Subgroups — C₃×#83823 #11860675

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#5798	C₂	1	2	yes	maximal, complemented
3	C₃×#5215	C₂	1	2	yes	maximal, complemented
4	C₃×#5152	C₂	1	4	yes	maximal, complemented
5	C₃×Dic₃×D₈	C₂	1	4	yes	maximal, complemented
6	C₃×#5106	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5101	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2948	—	3	1	no	maximal
9	#83823	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃²×D₄	C₂²	1	2	yes	—
11	C₂×C₃²×D₈	C₄	1	8	yes	complemented
12	C₂×C₃²×D₈	C₂²	1	2	yes	—
13	C₂×C₃²×D₈	C₂²	1	2	yes	—
14	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#217	—	2	4	no	—
16	C₃×D₄×Dic₃	—	2	4	no	—
17	C₃×D₄×Dic₃	C₂²	1	8	yes	complemented
18	C₃×#926	C₂²	1	2	yes	—
19	C₃×#926	C₂²	1	1	yes	characteristic
20	C₂×C₃×#208	C₂²	1	1	yes	characteristic
21	C₃×#832	C₂²	1	8	yes	complemented
22	C₃×#818	C₂²	1	2	yes	complemented
23	C₃×#817	C₂²	1	2	yes	complemented
24	C₃×#815	C₂²	1	2	yes	complemented
25	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
26	C₂²×C₃×D₈	—	2	1	no	—
27	C₂²×C₃×D₈	D₃	1	1	yes	characteristic
28	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic
29	C₃×#518	—	3	2	no	—
30	#5798	C₂×C₃	1	2	yes	complemented
31	C₃×#442	—	3	4	no	—
32	C₃×C₄×D₈	—	3	4	no	—
33	C₃×#427	—	3	1	no	—
34	C₃×#418	—	3	2	no	—
35	C₃×#405	—	3	1	no	—
36	#5215	C₂×C₃	1	2	yes	complemented
37	#5152	C₂×C₃	1	4	yes	complemented
38	Dic₃×D₈	C₂×C₃	1	4	yes	complemented
39	#5106	C₂×C₃	1	1	yes	characteristic, complemented
40	#5101	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃²	—	2	2	no	—
42	C₂×C₃²×D₄	—	2	2	no	—
43	C₂×C₃²×D₄	—	2	4	no	—
44	C₂×C₃²×D₄	C₂×C₄	1	8	yes	complemented
45	C₂×C₃²×D₄	C₂³	1	4	yes	—
46	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
47	C₂²×C₃×Dic₃	—	2	8	no	—
48	C₃²×D₈	C₂×C₄	1	8	yes	complemented
49	C₃²×D₈	C₂×C₄	1	8	yes	complemented
50	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
51	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
52	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
53	C₃×#217	—	2	2	no	—
54	C₃×#217	—	2	8	no	—
55	C₃×#217	D₄	1	2	yes	—
56	C₃×C₄⋊Dic₃	D₄	1	2	yes	—
57	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
58	C₃×C₄×Dic₃	—	2	2	no	—
59	C₃×C₄×Dic₃	C₂³	1	2	yes	—
60	C₃×#208	—	2	2	no	—
61	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
62	#2948	—	3	1	no	Sylow
63	C₂²×C₃×D₄	—	2	2	no	—
64	C₂²×C₃×D₄	C₂×D₃	1	2	yes	—
65	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
66	C₂×C₃×D₈	—	2	8	no	—
67	C₂×C₃×D₈	—	2	2	no	—
68	C₂×C₃×D₈	—	2	2	no	—
69	C₂×C₃×D₈	Dic₃	1	8	yes	complemented
70	C₂×C₃×D₈	C₃×C₄	1	8	yes	complemented
71	C₂×C₃×D₈	C₂×D₃	1	2	yes	—
72	C₂×C₃×D₈	C₂×D₃	1	2	yes	—
73	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
74	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
75	C₂×C₃×M₁₆	—	3	1	no	—
76	C₂²×C₃×C₈	—	2	1	no	—
77	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
79	C₃×C₄×D₄	—	3	8	no	—
80	C₃×C₄×D₄	—	6	4	no	—
81	C₃×#117	—	3	1	no	—
82	C₃×#117	—	3	2	no	—
83	C₂×C₃×C₂²⋊C₄	—	6	4	no	—
84	C₂×#217	—	2	4	no	—
85	D₄×Dic₃	—	2	4	no	—
86	D₄×Dic₃	C₂²×C₃	1	8	yes	complemented
87	#926	C₂²×C₃	1	2	yes	—
88	#926	C₂²×C₃	1	1	yes	characteristic
89	C₂×#208	C₂²×C₃	1	1	yes	characteristic
90	C₃×#107	—	3	2	no	—
91	C₃×#106	—	3	2	no	—
92	C₃×#102	—	3	8	no	—
93	C₃×#97	—	3	2	no	—
94	C₃×C₄×C₈	—	3	2	no	—
95	#832	C₂²×C₃	1	8	yes	complemented
96	#818	C₂²×C₃	1	2	yes	complemented
97	#817	C₂²×C₃	1	2	yes	complemented
98	#815	C₂²×C₃	1	2	yes	complemented
99	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
100	C₂³×C₃²	—	2	4	no	—
101	C₂³×C₃²	—	2	8	no	—
102	C₂³×C₃²	—	8	4	no	—
103	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
104	C₃²×D₄	—	2	8	no	—
105	C₃²×D₄	—	2	4	no	—
106	C₃²×D₄	C₂²×C₄	1	8	yes	—
107	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
108	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃²×C₄	#41	1	2	yes	—
110	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
111	C₂×C₃×Dic₃	—	2	4	no	—
112	C₂×C₃×Dic₃	—	8	8	no	—
113	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	—
114	C₃²×C₈	C₂²×C₄	1	2	yes	—
115	C₃²×C₈	C₂²×C₄	1	2	yes	—
116	C₃×C₃⋊C₈	—	2	2	no	—
117	C₂²×D₈	C₃×D₃	1	1	yes	characteristic
118	#518	—	3	2	no	—
119	#442	—	3	4	no	—
120	C₄×D₈	—	3	4	no	—
121	#427	—	3	1	no	—
122	#418	—	3	2	no	—
123	#405	—	3	1	no	—
124	C₂⁴×C₃	—	2	2	no	—
125	C₂⁴×C₃	—	2	2	no	—
126	C₂⁴×C₃	—	4	2	no	—
127	C₂×C₃×D₄	—	2	2	no	—
128	C₂×C₃×D₄	—	2	4	no	—
129	C₂×C₃×D₄	—	2	2	no	—
130	C₂×C₃×D₄	—	2	4	no	—
131	C₂×C₃×D₄	—	2	8	no	—
132	C₂×C₃×D₄	—	2	4	no	—
133	C₂×C₃×D₄	—	4	2	no	—
134	C₂×C₃×D₄	—	4	4	no	—
135	C₂×C₃×D₄	C₂×Dic₃	1	8	yes	complemented
136	C₂×C₃×D₄	C₂×C₃×C₄	1	8	yes	complemented
137	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
138	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	—	6	8	no	—
141	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
143	C₂²×Dic₃	—	2	8	no	—
144	C₃×D₈	—	2	8	no	—
145	C₃×D₈	—	2	8	no	—
146	C₃×D₈	C₂×Dic₃	1	8	yes	complemented
147	C₃×D₈	C₂×Dic₃	1	8	yes	complemented
148	C₃×D₈	C₂×C₃×C₄	1	8	yes	complemented
149	C₃×D₈	C₂×C₃×C₄	1	8	yes	complemented
150	C₃×M₁₆	—	6	2	no	—
151	C₂×C₃×C₈	—	2	4	no	—
152	C₂×C₃×C₈	—	2	1	no	—
153	C₂×C₃×C₈	—	2	1	no	—
154	C₂×C₃×C₈	—	3	2	no	—
155	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	complemented
156	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
157	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
158	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
159	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
161	C₃×C₄⋊C₄	—	3	2	no	—
162	C₃×C₄⋊C₄	—	3	4	no	—
163	C₃×C₂²⋊C₄	—	3	2	no	—
164	C₃×C₂²⋊C₄	—	6	8	no	—
165	C₃×C₂²⋊C₄	—	6	2	no	—
166	C₃×C₄²	—	3	2	no	—
167	C₃×C₄²	—	6	2	no	—
168	#217	—	2	2	no	—
169	#217	—	2	8	no	—
170	#217	C₃×D₄	1	2	yes	—
171	C₄⋊Dic₃	C₃×D₄	1	2	yes	—
172	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
173	C₄×Dic₃	—	2	2	no	—
174	C₄×Dic₃	C₂³×C₃	1	2	yes	—
175	#208	—	2	2	no	—
176	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
177	C₂²×C₃²	—	2	2	no	—
178	C₂²×C₃²	—	2	8	no	—
179	C₂²×C₃²	—	4	8	no	—
180	C₂²×C₃²	—	8	8	no	—
181	C₂²×C₃²	C₄×D₄	1	2	yes	—
182	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
183	C₃²×C₄	C₄×D₄	1	2	yes	—
184	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
185	C₃²×C₄	C₂×#41	1	1	yes	characteristic
186	C₃×Dic₃	—	2	4	no	—
187	C₃×Dic₃	—	4	4	no	—
188	C₂²×D₄	C₂×C₃×D₃	1	2	yes	—
189	C₂×D₈	C₃×Dic₃	1	8	yes	complemented
190	C₂×D₈	C₂×C₃×D₃	1	2	yes	—
191	C₂×D₈	C₂×C₃×D₃	1	2	yes	—
192	C₂×M₁₆	—	3	1	no	—
193	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
194	C₄×D₄	—	3	8	no	—
195	C₄×D₄	—	6	4	no	—
196	#117	—	3	1	no	—
197	#117	—	3	2	no	—
198	C₂×C₂²⋊C₄	—	6	4	no	—
199	#107	—	3	2	no	—
200	#106	—	3	2	no	—
201	#102	—	3	8	no	—
202	#97	—	3	2	no	—
203	C₄×C₈	—	3	2	no	—
204	C₂³×C₃	—	2	4	no	—
205	C₂³×C₃	—	2	4	no	—
206	C₂³×C₃	—	2	8	no	—
207	C₂³×C₃	—	2	8	no	—
208	C₂³×C₃	—	2	1	no	—
209	C₂³×C₃	—	4	4	no	—
210	C₂³×C₃	—	4	8	no	—
211	C₂³×C₃	—	8	4	no	—
212	C₂³×C₃	—	8	4	no	—
213	C₂³×C₃	—	8	8	no	—
214	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
215	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
216	C₃×D₄	—	2	8	no	—
217	C₃×D₄	—	2	8	no	—
218	C₃×D₄	—	2	4	no	—
219	C₃×D₄	—	2	4	no	—
220	C₃×D₄	—	2	8	no	—
221	C₃×D₄	—	4	8	no	—
222	C₃×D₄	—	4	4	no	—
223	C₃×D₄	C₂²×Dic₃	1	8	yes	—
224	C₃×D₄	C₂²×C₃×C₄	1	8	yes	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	3	4	no	—
230	C₂×C₃×C₄	—	6	4	no	—
231	C₂×C₃×C₄	—	24	8	no	—
232	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
233	C₂×C₃×C₄	#237	1	2	yes	—
234	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
235	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
236	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
237	C₂×C₃×C₄	C₃×#41	1	2	yes	—
238	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
240	C₂×Dic₃	—	2	4	no	—
241	C₂×Dic₃	—	8	8	no	—
242	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	—
243	C₃×C₈	—	2	2	no	—
244	C₃×C₈	—	2	2	no	—
245	C₃×C₈	—	6	2	no	—
246	C₃×C₈	C₂²×Dic₃	1	2	yes	—
247	C₃×C₈	C₂²×Dic₃	1	2	yes	—
248	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
249	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
250	C₃⋊C₈	—	2	2	no	—
251	C₂×C₃²	—	2	2	no	—
252	C₂×C₃²	—	4	8	no	—
253	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂×C₃²	#576	1	2	yes	—
255	C₂⁴	—	2	2	no	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	C₂×C₃×Dic₃	1	8	yes	complemented
259	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
260	C₂²×C₄	—	6	8	no	—
261	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
262	D₈	C₂×C₃×Dic₃	1	8	yes	complemented
263	D₈	C₂×C₃×Dic₃	1	8	yes	complemented
264	M₁₆	—	6	2	no	—
265	C₂×C₈	—	3	2	no	—
266	C₂×C₈	C₂×C₃×Dic₃	1	4	yes	complemented
267	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
268	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
269	C₄⋊C₄	—	3	2	no	—
270	C₄⋊C₄	—	3	4	no	—
271	C₂²⋊C₄	—	3	2	no	—
272	C₂²⋊C₄	—	6	8	no	—
273	C₂²⋊C₄	—	6	2	no	—
274	C₄²	—	3	2	no	—
275	C₄²	—	6	2	no	—
276	C₂²×C₃	—	2	4	no	—
277	C₂²×C₃	—	2	2	no	—
278	C₂²×C₃	—	2	2	no	—
279	C₂²×C₃	—	2	8	no	—
280	C₂²×C₃	—	2	8	no	—
281	C₂²×C₃	—	2	2	no	—
282	C₂²×C₃	—	2	1	no	—
283	C₂²×C₃	—	4	8	no	—
284	C₂²×C₃	—	4	8	no	—
285	C₂²×C₃	—	4	8	no	—
286	C₂²×C₃	—	8	8	no	—
287	C₂²×C₃	—	8	8	no	—
288	C₂²×C₃	—	8	8	no	—
289	C₂²×C₃	—	8	16	no	—
290	C₂²×C₃	D₄×Dic₃	1	2	yes	—
291	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
292	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
293	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
294	C₃×C₄	—	2	2	no	—
295	C₃×C₄	—	2	1	no	—
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	—	6	4	no	—
298	C₃×C₄	—	12	4	no	—
299	C₃×C₄	D₄×Dic₃	1	2	yes	—
300	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
301	C₃×C₄	C₂×#237	1	1	yes	characteristic
302	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
303	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
304	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
305	Dic₃	—	2	4	no	—
306	Dic₃	—	4	4	no	—
307	C₃²	#2948	1	1	yes	characteristic, complemented, Sylow
308	C₂³	—	2	4	no	—
309	C₂³	—	2	8	no	—
310	C₂³	—	8	4	no	—
311	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
312	D₄	—	2	8	no	—
313	D₄	—	2	4	no	—
314	D₄	C₂²×C₃×Dic₃	1	8	yes	—
315	C₂×C₄	—	3	4	no	—
316	C₂×C₄	—	6	4	no	—
317	C₂×C₄	—	24	8	no	—
318	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
319	C₂×C₄	C₃×#237	1	2	yes	—
320	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
321	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
322	C₈	—	6	2	no	—
323	C₈	C₂²×C₃×Dic₃	1	2	yes	—
324	C₈	C₂²×C₃×Dic₃	1	2	yes	—
325	C₂×C₃	—	2	4	no	—
326	C₂×C₃	—	2	2	no	—
327	C₂×C₃	—	2	2	no	—
328	C₂×C₃	—	2	2	no	—
329	C₂×C₃	—	2	1	no	—
330	C₂×C₃	—	4	8	no	—
331	C₂×C₃	—	4	8	no	—
332	C₂×C₃	—	8	8	no	—
333	C₂×C₃	#5757	1	2	yes	—
334	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
335	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
336	C₂×C₃	C₃×#576	1	2	yes	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	8	no	—
339	C₂²	—	4	8	no	—
340	C₂²	—	8	8	no	—
341	C₂²	C₃×D₄×Dic₃	1	2	yes	—
342	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
343	C₄	—	6	4	no	—
344	C₄	—	12	4	no	—
345	C₄	C₃×D₄×Dic₃	1	2	yes	—
346	C₄	C₂×C₃×#237	1	1	yes	characteristic
347	C₄	C₂³×C₃×Dic₃	1	1	yes	characteristic
348	C₃	—	2	1	no	—
349	C₃	#83823	1	1	yes	characteristic, direct product factor
350	C₃	C₃×#2948	1	1	yes	characteristic, complemented
351	C₂	—	2	2	no	—
352	C₂	—	4	8	no	—
353	C₂	C₃×#5757	1	2	yes	—
354	C₂	C₂×C₃×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting, prime radical	C₂²×C₃²×D₈	C₂
socle	C₂²×C₃²	C₂²×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂²×C₃×D₈	D₃
hypocenter	C₃	C₃×#2948
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×D₈

Complements

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

N	H ≅ G/N	type
2. C₃×#5798	C₂	semidirect
3. C₃×#5215	C₂	semidirect
4. C₃×#5152	C₂	semidirect
5. C₃×Dic₃×D₈	C₂	semidirect
6. C₃×#5106	C₂	semidirect
7. C₃×#5101	C₂	semidirect
9. #83823	C₃	direct (N × H)
11. C₂×C₃²×D₈	C₄	semidirect
17. C₃×D₄×Dic₃	C₂²	semidirect
21. C₃×#832	C₂²	semidirect
22. C₃×#818	C₂²	semidirect
23. C₃×#817	C₂²	semidirect
24. C₃×#815	C₂²	semidirect
25. C₃×C₈×Dic₃	C₂²	semidirect
30. #5798	C₂×C₃	semidirect
36. #5215	C₂×C₃	semidirect
37. #5152	C₂×C₃	semidirect
38. Dic₃×D₈	C₂×C₃	semidirect
39. #5106	C₂×C₃	semidirect
40. #5101	C₂×C₃	semidirect
44. C₂×C₃²×D₄	C₂×C₄	semidirect
48. C₃²×D₈	C₂×C₄	semidirect
49. C₃²×D₈	C₂×C₄	semidirect
50. C₂×C₃²×C₈	C₂×C₄	semidirect
69. C₂×C₃×D₈	Dic₃	semidirect
70. C₂×C₃×D₈	C₃×C₄	semidirect
86. D₄×Dic₃	C₂²×C₃	semidirect
95. #832	C₂²×C₃	semidirect
96. #818	C₂²×C₃	semidirect
97. #817	C₂²×C₃	semidirect
98. #815	C₂²×C₃	semidirect
99. C₈×Dic₃	C₂²×C₃	semidirect
135. C₂×C₃×D₄	C₂×Dic₃	semidirect
136. C₂×C₃×D₄	C₂×C₃×C₄	semidirect
146. C₃×D₈	C₂×Dic₃	semidirect
147. C₃×D₈	C₂×Dic₃	semidirect
148. C₃×D₈	C₂×C₃×C₄	semidirect
149. C₃×D₈	C₂×C₃×C₄	semidirect
155. C₂×C₃×C₈	C₂×Dic₃	semidirect
156. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
189. C₂×D₈	C₃×Dic₃	semidirect
258. C₂×D₄	C₂×C₃×Dic₃	semidirect
262. D₈	C₂×C₃×Dic₃	semidirect
263. D₈	C₂×C₃×Dic₃	semidirect
266. C₂×C₈	C₂×C₃×Dic₃	semidirect
307. C₃²	#2948	semidirect
349. C₃	#83823	direct (N × H)
350. C₃	C₃×#2948	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃²×D₈	2
C₃×#5798	2
C₃×#5215	2
C₃×#5152	2
C₃×Dic₃×D₈	2
C₃×#5106	2
C₃×#5101	2
C₃×#2948	3
#83823	3

Subgroups — C3×#83823 #11860675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83823 #11860675