no	—
248	C₂×C₃²	—	2	4	no	—
249	C₂×C₃²	—	2	8	no	—
250	C₂×C₃²	—	4	8	no	—
251	C₂×C₃²	—	12	4	no	—
252	C₂×C₃²	C₂²×D₁₂	1	1	yes	characteristic
253	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
254	C₃×D₃	—	4	16	no	—
255	#41	—	3	4	no	—
256	#41	—	3	4	no	—
257	#41	—	6	2	no	—
258	#41	—	6	2	no	—
259	C₂×Q₈	—	3	2	no	—
260	C₂×D₄	—	3	2	no	—
261	C₂×D₄	—	6	2	no	—
262	C₂²×C₄	—	6	2	no	—
263	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
264	Q₁₆	—	3	4	no	—
265	SD₁₆	—	3	8	no	—
266	D₈	—	3	4	no	—
267	M₁₆	C₂×C₃²×D₃	1	4	yes	complemented
268	C₂×C₈	C₂×C₃²×D₃	1	2	yes	complemented
269	C₂²×C₃	—	2	4	no	—
270	C₂²×C₃	—	2	8	no	—
271	C₂²×C₃	—	4	4	no	—
272	C₂²×C₃	—	4	1	no	—
273	C₂²×C₃	—	4	8	no	—
274	C₂²×C₃	—	6	16	no	—
275	C₂²×C₃	—	12	16	no	—
276	C₂²×C₃	C₂×C₃×D₁₂	1	8	yes	—
277	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
278	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
279	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
280	C₂×D₃	—	2	4	no	—
281	C₂×D₃	—	4	4	no	—
282	C₃×C₄	—	2	4	no	—
283	C₃×C₄	—	2	4	no	—
284	C₃×C₄	—	2	8	no	—
285	C₃×C₄	—	6	16	no	—
286	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
287	C₃×C₄	C₂×C₃×D₁₂	1	8	yes	—
288	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
289	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
290	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
291	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
292	Dic₃	—	2	4	no	—
293	C₃²	—	2	4	no	—
294	C₃²	#5748	1	1	yes	characteristic, direct product factor
295	C₃²	C₃×#575	1	4	yes	complemented
296	C₂³	—	6	2	no	—
297	C₂³	C₃²×D₁₂	1	1	yes	characteristic
298	Q₈	—	3	4	no	—
299	Q₈	—	6	2	no	—
300	D₄	—	3	4	no	—
301	D₄	—	6	4	no	—
302	D₄	—	6	4	no	—
303	D₄	—	6	2	no	—
304	C₂×C₄	—	6	2	no	—
305	C₂×C₄	—	6	4	no	—
306	C₂×C₄	—	6	4	no	—
307	C₂×C₄	C₃²×D₁₂	1	2	yes	—
308	C₂×C₄	C₃²×D₁₂	1	1	yes	characteristic
309	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
310	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
311	C₈	C₂²×C₃²×D₃	1	4	yes	—
312	C₂×C₃	—	2	8	no	—
313	C₂×C₃	—	2	8	no	—
314	C₂×C₃	—	2	4	no	—
315	C₂×C₃	—	2	2	no	—
316	C₂×C₃	—	2	1	no	—
317	C₂×C₃	—	2	4	no	—
318	C₂×C₃	—	4	8	no	—
319	C₂×C₃	—	12	16	no	—
320	C₂×C₃	C₂²×C₃×D₁₂	1	4	yes	—
321	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
322	D₃	—	4	4	no	—
323	C₂²	—	4	1	no	—
324	C₂²	—	6	4	no	—
325	C₂²	—	12	4	no	—
326	C₂²	C₂×C₃²×D₁₂	1	2	yes	—
327	C₂²	C₂×C₃²×D₁₂	1	1	yes	characteristic
328	C₄	—	6	4	no	—
329	C₄	C₂×C₃²×D₁₂	1	1	yes	characteristic
330	C₄	C₂×C₃²×D₁₂	1	2	yes	—
331	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
332	C₃	—	2	4	no	—
333	C₃	C₃×#5748	1	4	yes	direct product factor
334	C₃	C₃²×#575	1	1	yes	characteristic, complemented
335	C₂	—	2	2	no	—
336	C₂	—	2	1	no	—
337	C₂	—	12	4	no	—
338	C₂	C₂²×C₃²×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₃²×C₄	C₂×D₁₂
commutator, cosocle	C₃×C₄	C₂⁴×C₃²
Frattini	C₄	C₂³×C₃²×D₃
Fitting	C₂×C₃³×M₁₆	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₂×C₃²×M₁₆	D₃
hypocenter	C₃	C₃²×#575
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃²×C₄ ◁ C₂²×C₃²×C₄ ◁ C₂×C₃²×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#235	C₂	semidirect
2. C₂×C₃³×M₁₆	C₂	semidirect
3. C₃²×#909	C₂	semidirect
4. C₃²×#908	C₂	semidirect
5. C₃²×#904	C₂	semidirect
7. C₃×#5748	C₃	direct (N × H)
13. C₃²×#235	C₂²	semidirect
14. C₂×C₃²×D₁₂	C₂²	semidirect
16. C₂×C₃²×Dic₆	C₂²	semidirect
17. C₃³×M₁₆	C₂²	semidirect
18. C₂×C₃³×C₈	C₂²	semidirect
19. C₃²×Dic₁₂	C₂²	semidirect
20. C₃²×D₂₄	C₂²	semidirect
21. C₃²×#204	C₂²	semidirect
23. C₂×C₃×#235	C₂×C₃	semidirect
28. C₂×C₃²×M₁₆	D₃	semidirect
29. C₂×C₃²×M₁₆	C₂×C₃	semidirect
30. C₃×#909	C₂×C₃	semidirect
31. C₃×#908	C₂×C₃	semidirect
32. C₃×#904	C₂×C₃	semidirect
50. #5748	C₃²	direct (N × H)
66. C₃×#235	C₂²×C₃	semidirect
67. C₂×C₃×D₁₂	C₂²×C₃	semidirect
69. C₂×C₃×Dic₆	C₂²×C₃	semidirect
74. C₃²×M₁₆	C₂×D₃	semidirect
75. C₃²×M₁₆	C₂²×C₃	semidirect
77. C₂×C₃²×C₈	C₂×D₃	semidirect
78. C₂×C₃²×C₈	C₂²×C₃	semidirect
79. C₃×Dic₁₂	C₂²×C₃	semidirect
80. C₃×D₂₄	C₂²×C₃	semidirect
81. C₃×#204	C₂²×C₃	semidirect
92. C₂×#235	C₂×C₃²	semidirect
97. C₂×C₃×M₁₆	C₃×D₃	semidirect
98. C₂×C₃×M₁₆	C₂×C₃²	semidirect
99. #909	C₂×C₃²	semidirect
100. #908	C₂×C₃²	semidirect
101. #904	C₂×C₃²	semidirect
160. #235	C₂²×C₃²	semidirect
161. C₂×D₁₂	C₂²×C₃²	semidirect
163. C₂×Dic₆	C₂²×C₃²	semidirect
168. C₃×M₁₆	C₂×C₃×D₃	semidirect
169. C₃×M₁₆	C₂²×C₃²	semidirect
171. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
172. C₂×C₃×C₈	C₂²×C₃²	semidirect
173. Dic₁₂	C₂²×C₃²	semidirect
174. D₂₄	C₂²×C₃²	semidirect
175. #204	C₂²×C₃²	semidirect
204. C₂×M₁₆	C₃²×D₃	semidirect
205. C₃³	#575	semidirect
267. M₁₆	C₂×C₃²×D₃	semidirect
268. C₂×C₈	C₂×C₃²×D₃	semidirect
294. C₃²	#5748	direct (N × H)
295. C₃²	C₃×#575	semidirect
333. C₃	C₃×#5748	direct (N × H)
334. C₃	C₃²×#575	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#235	2
C₂×C₃³×M₁₆	2
C₃²×#909	2
C₃²×#908	2
C₃²×#904	2
C₃²×#575	3
C₃×#5748	3

Subgroups — C32×#5748 #13179125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5748 #13179125