Subgroups — C₃×#79166 #11860197

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic
2	C₃×#5522	C₂	1	2	yes	maximal, complemented
3	C₃²×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#815	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5002	C₂	1	2	yes	maximal, complemented
6	C₃×#4889	C₂	1	4	yes	maximal, complemented
7	C₃×#4869	C₂	1	2	yes	maximal, complemented
8	C₃×#4853	C₂	1	2	yes	maximal, complemented
9	C₃×#2943	—	3	1	no	maximal
10	#79166	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#235	C₂²	1	2	yes	—
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₃²×#117	C₂²	1	2	yes	—
14	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
17	C₃×#904	C₄	1	8	yes	complemented
18	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×#204	C₂²	1	2	yes	—
20	C₃×#893	C₂²	1	4	yes	—
21	C₃×#887	C₂²	1	4	yes	—
22	C₃×#67⋊C₄	—	2	4	no	—
23	C₃×#872	—	2	2	no	—
24	C₃×C₄²×D₃	—	2	2	no	—
25	C₃²×#107	C₂²	1	2	yes	—
26	C₃²×#106	C₂²	1	2	yes	—
27	C₃×#815	C₂²	1	2	yes	—
28	C₃×#815	C₂²	1	2	yes	—
29	C₃×#810	C₂²	1	4	yes	—
30	C₃×#809	C₂²	1	4	yes	—
31	C₂×C₃×#135	—	3	1	no	—
32	C₃×C₄×#41	—	3	2	no	—
33	C₂×#904	C₂×C₃	1	1	yes	characteristic
34	#5522	C₂×C₃	1	2	yes	complemented
35	C₃×#442	—	3	2	no	—
36	C₃×#441	—	3	2	no	—
37	C₃×#440	—	3	4	no	—
38	C₃×#427	—	2	1	no	—
39	C₃×#427	D₃	1	1	yes	characteristic, complemented
40	C₃×#427	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×#416	—	3	2	no	—
42	C₂×C₃×#97	—	3	1	no	—
43	C₂×#815	C₂×C₃	1	1	yes	characteristic, complemented
44	#5002	C₂×C₃	1	2	yes	complemented
45	#4889	C₂×C₃	1	4	yes	complemented
46	#4869	C₂×C₃	1	2	yes	complemented
47	#4853	C₂×C₃	1	2	yes	complemented
48	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃×#67	—	2	2	no	—
50	C₂²×C₃×Dic₃	D₄	1	2	yes	—
51	C₃×#235	—	2	4	no	—
52	C₃×#235	C₂×C₄	1	8	yes	complemented
53	C₂×C₃×D₁₂	C₂³	1	2	yes	—
54	C₂×C₃×C₄×D₃	—	2	2	no	—
55	C₂×C₃×C₄×D₃	—	2	4	no	—
56	C₂×C₃×Dic₆	C₂³	1	2	yes	—
57	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
58	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
59	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
60	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
61	C₃²×C₂²⋊C₄	—	2	2	no	—
62	C₃²×C₄²	—	2	2	no	—
63	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₃×Dic₃⋊C₄	—	2	4	no	—
65	C₃×C₄×Dic₃	—	2	4	no	—
66	C₃×C₄×Dic₃	D₄	1	2	yes	—
67	C₃×C₄×Dic₃	C₂³	1	2	yes	—
68	C₂×C₃×C₃⋊C₈	—	2	2	no	—
69	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
70	C₃×Dic₁₂	C₂×C₄	1	4	yes	complemented
71	C₃×D₂₄	C₂×C₄	1	4	yes	complemented
72	C₃×#204	C₂×C₄	1	8	yes	complemented
73	#2943	—	3	1	no	Sylow
74	C₂×C₃×#41	—	3	2	no	—
75	C₂×#235	C₂²×C₃	1	2	yes	—
76	C₃×#135	—	3	8	no	—
77	C₂×C₃×Q₁₆	—	3	1	no	—
78	C₂×C₃×SD₁₆	—	3	2	no	—
79	C₂×C₃×D₈	—	3	1	no	—
80	C₂²×C₃×C₈	—	2	1	no	—
81	C₂²×C₃×C₈	—	3	1	no	—
82	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
83	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
84	C₃×C₄×Q₈	—	3	4	no	—
85	C₃×C₄×D₄	—	3	4	no	—
86	C₃×C₄×D₄	—	6	4	no	—
87	C₃×#117	—	2	2	no	—
88	C₃×#117	—	6	2	no	—
89	C₃×#117	C₂×D₃	1	2	yes	—
90	C₃×#117	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₄²	—	3	1	no	—
92	C₂×C₃×C₄²	—	6	2	no	—
93	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
95	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
96	#904	C₃×C₄	1	8	yes	complemented
97	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×#204	C₂²×C₃	1	2	yes	—
99	#893	C₂²×C₃	1	4	yes	—
100	#887	C₂²×C₃	1	4	yes	—
101	#67⋊C₄	—	2	4	no	—
102	#872	—	2	2	no	—
103	C₄²×D₃	—	2	2	no	—
104	C₃×#107	—	2	2	no	—
105	C₃×#107	C₂×D₃	1	2	yes	—
106	C₃×#107	C₂²×C₃	1	2	yes	—
107	C₃×#106	—	2	2	no	—
108	C₃×#106	C₂×D₃	1	2	yes	—
109	C₃×#106	C₂²×C₃	1	2	yes	—
110	C₃×#103	—	3	4	no	—
111	C₃×#102	—	3	4	no	—
112	C₃×#97	—	3	2	no	—
113	C₃×#97	—	3	2	no	—
114	#815	C₂²×C₃	1	2	yes	—
115	#815	C₂²×C₃	1	2	yes	—
116	#810	C₂²×C₃	1	4	yes	—
117	#809	C₂²×C₃	1	4	yes	—
118	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₃×D₃	—	2	2	no	—
120	C₂×C₃²×C₄	—	2	4	no	—
121	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
122	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	#41	1	2	yes	—
124	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
125	C₃×#67	—	2	8	no	—
126	C₂×C₃×Dic₃	—	2	2	no	—
127	C₂×C₃×Dic₃	—	4	2	no	—
128	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	—
129	C₃×D₁₂	—	2	2	no	—
130	C₃×D₁₂	C₂²×C₄	1	4	yes	—
131	C₃×C₄×D₃	—	2	8	no	—
132	C₃×C₄×D₃	—	4	8	no	—
133	C₃×Dic₆	—	2	2	no	—
134	C₃×Dic₆	C₂²×C₄	1	4	yes	—
135	C₃²×C₈	C₂²×C₄	1	2	yes	—
136	C₃²×C₈	C₂²×C₄	1	2	yes	—
137	C₃×C₃⋊C₈	—	2	2	no	—
138	C₂×#135	—	3	1	no	—
139	C₄×#41	—	3	2	no	—
140	#442	—	3	2	no	—
141	#441	—	3	2	no	—
142	#440	—	3	4	no	—
143	#427	C₃×D₃	1	1	yes	characteristic, complemented
144	#416	—	3	2	no	—
145	C₂×#97	—	3	1	no	—
146	C₃×#41	—	3	8	no	—
147	C₃×#41	—	6	4	no	—
148	C₂×C₃×Q₈	—	3	2	no	—
149	C₂×C₃×D₄	—	3	2	no	—
150	C₂×C₃×D₄	—	6	2	no	—
151	C₂²×C₃×C₄	—	2	1	no	—
152	C₂²×C₃×C₄	—	3	2	no	—
153	C₂²×C₃×C₄	—	6	4	no	—
154	C₂²×C₃×C₄	—	6	2	no	—
155	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂×#67	—	2	2	no	—
158	C₂²×Dic₃	C₃×D₄	1	2	yes	—
159	#235	—	2	4	no	—
160	#235	C₂×C₃×C₄	1	8	yes	complemented
161	C₂×D₁₂	C₂³×C₃	1	2	yes	—
162	C₂×C₄×D₃	—	2	2	no	—
163	C₂×C₄×D₃	—	2	4	no	—
164	C₂×Dic₆	C₂³×C₃	1	2	yes	—
165	C₃×Q₁₆	—	3	4	no	—
166	C₃×SD₁₆	—	3	8	no	—
167	C₃×D₈	—	3	4	no	—
168	C₂×C₃×C₈	—	2	4	no	—
169	C₂×C₃×C₈	—	2	1	no	—
170	C₂×C₃×C₈	—	2	1	no	—
171	C₂×C₃×C₈	—	3	2	no	—
172	C₂×C₃×C₈	—	6	2	no	—
173	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
174	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
175	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
176	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
177	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
179	C₃×C₄⋊C₄	—	2	4	no	—
180	C₃×C₄⋊C₄	—	6	4	no	—
181	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
182	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
183	C₃×C₂²⋊C₄	—	2	2	no	—
184	C₃×C₂²⋊C₄	—	2	2	no	—
185	C₃×C₂²⋊C₄	—	4	2	no	—
186	C₃×C₂²⋊C₄	—	6	4	no	—
187	C₃×C₄²	—	2	2	no	—
188	C₃×C₄²	—	2	2	no	—
189	C₃×C₄²	—	3	2	no	—
190	C₃×C₄²	—	3	2	no	—
191	C₃×C₄²	—	4	2	no	—
192	C₃×C₄²	—	6	4	no	—
193	(C₂×D₃)⋊C₄	—	2	4	no	—
194	Dic₃⋊C₄	—	2	4	no	—
195	C₄×Dic₃	—	2	4	no	—
196	C₄×Dic₃	C₃×D₄	1	2	yes	—
197	C₄×Dic₃	C₂³×C₃	1	2	yes	—
198	C₂×C₃⋊C₈	—	2	2	no	—
199	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
200	Dic₁₂	C₂×C₃×C₄	1	4	yes	complemented
201	D₂₄	C₂×C₃×C₄	1	4	yes	complemented
202	#204	C₂×C₃×C₄	1	8	yes	complemented
203	C₂²×C₃²	—	2	2	no	—
204	C₂²×C₃²	C₄×D₄	1	2	yes	—
205	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₃×D₃	—	2	4	no	—
207	C₂×C₃×D₃	—	4	4	no	—
208	C₃²×C₄	—	4	4	no	—
209	C₃²×C₄	C₄×D₄	1	2	yes	—
210	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
211	C₃²×C₄	C₂×#41	1	1	yes	characteristic
212	C₃×Dic₃	—	2	4	no	—
213	C₃×Dic₃	—	2	4	no	—
214	C₂×#41	—	3	2	no	—
215	#135	—	3	8	no	—
216	C₂×Q₁₆	—	3	1	no	—
217	C₂×SD₁₆	—	3	2	no	—
218	C₂×D₈	—	3	1	no	—
219	C₂²×C₈	—	3	1	no	—
220	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
221	C₄×Q₈	—	3	4	no	—
222	C₄×D₄	—	3	4	no	—
223	C₄×D₄	—	6	4	no	—
224	#117	—	6	2	no	—
225	#117	C₂×C₃×D₃	1	2	yes	—
226	C₂×C₄²	—	3	1	no	—
227	C₂×C₄²	—	6	2	no	—
228	#107	C₂×C₃×D₃	1	2	yes	—
229	#106	C₂×C₃×D₃	1	2	yes	—
230	#103	—	3	4	no	—
231	#102	—	3	4	no	—
232	#97	—	3	2	no	—
233	#97	—	3	2	no	—
234	C₂³×C₃	—	2	1	no	—
235	C₂³×C₃	—	6	2	no	—
236	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
237	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂²×D₃	—	2	2	no	—
239	C₃×Q₈	—	3	4	no	—
240	C₃×Q₈	—	6	2	no	—
241	C₃×D₄	—	3	4	no	—
242	C₃×D₄	—	6	8	no	—
243	C₃×D₄	—	6	2	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	3	4	no	—
251	C₂×C₃×C₄	—	4	4	no	—
252	C₂×C₃×C₄	—	6	2	no	—
253	C₂×C₃×C₄	—	6	8	no	—
254	C₂×C₃×C₄	—	12	8	no	—
255	C₂×C₃×C₄	—	12	2	no	—
256	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
257	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	#239	1	2	yes	—
259	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
260	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₃×#41	1	2	yes	—
262	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
264	#67	—	2	8	no	—
265	C₂×Dic₃	—	2	2	no	—
266	C₂×Dic₃	—	4	2	no	—
267	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	—
268	D₁₂	—	2	2	no	—
269	D₁₂	C₂²×C₃×C₄	1	4	yes	—
270	C₄×D₃	—	2	8	no	—
271	C₄×D₃	—	4	8	no	—
272	Dic₆	—	2	2	no	—
273	Dic₆	C₂²×C₃×C₄	1	4	yes	—
274	C₃×C₈	—	2	2	no	—
275	C₃×C₈	—	2	2	no	—
276	C₃×C₈	—	6	2	no	—
277	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
278	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
279	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
280	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
281	C₃⋊C₈	—	2	2	no	—
282	C₂×C₃²	—	2	2	no	—
283	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
284	C₂×C₃²	#575	1	2	yes	—
285	C₃×D₃	—	4	4	no	—
286	#41	—	3	8	no	—
287	#41	—	6	4	no	—
288	C₂×Q₈	—	3	2	no	—
289	C₂×D₄	—	3	2	no	—
290	C₂×D₄	—	6	2	no	—
291	C₂²×C₄	—	3	2	no	—
292	C₂²×C₄	—	6	4	no	—
293	C₂²×C₄	—	6	2	no	—
294	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
295	Q₁₆	—	3	4	no	—
296	SD₁₆	—	3	8	no	—
297	D₈	—	3	4	no	—
298	C₂×C₈	—	3	2	no	—
299	C₂×C₈	—	6	2	no	—
300	C₂×C₈	C₃×C₄×D₃	1	4	yes	complemented
301	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
302	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
303	C₄⋊C₄	—	6	4	no	—
304	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	6	4	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	3	2	no	—
309	C₄²	—	3	2	no	—
310	C₄²	—	6	4	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	4	2	no	—
316	C₂²×C₃	—	6	4	no	—
317	C₂²×C₃	—	12	4	no	—
318	C₂²×C₃	#893	1	2	yes	—
319	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
320	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
321	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
322	C₂×D₃	—	2	4	no	—
323	C₂×D₃	—	4	4	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	4	4	no	—
328	C₃×C₄	—	4	4	no	—
329	C₃×C₄	—	6	4	no	—
330	C₃×C₄	—	6	4	no	—
331	C₃×C₄	—	8	4	no	—
332	C₃×C₄	#893	1	2	yes	—
333	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
334	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
335	C₃×C₄	C₂×#239	1	1	yes	characteristic
336	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
337	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
338	Dic₃	—	2	4	no	—
339	Dic₃	—	2	4	no	—
340	C₃²	#2943	1	1	yes	characteristic, complemented, Sylow
341	C₂³	—	6	2	no	—
342	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
343	Q₈	—	3	4	no	—
344	Q₈	—	6	2	no	—
345	D₄	—	3	4	no	—
346	D₄	—	6	8	no	—
347	D₄	—	6	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	3	4	no	—
350	C₂×C₄	—	6	2	no	—
351	C₂×C₄	—	6	8	no	—
352	C₂×C₄	—	12	8	no	—
353	C₂×C₄	—	12	2	no	—
354	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
355	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
356	C₂×C₄	C₃×#239	1	2	yes	—
357	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
358	C₈	—	6	2	no	—
359	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
360	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
361	C₂×C₃	—	2	2	no	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	2	no	—
365	C₂×C₃	—	4	2	no	—
366	C₂×C₃	—	12	4	no	—
367	C₂×C₃	C₂×#893	1	1	yes	characteristic
368	C₂×C₃	#5768	1	2	yes	—
369	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
370	C₂×C₃	C₃×#575	1	2	yes	—
371	D₃	—	4	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	6	4	no	—
374	C₂²	—	12	4	no	—
375	C₂²	C₃×#893	1	2	yes	—
376	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
377	C₄	—	4	4	no	—
378	C₄	—	6	4	no	—
379	C₄	—	6	4	no	—
380	C₄	C₃×#893	1	2	yes	—
381	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
382	C₄	C₂×C₃×#239	1	1	yes	characteristic
383	C₃	—	2	1	no	—
384	C₃	#79166	1	1	yes	characteristic, direct product factor
385	C₃	C₃×#2943	1	1	yes	characteristic, complemented
386	C₂	—	2	2	no	—
387	C₂	—	12	4	no	—
388	C₂	C₂×C₃×#893	1	1	yes	characteristic
389	C₂	C₃×#5768	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#427	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#427	D₃
hypocenter	C₃	C₃×#2943
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#427

Complements

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

N	H ≅ G/N	type
2. C₃×#5522	C₂	semidirect
3. C₃²×#427	C₂	semidirect
4. C₂×C₃×#815	C₂	semidirect
5. C₃×#5002	C₂	semidirect
6. C₃×#4889	C₂	semidirect
7. C₃×#4869	C₂	semidirect
8. C₃×#4853	C₂	semidirect
10. #79166	C₃	direct (N × H)
17. C₃×#904	C₄	semidirect
34. #5522	C₂×C₃	semidirect
39. C₃×#427	D₃	semidirect
40. C₃×#427	C₂×C₃	semidirect
43. C₂×#815	C₂×C₃	semidirect
44. #5002	C₂×C₃	semidirect
45. #4889	C₂×C₃	semidirect
46. #4869	C₂×C₃	semidirect
47. #4853	C₂×C₃	semidirect
52. C₃×#235	C₂×C₄	semidirect
57. C₂×C₃²×C₈	C₂×C₄	semidirect
70. C₃×Dic₁₂	C₂×C₄	semidirect
71. C₃×D₂₄	C₂×C₄	semidirect
72. C₃×#204	C₂×C₄	semidirect
96. #904	C₃×C₄	semidirect
143. #427	C₃×D₃	semidirect
160. #235	C₂×C₃×C₄	semidirect
173. C₂×C₃×C₈	C₄×D₃	semidirect
174. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
200. Dic₁₂	C₂×C₃×C₄	semidirect
201. D₂₄	C₂×C₃×C₄	semidirect
202. #204	C₂×C₃×C₄	semidirect
300. C₂×C₈	C₃×C₄×D₃	semidirect
340. C₃²	#2943	semidirect
384. C₃	#79166	direct (N × H)
385. C₃	C₃×#2943	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#904	2
C₃×#5522	2
C₃²×#427	2
C₂×C₃×#815	2
C₃×#5002	2
C₃×#4889	2
C₃×#4869	2
C₃×#4853	2
C₃×#2943	3
#79166	3

Subgroups — C3×#79166 #11860197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79166 #11860197