Subgroups — C₃⋊D₃×#7333 #72245461

Order 4608.

996 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72245441	C₂	1	1	yes	maximal, characteristic, complemented
2	#72245413	C₂	1	1	yes	maximal, characteristic, complemented
3	#72245373	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#7333	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃⋊D₃×#1398	C₂	1	1	yes	maximal, characteristic
6	C₃⋊D₃×#1398	C₂	1	1	yes	maximal, characteristic
7	D₃×#7333	—	3	4	no	maximal
8	C₃⋊D₃×#1313	C₂	1	1	yes	maximal, characteristic
9	C₃⋊D₃×M₆₄	C₄	1	2	yes	—
10	C₃⋊D₃×M₆₄	C₄	1	2	yes	—
11	C₃⋊D₃×#346	C₄	1	1	yes	characteristic
12	C₃⋊D₃×#346	C₂²	1	1	yes	characteristic
13	C₃⋊D₃×#322	C₄	1	1	yes	characteristic
14	#11772675	C₂²	1	1	yes	characteristic
15	#11772675	C₂²	1	1	yes	characteristic
16	#11772672	C₄	1	2	yes	—
17	#11772672	C₄	1	2	yes	—
18	#11771325	C₄	1	1	yes	characteristic
19	#11771322	C₄	1	1	yes	characteristic
20	#11771319	C₂²	1	1	yes	characteristic
21	C₃²×#1398	C₂²	1	1	yes	characteristic
22	C₃²×#1398	C₂²	1	1	yes	characteristic
23	C₃²×#1313	C₂²	1	1	yes	characteristic
24	D₃×#1398	—	3	4	no	—
25	D₃×#1398	—	3	4	no	—
26	D₃×#1313	—	3	4	no	—
27	#10682524	—	3	4	no	—
28	#10682523	—	3	4	no	—
29	#10682522	—	3	4	no	—
30	C₃×#7333	D₃	1	4	yes	complemented
31	C₂×C₁₆×C₃⋊D₃	—	2	1	no	—
32	C₂×C₁₆×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₁₆×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
34	C₄×C₈×C₃⋊D₃	—	2	1	no	—
35	C₄×C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
36	C₃²×M₆₄	C₂×C₄	1	2	yes	—
37	C₃²×M₆₄	C₂×C₄	1	2	yes	—
38	C₃²×#346	C₂×C₄	1	1	yes	characteristic
39	C₃²×#346	C₂³	1	1	yes	characteristic
40	C₃²×#322	C₂×C₄	1	1	yes	characteristic
41	#10589368	—	2	1	no	—
42	#10589368	C₂×C₄	1	1	yes	characteristic
43	#10589368	C₂×C₄	1	1	yes	characteristic
44	#10589365	C₂×C₄	1	2	yes	—
45	#10589365	C₂×C₄	1	2	yes	—
46	#10589327	C₂×C₄	1	1	yes	characteristic
47	#10589327	C₂×C₄	1	1	yes	characteristic
48	#10589321	C₂×C₄	1	1	yes	characteristic
49	#10589320	—	2	1	no	—
50	#10589313	—	2	2	no	—
51	#10589313	C₈	1	4	yes	complemented
52	C₃⋊D₃×C₃₂	—	2	2	no	—
53	C₃⋊D₃×C₃₂	C₈	1	4	yes	complemented
54	C₂×#7333	—	9	1	no	Sylow
55	D₃×M₆₄	—	3	8	no	—
56	D₃×M₆₄	—	3	8	no	—
57	D₃×#346	—	3	4	no	—
58	D₃×#346	—	3	4	no	—
59	D₃×#322	—	3	4	no	—
60	C₃×#1398	C₂×D₃	1	4	yes	—
61	C₃×#1398	C₂×D₃	1	4	yes	—
62	C₃×#1313	C₂×D₃	1	4	yes	—
63	#67600	—	3	8	no	—
64	#67600	—	3	8	no	—
65	#67519	—	3	4	no	—
66	#67519	—	3	4	no	—
67	#67512	—	3	4	no	—
68	#67511	—	3	4	no	—
69	#67442	—	3	4	no	—
70	C₂×C₈×C₃⋊D₃	—	4	1	no	—
71	C₂×C₈×C₃⋊D₃	C₄²	1	1	yes	characteristic
72	C₂×C₈×C₃⋊D₃	M₁₆	1	1	yes	characteristic
73	C₄²×C₃⋊D₃	M₁₆	1	1	yes	characteristic
74	C₂×C₃²×C₁₆	—	2	1	no	—
75	C₂×C₃²×C₁₆	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₃²×C₁₆	C₂²×C₄	1	1	yes	characteristic
77	C₃²×C₄×C₈	—	2	1	no	—
78	C₃²×C₄×C₈	C₂²×C₄	1	1	yes	characteristic
79	C₈×C₃⋊Dic₃	—	4	1	no	—
80	C₈×C₃⋊Dic₃	C₄²	1	1	yes	characteristic
81	C₈×C₃⋊Dic₃	M₁₆	1	1	yes	characteristic
82	C₂×C₃⋊(C₃⋊C₁₆)	—	2	1	no	—
83	C₂×C₃⋊(C₃⋊C₁₆)	C₄²	1	1	yes	characteristic
84	C₂×C₃⋊(C₃⋊C₁₆)	C₄²	1	1	yes	characteristic
85	C₄×C₃⋊(C₃⋊C₈)	—	2	1	no	—
86	C₄×C₃⋊(C₃⋊C₈)	M₁₆	1	1	yes	characteristic
87	C₁₆×C₃⋊D₃	—	4	1	no	—
88	C₁₆×C₃⋊D₃	—	4	1	no	—
89	C₁₆×C₃⋊D₃	C₂×C₈	1	2	yes	—
90	C₁₆×C₃⋊D₃	C₂×C₈	1	2	yes	—
91	C₁₆×C₃⋊D₃	M₁₆	1	2	yes	—
92	C₁₆×C₃⋊D₃	M₁₆	1	2	yes	—
93	C₃²×C₃₂	—	2	2	no	—
94	C₃²×C₃₂	C₂×C₈	1	4	yes	complemented
95	C₃⋊(C₃⋊C₃₂)	—	2	2	no	—
96	C₃⋊(C₃⋊C₃₂)	C₂×C₈	1	4	yes	complemented
97	C₂×#1398	—	9	1	no	—
98	C₂×#1398	—	9	1	no	—
99	C₂×#1313	—	9	1	no	—
100	#7333	—	9	1	no	—
101	#7333	—	9	1	no	—
102	#7333	—	9	1	no	—
103	#7333	C₃⋊D₃	1	1	yes	characteristic, direct product factor
104	C₂×D₃×C₁₆	—	3	4	no	—
105	C₂×D₃×C₁₆	—	3	4	no	—
106	C₂×D₃×C₁₆	—	6	4	no	—
107	C₄×D₃×C₈	—	3	4	no	—
108	C₄×D₃×C₈	—	6	4	no	—
109	C₃×M₆₄	C₄×D₃	1	8	yes	—
110	C₃×M₆₄	C₄×D₃	1	8	yes	—
111	C₃×#346	C₄×D₃	1	4	yes	—
112	C₃×#346	C₂²×D₃	1	4	yes	—
113	C₃×#322	C₄×D₃	1	4	yes	—
114	#4502	—	3	4	no	—
115	#4502	—	3	4	no	—
116	#4502	—	6	4	no	—
117	#4499	—	3	8	no	—
118	#4499	—	3	8	no	—
119	#4461	—	3	4	no	—
120	#4461	—	3	4	no	—
121	#4455	—	3	4	no	—
122	#4454	—	6	4	no	—
123	#4447	—	3	16	no	—
124	#4447	—	6	8	no	—
125	D₃×C₃₂	—	3	16	no	—
126	D₃×C₃₂	—	6	8	no	—
127	C₂×C₄×C₃⋊D₃	—	2	1	no	—
128	C₂×C₄×C₃⋊D₃	#97	1	1	yes	characteristic
129	C₂×C₃²×C₈	—	4	1	no	—
130	C₂×C₃²×C₈	C₂×C₄²	1	1	yes	characteristic
131	C₂×C₃²×C₈	C₂×M₁₆	1	1	yes	characteristic
132	C₃²×C₄²	C₂×M₁₆	1	1	yes	characteristic
133	C₄×C₃⋊Dic₃	—	2	1	no	—
134	C₄×C₃⋊Dic₃	#97	1	1	yes	characteristic
135	C₂×C₃⋊(C₃⋊C₈)	—	4	1	no	—
136	C₂×C₃⋊(C₃⋊C₈)	#97	1	1	yes	characteristic
137	C₂×C₃⋊(C₃⋊C₈)	#97	1	1	yes	characteristic
138	C₈×C₃⋊D₃	—	2	1	no	—
139	C₈×C₃⋊D₃	—	2	1	no	—
140	C₈×C₃⋊D₃	—	8	2	no	—
141	C₈×C₃⋊D₃	C₄×C₈	1	1	yes	characteristic
142	C₈×C₃⋊D₃	C₄×C₈	1	1	yes	characteristic
143	C₈×C₃⋊D₃	#97	1	1	yes	characteristic
144	C₈×C₃⋊D₃	#97	1	1	yes	characteristic
145	C₃²×C₁₆	—	4	1	no	—
146	C₃²×C₁₆	C₂²×C₈	1	2	yes	—
147	C₃²×C₁₆	C₂×M₁₆	1	2	yes	—
148	C₃⋊(C₃⋊C₁₆)	—	4	1	no	—
149	C₃⋊(C₃⋊C₁₆)	C₄×C₈	1	2	yes	—
150	C₃⋊(C₃⋊C₁₆)	#97	1	2	yes	—
151	C₂×M₆₄	—	9	2	no	—
152	C₂×M₆₄	—	9	2	no	—
153	C₂×#346	—	9	1	no	—
154	C₂×#346	—	9	1	no	—
155	C₂×#322	—	9	1	no	—
156	#1398	—	9	2	no	—
157	#1398	—	9	2	no	—
158	#1398	—	9	1	no	—
159	#1398	—	9	1	no	—
160	#1398	C₂×C₃⋊D₃	1	1	yes	characteristic
161	#1398	C₂×C₃⋊D₃	1	1	yes	characteristic
162	#1313	—	9	1	no	—
163	#1313	—	9	1	no	—
164	#1313	—	9	1	no	—
165	#1313	C₂×C₃⋊D₃	1	1	yes	characteristic
166	C₂×D₃×C₈	—	3	4	no	—
167	C₂×D₃×C₈	—	3	4	no	—
168	C₂×D₃×C₈	—	12	4	no	—
169	C₄²×D₃	—	3	4	no	—
170	C₂×C₃×C₁₆	—	2	4	no	—
171	C₂×C₃×C₁₆	C₂×C₄×D₃	1	4	yes	—
172	C₂×C₃×C₁₆	C₂×C₄×D₃	1	4	yes	—
173	C₃×C₄×C₈	—	2	4	no	—
174	C₃×C₄×C₈	C₂×C₄×D₃	1	4	yes	—
175	C₈×Dic₃	—	3	4	no	—
176	C₈×Dic₃	—	3	4	no	—
177	C₈×Dic₃	—	12	4	no	—
178	C₂×C₃⋊C₁₆	—	3	4	no	—
179	C₂×C₃⋊C₁₆	—	3	4	no	—
180	C₂×C₃⋊C₁₆	—	6	4	no	—
181	C₄×C₃⋊C₈	—	3	4	no	—
182	C₄×C₃⋊C₈	—	6	4	no	—
183	D₃×C₁₆	—	3	8	no	—
184	D₃×C₁₆	—	3	8	no	—
185	D₃×C₁₆	—	3	8	no	—
186	D₃×C₁₆	—	3	8	no	—
187	D₃×C₁₆	—	12	4	no	—
188	D₃×C₁₆	—	12	4	no	—
189	C₃×C₃₂	—	2	8	no	—
190	C₃×C₃₂	D₃×C₈	1	16	yes	complemented
191	C₃⋊C₃₂	—	3	16	no	—
192	C₃⋊C₃₂	—	6	8	no	—
193	C₂²×C₃⋊D₃	#347	1	1	yes	characteristic
194	C₂×C₃²×C₄	—	2	1	no	—
195	C₂×C₃²×C₄	C₂×#97	1	1	yes	characteristic
196	C₂×C₃⋊Dic₃	—	2	1	no	—
197	C₂×C₃⋊Dic₃	#347	1	1	yes	characteristic
198	C₄×C₃⋊D₃	—	4	2	no	—
199	C₄×C₃⋊D₃	#322	1	1	yes	characteristic
200	C₄×C₃⋊D₃	#322	1	1	yes	characteristic
201	C₄×C₃⋊D₃	#347	1	1	yes	characteristic
202	C₄×C₃⋊D₃	#347	1	1	yes	characteristic
203	C₃²×C₈	—	2	1	no	—
204	C₃²×C₈	—	8	1	no	—
205	C₃²×C₈	C₂×C₄×C₈	1	1	yes	characteristic
206	C₃²×C₈	C₂×#97	1	1	yes	characteristic
207	C₃⋊(C₃⋊C₈)	—	2	1	no	—
208	C₃⋊(C₃⋊C₈)	—	8	1	no	—
209	C₃⋊(C₃⋊C₈)	#322	1	1	yes	characteristic
210	C₃⋊(C₃⋊C₈)	#322	1	1	yes	characteristic
211	C₂²×C₁₆	—	9	1	no	—
212	C₂²×C₁₆	—	9	1	no	—
213	C₂²×C₁₆	—	18	1	no	—
214	C₂×C₄×C₈	—	9	1	no	—
215	C₂×C₄×C₈	—	18	1	no	—
216	M₆₄	—	9	2	no	—
217	M₆₄	—	9	4	no	—
218	M₆₄	—	9	2	no	—
219	M₆₄	—	18	2	no	—
220	M₆₄	C₄×C₃⋊D₃	1	2	yes	—
221	M₆₄	C₄×C₃⋊D₃	1	2	yes	—
222	C₂×C₃₂	—	9	4	no	—
223	C₂×C₃₂	—	18	2	no	—
224	#346	—	9	1	no	—
225	#346	—	9	1	no	—
226	#346	—	9	1	no	—
227	#346	—	9	1	no	—
228	#346	—	18	1	no	—
229	#346	C₄×C₃⋊D₃	1	1	yes	characteristic
230	#346	C₂²×C₃⋊D₃	1	1	yes	characteristic
231	#322	—	9	1	no	—
232	#322	—	18	1	no	—
233	#322	C₄×C₃⋊D₃	1	1	yes	characteristic
234	C₂×C₄×D₃	—	3	4	no	—
235	C₂×C₄×D₃	—	6	4	no	—
236	C₂×C₃×C₈	—	4	4	no	—
237	C₂×C₃×C₈	C₄²×D₃	1	4	yes	—
238	C₂×C₃×C₈	D₃×M₁₆	1	4	yes	—
239	C₃×C₄²	D₃×M₁₆	1	4	yes	—
240	C₄×Dic₃	—	3	4	no	—
241	C₄×Dic₃	—	6	4	no	—
242	C₂×C₃⋊C₈	—	3	4	no	—
243	C₂×C₃⋊C₈	—	3	4	no	—
244	C₂×C₃⋊C₈	—	12	4	no	—
245	D₃×C₈	—	3	4	no	—
246	D₃×C₈	—	3	4	no	—
247	D₃×C₈	—	3	4	no	—
248	D₃×C₈	—	3	4	no	—
249	D₃×C₈	—	6	4	no	—
250	D₃×C₈	—	6	4	no	—
251	D₃×C₈	—	24	8	no	—
252	C₃×C₁₆	—	4	4	no	—
253	C₃×C₁₆	C₂×D₃×C₈	1	8	yes	—
254	C₃×C₁₆	D₃×M₁₆	1	8	yes	—
255	C₃⋊C₁₆	—	3	8	no	—
256	C₃⋊C₁₆	—	3	8	no	—
257	C₃⋊C₁₆	—	12	4	no	—
258	C₂²×C₃²	C₂×#347	1	1	yes	characteristic
259	C₂×C₃⋊D₃	—	2	2	no	—
260	C₂×C₃⋊D₃	#1313	1	1	yes	characteristic
261	C₂×C₃⋊D₃	#1313	1	1	yes	characteristic
262	C₃²×C₄	—	4	1	no	—
263	C₃²×C₄	C₂×#322	1	1	yes	characteristic
264	C₃²×C₄	C₂×#347	1	1	yes	characteristic
265	C₃⋊Dic₃	—	4	1	no	—
266	C₃⋊Dic₃	#1313	1	1	yes	characteristic
267	C₃⋊Dic₃	#1313	1	1	yes	characteristic
268	C₂²×C₈	—	9	1	no	—
269	C₂²×C₈	—	9	1	no	—
270	C₂²×C₈	—	36	1	no	—
271	C₂×C₄²	—	9	1	no	—
272	C₂×C₁₆	—	2	1	no	—
273	C₂×C₁₆	—	9	1	no	—
274	C₂×C₁₆	—	9	1	no	—
275	C₂×C₁₆	—	9	2	no	—
276	C₂×C₁₆	—	9	2	no	—
277	C₂×C₁₆	—	9	2	no	—
278	C₂×C₁₆	—	9	2	no	—
279	C₂×C₁₆	—	18	1	no	—
280	C₂×C₁₆	—	36	1	no	—
281	C₂×C₁₆	—	36	1	no	—
282	C₂×C₁₆	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
283	C₂×C₁₆	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	9	1	no	—
286	C₄×C₈	—	9	1	no	—
287	C₄×C₈	—	9	1	no	—
288	C₄×C₈	—	18	1	no	—
289	C₄×C₈	—	36	1	no	—
290	C₄×C₈	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
291	C₃₂	—	2	2	no	—
292	C₃₂	—	9	4	no	—
293	C₃₂	—	18	2	no	—
294	C₃₂	C₈×C₃⋊D₃	1	4	yes	complemented
295	C₂²×D₃	—	3	4	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	D₃×#97	1	4	yes	—
298	C₂×Dic₃	—	3	4	no	—
299	C₂×Dic₃	—	6	4	no	—
300	C₄×D₃	—	3	4	no	—
301	C₄×D₃	—	3	4	no	—
302	C₄×D₃	—	3	4	no	—
303	C₄×D₃	—	3	4	no	—
304	C₄×D₃	—	12	8	no	—
305	C₃×C₈	—	2	4	no	—
306	C₃×C₈	—	8	4	no	—
307	C₃×C₈	C₄×D₃×C₈	1	4	yes	—
308	C₃×C₈	D₃×#97	1	4	yes	—
309	C₃⋊C₈	—	3	4	no	—
310	C₃⋊C₈	—	3	4	no	—
311	C₃⋊C₈	—	6	4	no	—
312	C₃⋊C₈	—	24	4	no	—
313	C₂×C₃²	—	2	1	no	—
314	C₂×C₃²	C₂×#1313	1	1	yes	characteristic
315	C₃⋊D₃	—	2	1	no	—
316	C₃⋊D₃	#7333	1	2	yes	direct product factor
317	C₂²×C₄	—	9	1	no	—
318	C₂²×C₄	—	18	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	9	1	no	—
321	C₂×C₈	—	9	1	no	—
322	C₂×C₈	—	9	1	no	—
323	C₂×C₈	—	9	1	no	—
324	C₂×C₈	—	9	1	no	—
325	C₂×C₈	—	9	1	no	—
326	C₂×C₈	—	18	1	no	—
327	C₂×C₈	—	18	1	no	—
328	C₂×C₈	—	36	1	no	—
329	C₂×C₈	—	72	2	no	—
330	C₂×C₈	C₄²×C₃⋊D₃	1	1	yes	characteristic
331	C₂×C₈	M₁₆×C₃⋊D₃	1	1	yes	characteristic
332	C₄²	—	9	1	no	—
333	C₄²	—	18	1	no	—
334	C₄²	M₁₆×C₃⋊D₃	1	1	yes	characteristic
335	C₁₆	—	4	1	no	—
336	C₁₆	—	9	2	no	—
337	C₁₆	—	9	2	no	—
338	C₁₆	—	36	1	no	—
339	C₁₆	C₂×C₈×C₃⋊D₃	1	2	yes	—
340	C₁₆	M₁₆×C₃⋊D₃	1	2	yes	—
341	C₂²×C₃	D₃×#347	1	4	yes	—
342	C₂×D₃	—	3	4	no	—
343	C₂×D₃	—	3	4	no	—
344	C₂×D₃	—	6	8	no	—
345	C₃×C₄	—	4	4	no	—
346	C₃×C₄	D₃×#322	1	4	yes	—
347	C₃×C₄	D₃×#347	1	4	yes	—
348	Dic₃	—	3	4	no	—
349	Dic₃	—	3	4	no	—
350	Dic₃	—	12	4	no	—
351	C₃²	C₂×#7333	1	1	yes	characteristic, complemented, Sylow
352	C₂³	—	9	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	9	1	no	—
355	C₂×C₄	—	9	1	no	—
356	C₂×C₄	—	9	1	no	—
357	C₂×C₄	—	9	1	no	—
358	C₂×C₄	—	9	1	no	—
359	C₂×C₄	—	18	1	no	—
360	C₂×C₄	—	36	2	no	—
361	C₂×C₄	C₃⋊D₃×#97	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	8	1	no	—
364	C₈	—	9	1	no	—
365	C₈	—	9	1	no	—
366	C₈	—	18	1	no	—
367	C₈	—	72	1	no	—
368	C₈	C₄×C₈×C₃⋊D₃	1	1	yes	characteristic
369	C₈	C₃⋊D₃×#97	1	1	yes	characteristic
370	C₂×C₃	—	2	4	no	—
371	C₂×C₃	D₃×#1313	1	4	yes	—
372	D₃	—	3	8	no	—
373	D₃	—	6	4	no	—
374	C₂²	—	9	1	no	—
375	C₂²	—	9	1	no	—
376	C₂²	—	18	2	no	—
377	C₂²	C₃⋊D₃×#347	1	1	yes	characteristic
378	C₄	—	4	1	no	—
379	C₄	—	9	1	no	—
380	C₄	—	9	1	no	—
381	C₄	—	36	1	no	—
382	C₄	C₃⋊D₃×#322	1	1	yes	characteristic
383	C₄	C₃⋊D₃×#347	1	1	yes	characteristic
384	C₃	D₃×#7333	1	4	yes	complemented
385	C₂	—	2	1	no	—
386	C₂	—	9	2	no	—
387	C₂	—	18	1	no	—
388	C₂	C₃⋊D₃×#1313	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₃⋊D₃×#322
commutator	C₃²×C₈	C₂×C₄×C₈
Frattini	#346	C₂²×C₃⋊D₃
Fitting	C₃²×#7333	C₂
socle	C₂×C₃²	C₂×#1313
prime radical	C₂²×C₃⋊D₃	#347
cosocle	C₃²×#346	C₂³
hypercenter	#7333	C₃⋊D₃
hypocenter	C₃²	C₂×#7333
LCS	G ▷ C₃²×C₈ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ #346 ◁ #7333

Complements

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

N	H ≅ G/N	type
1. #72245441	C₂	semidirect
2. #72245413	C₂	semidirect
3. #72245373	C₂	semidirect
4. C₃²×#7333	C₂	semidirect
30. C₃×#7333	D₃	semidirect
51. #10589313	C₈	semidirect
53. C₃⋊D₃×C₃₂	C₈	semidirect
94. C₃²×C₃₂	C₂×C₈	semidirect
96. C₃⋊(C₃⋊C₃₂)	C₂×C₈	semidirect
103. #7333	C₃⋊D₃	direct (N × H)
190. C₃×C₃₂	D₃×C₈	semidirect
294. C₃₂	C₈×C₃⋊D₃	semidirect
316. C₃⋊D₃	#7333	direct (N × H)
351. C₃²	C₂×#7333	semidirect
384. C₃	D₃×#7333	semidirect

Maximal subgroups

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

subgroup	index
#72245441	2
#72245413	2
#72245373	2
C₃²×#7333	2
C₃⋊D₃×#1398	2
D₃×#7333	3
C₃⋊D₃×#1313	2

Subgroups — C3⋊D3×#7333 #72245461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×#7333 #72245461