Subgroups — C₃×#69770 #11790131

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic
4	C₃×#4928	C₂	1	2	yes	maximal
5	C₃×#4551	C₂	1	2	yes	maximal
6	C₃×#1942	—	3	1	no	maximal
7	#69770	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
12	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
13	C₂×C₃×Dic₃⋊C₄	—	2	2	no	—
14	C₃²×C₄×C₈	—	2	2	no	—
15	C₃×C₃⋊#95	—	2	2	no	—
16	C₃×#818	—	2	2	no	—
17	C₃×#818	C₄	1	4	yes	complemented
18	C₂×C₃×#107	—	3	1	no	—
19	C₂×C₃×#107	—	3	1	no	—
20	C₂×C₃×C₄×C₈	—	2	1	no	—
21	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
22	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
23	C₃×#389	—	3	2	no	—
24	C₂×#818	C₂×C₃	1	1	yes	characteristic
25	C₂×#818	C₂×C₃	1	1	yes	characteristic
26	#4928	C₂×C₃	1	2	yes	—
27	C₃×#340	—	3	2	no	—
28	#4551	C₂×C₃	1	2	yes	—
29	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
30	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
31	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
32	C₂²×C₃×Dic₃	—	2	2	no	—
33	C₂²×C₃×Dic₃	—	2	2	no	—
34	C₂×C₃²×C₈	—	2	1	no	—
35	C₂×C₃²×C₈	—	2	1	no	—
36	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
37	C₂×C₃²×C₈	D₄	1	2	yes	—
38	C₂×C₃²×C₈	Q₈	1	2	yes	—
39	C₂×C₃²×C₈	Q₈	1	2	yes	—
40	C₃²×C₄²	—	2	1	no	—
41	C₃²×C₄²	—	2	1	no	—
42	C₃×C₄⋊Dic₃	—	2	2	no	—
43	C₃×C₄⋊Dic₃	—	2	2	no	—
44	C₃×C₄⋊Dic₃	—	2	2	no	—
45	C₃×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
46	C₃×Dic₃⋊C₄	—	4	4	no	—
47	#1942	—	3	1	no	Sylow
48	C₂²×C₃×C₈	—	2	1	no	—
49	C₂²×C₃×C₈	—	2	1	no	—
50	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
51	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
52	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
53	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
54	C₂×C₃×C₄⋊C₄	—	3	2	no	—
55	C₂×C₃×C₄⋊C₄	—	3	2	no	—
56	C₂×C₃×C₄⋊C₄	—	6	2	no	—
57	C₂×C₃×C₄²	—	2	1	no	—
58	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
59	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
61	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
62	C₂×Dic₃⋊C₄	—	2	2	no	—
63	C₃×#107	—	3	4	no	—
64	C₃×#107	—	6	2	no	—
65	C₃×C₄×C₈	—	2	4	no	—
66	C₃×C₄×C₈	—	2	2	no	—
67	C₃×C₄×C₈	—	2	2	no	—
68	C₃×#95	—	6	2	no	—
69	C₃⋊#95	—	2	2	no	—
70	#818	—	2	2	no	—
71	#818	C₃×C₄	1	4	yes	complemented
72	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
73	C₂×C₃²×C₄	—	2	1	no	—
74	C₂×C₃²×C₄	—	2	1	no	—
75	C₂×C₃²×C₄	—	2	1	no	—
76	C₂×C₃²×C₄	—	2	1	no	—
77	C₂×C₃²×C₄	D₈	1	2	yes	—
78	C₂×C₃²×C₄	Q₁₆	1	2	yes	—
79	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
81	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
82	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
83	C₂×C₃²×C₄	#41	1	1	yes	characteristic
84	C₂×C₃²×C₄	#41	1	1	yes	characteristic
85	C₂×C₃×Dic₃	—	2	4	no	—
86	C₂×C₃×Dic₃	—	4	2	no	—
87	C₂×C₃×Dic₃	—	4	2	no	—
88	C₂×C₃×Dic₃	—	4	2	no	—
89	C₂×C₃×Dic₃	—	4	2	no	—
90	C₂×C₃×Dic₃	—	4	2	no	—
91	C₃²×C₈	—	2	2	no	—
92	C₃²×C₈	C₄⋊C₄	1	4	yes	complemented
93	C₂×#107	—	3	1	no	—
94	C₂×#107	—	3	1	no	—
95	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic
96	#389	—	3	2	no	—
97	#340	—	3	2	no	—
98	C₂²×C₃×C₄	—	2	1	no	—
99	C₂²×C₃×C₄	—	2	1	no	—
100	C₂²×C₃×C₄	—	2	1	no	—
101	C₂²×C₃×C₄	—	6	2	no	—
102	C₂²×C₃×C₄	—	6	2	no	—
103	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
104	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
105	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
106	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
107	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
108	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
109	C₂²×Dic₃	—	2	2	no	—
110	C₂²×Dic₃	—	2	2	no	—
111	C₂×C₃×C₈	—	2	2	no	—
112	C₂×C₃×C₈	—	2	2	no	—
113	C₂×C₃×C₈	—	2	1	no	—
114	C₂×C₃×C₈	—	2	1	no	—
115	C₂×C₃×C₈	—	2	1	no	—
116	C₂×C₃×C₈	—	2	1	no	—
117	C₂×C₃×C₈	—	2	2	no	—
118	C₂×C₃×C₈	—	2	2	no	—
119	C₂×C₃×C₈	—	2	2	no	—
120	C₂×C₃×C₈	—	2	2	no	—
121	C₂×C₃×C₈	Dic₆	1	2	yes	—
122	C₂×C₃×C₈	Dic₆	1	2	yes	—
123	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
124	C₂×C₃×C₈	#67	1	2	yes	—
125	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
126	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
127	C₂×C₃×C₈	C₃×Q₈	1	2	yes	—
128	C₂×C₃×C₈	C₃×Q₈	1	2	yes	—
129	C₃×C₄⋊C₄	—	3	4	no	—
130	C₃×C₄⋊C₄	—	6	2	no	—
131	C₃×C₄⋊C₄	—	6	2	no	—
132	C₃×C₄⋊C₄	—	6	2	no	—
133	C₃×C₄⋊C₄	—	12	4	no	—
134	C₃×C₄²	—	2	2	no	—
135	C₃×C₄²	—	2	2	no	—
136	C₃×C₄²	—	2	1	no	—
137	C₃×C₄²	—	2	1	no	—
138	C₃×C₄²	—	2	1	no	—
139	C₃×C₄²	—	2	1	no	—
140	C₄⋊Dic₃	—	2	2	no	—
141	C₄⋊Dic₃	—	2	2	no	—
142	C₄⋊Dic₃	—	2	2	no	—
143	C₄⋊Dic₃	C₂×C₃×C₄	1	4	yes	—
144	Dic₃⋊C₄	—	4	4	no	—
145	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
146	C₂²×C₃²	#121	1	1	yes	characteristic
147	C₂²×C₃²	C₄⋊Q₈	1	1	yes	characteristic
148	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
149	C₂²×C₃²	C₂×Q₁₆	1	1	yes	characteristic
150	C₂²×C₃²	#135	1	1	yes	characteristic
151	C₂²×C₃²	#135	1	1	yes	characteristic
152	C₃²×C₄	—	2	2	no	—
153	C₃²×C₄	—	2	2	no	—
154	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₃²×C₄	C₄×Q₈	1	1	yes	characteristic
156	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
157	C₃²×C₄	#125	1	1	yes	characteristic
158	C₃×Dic₃	—	4	4	no	—
159	C₃×Dic₃	—	8	2	no	—
160	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
161	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
162	C₂×C₄⋊C₄	—	3	2	no	—
163	C₂×C₄⋊C₄	—	3	2	no	—
164	C₂×C₄⋊C₄	—	6	2	no	—
165	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
166	#107	—	3	4	no	—
167	#107	—	6	2	no	—
168	C₄×C₈	—	2	2	no	—
169	#95	—	6	2	no	—
170	C₂³×C₃	—	2	1	no	—
171	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
172	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
173	C₂×C₃×C₄	—	2	2	no	—
174	C₂×C₃×C₄	—	2	2	no	—
175	C₂×C₃×C₄	—	2	2	no	—
176	C₂×C₃×C₄	—	2	2	no	—
177	C₂×C₃×C₄	—	2	1	no	—
178	C₂×C₃×C₄	—	2	1	no	—
179	C₂×C₃×C₄	—	2	1	no	—
180	C₂×C₃×C₄	—	2	1	no	—
181	C₂×C₃×C₄	—	2	1	no	—
182	C₂×C₃×C₄	—	2	1	no	—
183	C₂×C₃×C₄	—	2	1	no	—
184	C₂×C₃×C₄	—	2	1	no	—
185	C₂×C₃×C₄	—	2	2	no	—
186	C₂×C₃×C₄	—	2	2	no	—
187	C₂×C₃×C₄	—	2	1	no	—
188	C₂×C₃×C₄	—	2	1	no	—
189	C₂×C₃×C₄	—	2	1	no	—
190	C₂×C₃×C₄	—	2	1	no	—
191	C₂×C₃×C₄	—	2	1	no	—
192	C₂×C₃×C₄	—	2	1	no	—
193	C₂×C₃×C₄	—	6	4	no	—
194	C₂×C₃×C₄	—	12	2	no	—
195	C₂×C₃×C₄	—	12	2	no	—
196	C₂×C₃×C₄	—	12	2	no	—
197	C₂×C₃×C₄	—	12	2	no	—
198	C₂×C₃×C₄	—	12	2	no	—
199	C₂×C₃×C₄	D₂₄	1	2	yes	—
200	C₂×C₃×C₄	Dic₁₂	1	2	yes	—
201	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
202	C₂×C₃×C₄	C₃×Q₁₆	1	2	yes	—
203	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
204	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
205	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
206	C₂×C₃×C₄	#235	1	1	yes	characteristic
207	C₂×C₃×C₄	#235	1	1	yes	characteristic
208	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
209	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
210	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
211	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
212	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
213	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
214	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
215	C₂×Dic₃	—	2	4	no	—
216	C₂×Dic₃	—	4	2	no	—
217	C₂×Dic₃	—	4	2	no	—
218	C₂×Dic₃	—	4	2	no	—
219	C₂×Dic₃	—	4	2	no	—
220	C₂×Dic₃	—	4	2	no	—
221	C₃×C₈	—	2	4	no	—
222	C₃×C₈	—	2	2	no	—
223	C₃×C₈	—	2	2	no	—
224	C₃×C₈	—	2	4	no	—
225	C₃×C₈	Dic₃⋊C₄	1	4	yes	complemented
226	C₃×C₈	C₃×C₄⋊C₄	1	4	yes	complemented
227	C₂×C₃²	#389	1	1	yes	characteristic
228	C₂×C₃²	C₄×D₈	1	1	yes	characteristic
229	C₂×C₃²	C₄×Q₁₆	1	1	yes	characteristic
230	C₂×C₃²	#466	1	1	yes	characteristic
231	C₂×C₃²	#467	1	1	yes	characteristic
232	C₂×C₃²	#499	1	1	yes	characteristic
233	C₂×C₃²	#500	1	1	yes	characteristic
234	C₂²×C₄	—	6	2	no	—
235	C₂²×C₄	—	6	2	no	—
236	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
237	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
239	C₂×C₈	—	2	1	no	—
240	C₂×C₈	—	2	1	no	—
241	C₂×C₈	C₃×Dic₆	1	2	yes	—
242	C₂×C₈	C₃×Dic₆	1	2	yes	—
243	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
244	C₂×C₈	C₃×#67	1	2	yes	—
245	C₄⋊C₄	—	3	4	no	—
246	C₄⋊C₄	—	6	2	no	—
247	C₄⋊C₄	—	6	2	no	—
248	C₄⋊C₄	—	6	2	no	—
249	C₄⋊C₄	—	12	4	no	—
250	C₄²	—	2	1	no	—
251	C₄²	—	2	1	no	—
252	C₂²×C₃	—	2	1	no	—
253	C₂²×C₃	—	2	1	no	—
254	C₂²×C₃	—	2	1	no	—
255	C₂²×C₃	—	2	1	no	—
256	C₂²×C₃	—	2	1	no	—
257	C₂²×C₃	—	2	1	no	—
258	C₂²×C₃	—	2	1	no	—
259	C₂²×C₃	#869	1	1	yes	characteristic
260	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
261	C₂²×C₃	C₂×D₂₄	1	1	yes	characteristic
262	C₂²×C₃	#904	1	1	yes	characteristic
263	C₂²×C₃	#904	1	1	yes	characteristic
264	C₂²×C₃	C₂×Dic₁₂	1	1	yes	characteristic
265	C₂²×C₃	#930	1	1	yes	characteristic
266	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
267	C₂²×C₃	C₃×#121	1	1	yes	characteristic
268	C₂²×C₃	C₃×C₄⋊Q₈	1	1	yes	characteristic
269	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
270	C₂²×C₃	C₂×C₃×Q₁₆	1	1	yes	characteristic
271	C₂²×C₃	C₃×#135	1	1	yes	characteristic
272	C₂²×C₃	C₃×#135	1	1	yes	characteristic
273	C₃×C₄	—	2	4	no	—
274	C₃×C₄	—	2	4	no	—
275	C₃×C₄	—	2	2	no	—
276	C₃×C₄	—	2	2	no	—
277	C₃×C₄	—	2	2	no	—
278	C₃×C₄	—	2	2	no	—
279	C₃×C₄	—	2	1	no	—
280	C₃×C₄	—	2	1	no	—
281	C₃×C₄	—	2	1	no	—
282	C₃×C₄	—	2	1	no	—
283	C₃×C₄	—	12	4	no	—
284	C₃×C₄	—	24	2	no	—
285	C₃×C₄	C₄×Dic₆	1	1	yes	characteristic
286	C₃×C₄	#870	1	1	yes	characteristic
287	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
288	C₃×C₄	#924	1	1	yes	characteristic
289	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
290	C₃×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
291	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
292	C₃×C₄	C₃×#125	1	1	yes	characteristic
293	Dic₃	—	4	4	no	—
294	Dic₃	—	8	2	no	—
295	C₃²	#1942	1	1	yes	characteristic, complemented, Sylow
296	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	6	4	no	—
302	C₂×C₄	—	12	2	no	—
303	C₂×C₄	—	12	2	no	—
304	C₂×C₄	—	12	2	no	—
305	C₂×C₄	—	12	2	no	—
306	C₂×C₄	—	12	2	no	—
307	C₂×C₄	C₃×D₂₄	1	2	yes	—
308	C₂×C₄	C₃×Dic₁₂	1	2	yes	—
309	C₂×C₄	C₂×C₃×Dic₆	1	1	yes	characteristic
310	C₂×C₄	C₂×C₃×Dic₆	1	1	yes	characteristic
311	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
312	C₂×C₄	C₃×#235	1	1	yes	characteristic
313	C₂×C₄	C₃×#235	1	1	yes	characteristic
314	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
315	C₈	—	2	2	no	—
316	C₈	C₃×Dic₃⋊C₄	1	4	yes	complemented
317	C₂×C₃	—	2	1	no	—
318	C₂×C₃	—	2	1	no	—
319	C₂×C₃	—	2	1	no	—
320	C₂×C₃	—	2	1	no	—
321	C₂×C₃	—	2	1	no	—
322	C₂×C₃	—	2	1	no	—
323	C₂×C₃	—	2	1	no	—
324	C₂×C₃	#4682	1	1	yes	characteristic
325	C₂×C₃	#4683	1	1	yes	characteristic
326	C₂×C₃	C₄×D₂₄	1	1	yes	characteristic
327	C₂×C₃	C₄×Dic₁₂	1	1	yes	characteristic
328	C₂×C₃	#4928	1	1	yes	characteristic
329	C₂×C₃	#5115	1	1	yes	characteristic
330	C₂×C₃	#5116	1	1	yes	characteristic
331	C₂×C₃	C₃×#389	1	1	yes	characteristic
332	C₂×C₃	C₃×C₄×D₈	1	1	yes	characteristic
333	C₂×C₃	C₃×C₄×Q₁₆	1	1	yes	characteristic
334	C₂×C₃	C₃×#466	1	1	yes	characteristic
335	C₂×C₃	C₃×#467	1	1	yes	characteristic
336	C₂×C₃	C₃×#499	1	1	yes	characteristic
337	C₂×C₃	C₃×#500	1	1	yes	characteristic
338	C₂²	C₃×#869	1	1	yes	characteristic
339	C₂²	C₃×C₄×D₁₂	1	1	yes	characteristic
340	C₂²	C₂×C₃×D₂₄	1	1	yes	characteristic
341	C₂²	C₃×#904	1	1	yes	characteristic
342	C₂²	C₃×#904	1	1	yes	characteristic
343	C₂²	C₂×C₃×Dic₁₂	1	1	yes	characteristic
344	C₂²	C₃×#930	1	1	yes	characteristic
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	12	4	no	—
348	C₄	—	24	2	no	—
349	C₄	C₃×C₄×Dic₆	1	1	yes	characteristic
350	C₄	C₃×#870	1	1	yes	characteristic
351	C₄	C₂×C₃×Dic₃⋊C₄	1	1	yes	characteristic
352	C₄	C₃×#924	1	1	yes	characteristic
353	C₃	—	2	1	no	—
354	C₃	#69770	1	1	yes	characteristic, direct product factor
355	C₃	C₃×#1942	1	1	yes	characteristic, complemented
356	C₂	C₃×#4682	1	1	yes	characteristic
357	C₂	C₃×#4683	1	1	yes	characteristic
358	C₂	C₃×C₄×D₂₄	1	1	yes	characteristic
359	C₂	C₃×C₄×Dic₁₂	1	1	yes	characteristic
360	C₂	C₃×#4928	1	1	yes	characteristic
361	C₂	C₃×#5115	1	1	yes	characteristic
362	C₂	C₃×#5116	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle, prime radical	C₂³×C₃²	C₂×D₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₃×#1942
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
7. #69770	C₃	direct (N × H)
17. C₃×#818	C₄	semidirect
71. #818	C₃×C₄	semidirect
92. C₃²×C₈	C₄⋊C₄	semidirect
225. C₃×C₈	Dic₃⋊C₄	semidirect
226. C₃×C₈	C₃×C₄⋊C₄	semidirect
295. C₃²	#1942	semidirect
316. C₈	C₃×Dic₃⋊C₄	semidirect
354. C₃	#69770	direct (N × H)
355. C₃	C₃×#1942	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄×C₈	2
C₂×C₃×#818	2
C₃×#4928	2
C₃×#4551	2
C₃×#1942	3
#69770	3

Subgroups — C3×#69770 #11790131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69770 #11790131