Subgroups — C₃×#3511 #87395

Order 384.

1104 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#556	C₂	1	2	yes	maximal, complemented
2	C₃×#555	C₂	1	2	yes	maximal, complemented
3	C₃×#554	C₂	1	2	yes	maximal, complemented
4	C₃×#553	C₂	1	4	yes	maximal, complemented
5	C₃×#548	C₂	1	4	yes	maximal, complemented
6	C₃×#547	C₂	1	2	yes	maximal, complemented
7	C₃×#542	C₂	1	4	yes	maximal, complemented
8	C₃×#537	C₂	1	2	yes	maximal, complemented
9	C₃×#533	C₂	1	2	yes	maximal, complemented
10	C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#532	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#520	C₂	1	2	yes	maximal, complemented
14	C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
15	#3511	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂×C₃×#41	C₂²	1	1	yes	characteristic
17	C₂×C₃×#41	C₂²	1	2	yes	—
18	C₂×C₃×#41	C₂²	1	4	yes	—
19	C₂²×C₃×Q₈	C₂²	1	2	yes	—
20	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃×#127	C₂²	1	1	yes	characteristic
26	C₃×#126	C₂²	1	8	yes	—
27	C₃×#125	C₂²	1	4	yes	—
28	C₃×#124	C₂²	1	2	yes	—
29	C₃×#124	C₂²	1	4	yes	—
30	C₃×#124	C₂²	1	8	yes	—
31	C₃×#123	C₂²	1	8	yes	—
32	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
33	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
34	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
35	C₃×C₂²⋊Q₈	C₂²	1	8	yes	—
36	C₃×#121	C₂²	1	4	yes	—
37	C₃×#121	C₂²	1	2	yes	—
38	C₃×#121	C₂²	1	2	yes	—
39	C₃×#121	C₂²	1	4	yes	—
40	C₃×#121	C₂²	1	4	yes	—
41	C₃×#121	C₂²	1	8	yes	—
42	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
43	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
44	C₃×C₄×Q₈	C₂²	1	4	yes	—
45	C₃×C₄×Q₈	C₂²	1	4	yes	—
46	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
47	C₃×C₄×D₄	C₂²	1	2	yes	—
48	C₃×C₄×D₄	C₂²	1	2	yes	—
49	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
50	C₃×C₄×D₄	C₂²	1	4	yes	—
51	C₃×C₄×D₄	C₂²	1	8	yes	—
52	C₃×C₄×D₄	C₂²	1	2	yes	—
53	C₃×C₄×D₄	C₂²	1	4	yes	—
54	C₃×C₄×D₄	C₂²	1	2	yes	—
55	C₃×#117	C₂²	1	1	yes	characteristic
56	C₃×#117	C₂²	1	2	yes	—
57	C₃×#117	C₂²	1	4	yes	—
58	C₃×#117	C₂²	1	4	yes	—
59	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
60	C₂×C₃×C₄⋊C₄	C₂²	1	4	yes	—
61	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
62	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
63	C₂×C₃×C₄²	C₂²	1	2	yes	—
64	#556	C₂×C₃	1	2	yes	complemented
65	#555	C₂×C₃	1	2	yes	complemented
66	#554	C₂×C₃	1	2	yes	complemented
67	#553	C₂×C₃	1	4	yes	complemented
68	#548	C₂×C₃	1	4	yes	complemented
69	#547	C₂×C₃	1	2	yes	complemented
70	#542	C₂×C₃	1	4	yes	complemented
71	#537	C₂×C₃	1	2	yes	complemented
72	#533	C₂×C₃	1	2	yes	complemented
73	#532	C₂×C₃	1	1	yes	characteristic, complemented
74	#532	C₂×C₃	1	2	yes	complemented
75	C₂×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
76	#520	C₂×C₃	1	2	yes	complemented
77	C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
78	C₃×#41	—	2	4	no	—
79	C₃×#41	—	2	8	no	—
80	C₃×#41	—	4	8	no	—
81	C₂×C₃×Q₈	—	4	4	no	—
82	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×Q₈	C₂³	1	2	yes	—
84	C₂×C₃×Q₈	C₂³	1	4	yes	—
85	C₂×C₃×Q₈	C₂³	1	4	yes	—
86	C₂×C₃×D₄	C₂³	1	2	yes	—
87	C₂×C₃×D₄	C₂³	1	2	yes	—
88	C₂×C₃×D₄	C₂³	1	4	yes	—
89	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
90	C₂×C₃×D₄	C₂³	1	2	yes	—
91	C₂×C₃×D₄	C₂³	1	2	yes	—
92	C₂×C₃×D₄	C₂³	1	8	yes	—
93	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄	C₂³	1	2	yes	—
95	C₂²×C₃×C₄	C₂³	1	2	yes	—
96	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄	C₂³	1	2	yes	—
98	C₂²×C₃×C₄	C₂³	1	4	yes	—
99	C₂²×C₃×C₄	C₂³	1	4	yes	—
100	C₂²×C₃×C₄	C₂³	1	8	yes	—
101	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
102	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₃×C₄⋊C₄	C₂³	1	4	yes	—
104	C₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₃×C₄⋊C₄	C₂³	1	8	yes	—
107	C₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₃×C₄⋊C₄	C₂³	1	8	yes	—
114	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
116	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
119	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
120	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₃×C₄²	C₂³	1	1	yes	characteristic
123	C₃×C₄²	C₂³	1	2	yes	—
124	C₃×C₄²	C₂³	1	1	yes	characteristic
125	C₃×C₄²	C₂³	1	2	yes	—
126	C₃×C₄²	C₂³	1	1	yes	characteristic
127	C₃×C₄²	C₂³	1	1	yes	characteristic
128	C₃×C₄²	C₂³	1	2	yes	—
129	C₃×C₄²	C₂³	1	8	yes	—
130	C₂×#41	C₂²×C₃	1	1	yes	characteristic
131	C₂×#41	C₂²×C₃	1	2	yes	—
132	C₂×#41	C₂²×C₃	1	4	yes	—
133	C₂²×Q₈	C₂²×C₃	1	2	yes	—
134	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
135	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
136	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
137	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
138	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
139	#127	C₂²×C₃	1	1	yes	characteristic
140	#126	C₂²×C₃	1	8	yes	—
141	#125	C₂²×C₃	1	4	yes	—
142	#124	C₂²×C₃	1	2	yes	—
143	#124	C₂²×C₃	1	4	yes	—
144	#124	C₂²×C₃	1	8	yes	—
145	#123	C₂²×C₃	1	8	yes	—
146	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
147	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
148	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
149	C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
150	#121	C₂²×C₃	1	4	yes	—
151	#121	C₂²×C₃	1	2	yes	—
152	#121	C₂²×C₃	1	2	yes	—
153	#121	C₂²×C₃	1	4	yes	—
154	#121	C₂²×C₃	1	4	yes	—
155	#121	C₂²×C₃	1	8	yes	—
156	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
157	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₄×Q₈	C₂²×C₃	1	4	yes	—
159	C₄×Q₈	C₂²×C₃	1	4	yes	—
160	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
161	C₄×D₄	C₂²×C₃	1	2	yes	—
162	C₄×D₄	C₂²×C₃	1	2	yes	—
163	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
164	C₄×D₄	C₂²×C₃	1	4	yes	—
165	C₄×D₄	C₂²×C₃	1	8	yes	—
166	C₄×D₄	C₂²×C₃	1	2	yes	—
167	C₄×D₄	C₂²×C₃	1	4	yes	—
168	C₄×D₄	C₂²×C₃	1	2	yes	—
169	#117	C₂²×C₃	1	1	yes	characteristic
170	#117	C₂²×C₃	1	2	yes	—
171	#117	C₂²×C₃	1	4	yes	—
172	#117	C₂²×C₃	1	4	yes	—
173	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
174	C₂×C₄⋊C₄	C₂²×C₃	1	4	yes	—
175	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
176	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
177	C₂×C₄²	C₂²×C₃	1	2	yes	—
178	C₂³×C₃	C₂⁴	1	2	yes	—
179	C₂³×C₃	C₂⁴	1	4	yes	—
180	C₂³×C₃	C₂⁴	1	1	yes	characteristic
181	C₃×Q₈	—	2	2	no	—
182	C₃×Q₈	—	2	4	no	—
183	C₃×Q₈	—	2	8	no	—
184	C₃×Q₈	—	4	4	no	—
185	C₃×D₄	—	2	4	no	—
186	C₃×D₄	—	2	8	no	—
187	C₃×D₄	—	2	2	no	—
188	C₃×D₄	—	2	4	no	—
189	C₃×D₄	—	2	4	no	—
190	C₃×D₄	—	2	4	no	—
191	C₃×D₄	—	4	8	no	—
192	C₂×C₃×C₄	—	2	8	no	—
193	C₂×C₃×C₄	—	2	4	no	—
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	2	4	no	—
196	C₂×C₃×C₄	—	2	2	no	—
197	C₂×C₃×C₄	—	2	4	no	—
198	C₂×C₃×C₄	—	4	4	no	—
199	C₂×C₃×C₄	—	4	8	no	—
200	C₂×C₃×C₄	#41	1	4	yes	complemented
201	C₂×C₃×C₄	C₂⁴	1	2	yes	—
202	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
203	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
204	C₂×C₃×C₄	C₂⁴	1	2	yes	—
205	C₂×C₃×C₄	C₂⁴	1	4	yes	—
206	C₂×C₃×C₄	C₂⁴	1	2	yes	—
207	C₂×C₃×C₄	C₂⁴	1	8	yes	—
208	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
209	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
210	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
211	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
212	#41	—	2	4	no	—
213	#41	—	2	8	no	—
214	#41	—	4	8	no	—
215	C₂×Q₈	—	4	4	no	—
216	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
217	C₂×Q₈	C₂³×C₃	1	2	yes	—
218	C₂×Q₈	C₂³×C₃	1	4	yes	—
219	C₂×Q₈	C₂³×C₃	1	4	yes	—
220	C₂×D₄	C₂³×C₃	1	2	yes	—
221	C₂×D₄	C₂³×C₃	1	2	yes	—
222	C₂×D₄	C₂³×C₃	1	4	yes	—
223	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
224	C₂×D₄	C₂³×C₃	1	2	yes	—
225	C₂×D₄	C₂³×C₃	1	2	yes	—
226	C₂×D₄	C₂³×C₃	1	8	yes	—
227	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
228	C₂²×C₄	C₂³×C₃	1	2	yes	—
229	C₂²×C₄	C₂³×C₃	1	2	yes	—
230	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
231	C₂²×C₄	C₂³×C₃	1	2	yes	—
232	C₂²×C₄	C₂³×C₃	1	4	yes	—
233	C₂²×C₄	C₂³×C₃	1	4	yes	—
234	C₂²×C₄	C₂³×C₃	1	8	yes	—
235	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
236	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
237	C₄⋊C₄	C₂³×C₃	1	4	yes	—
238	C₄⋊C₄	C₂³×C₃	1	4	yes	—
239	C₄⋊C₄	C₂³×C₃	1	4	yes	—
240	C₄⋊C₄	C₂³×C₃	1	8	yes	—
241	C₄⋊C₄	C₂³×C₃	1	4	yes	—
242	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
243	C₄⋊C₄	C₂³×C₃	1	2	yes	—
244	C₄⋊C₄	C₂³×C₃	1	2	yes	—
245	C₄⋊C₄	C₂³×C₃	1	2	yes	—
246	C₄⋊C₄	C₂³×C₃	1	2	yes	—
247	C₄⋊C₄	C₂³×C₃	1	8	yes	—
248	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
249	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
250	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
251	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
252	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
253	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
254	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
255	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
256	C₄²	C₂³×C₃	1	1	yes	characteristic
257	C₄²	C₂³×C₃	1	2	yes	—
258	C₄²	C₂³×C₃	1	1	yes	characteristic
259	C₄²	C₂³×C₃	1	2	yes	—
260	C₄²	C₂³×C₃	1	1	yes	characteristic
261	C₄²	C₂³×C₃	1	1	yes	characteristic
262	C₄²	C₂³×C₃	1	2	yes	—
263	C₄²	C₂³×C₃	1	8	yes	—
264	C₂²×C₃	—	2	1	no	—
265	C₂²×C₃	—	2	1	no	—
266	C₂²×C₃	—	2	2	no	—
267	C₂²×C₃	—	2	4	no	—
268	C₂²×C₃	—	2	2	no	—
269	C₂²×C₃	—	2	4	no	—
270	C₂²×C₃	—	2	2	no	—
271	C₂²×C₃	—	2	4	no	—
272	C₂²×C₃	C₂×#41	1	2	yes	—
273	C₂²×C₃	C₂⁵	1	1	yes	characteristic
274	C₃×C₄	—	2	4	no	—
275	C₃×C₄	—	2	2	no	—
276	C₃×C₄	—	2	2	no	—
277	C₃×C₄	—	2	1	no	—
278	C₃×C₄	—	2	8	no	—
279	C₃×C₄	—	2	2	no	—
280	C₃×C₄	—	2	1	no	—
281	C₃×C₄	C₂×#41	1	2	yes	—
282	C₃×C₄	C₂×#41	1	2	yes	—
283	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
284	C₃×C₄	2₋¹⁺⁴	1	2	yes	—
285	C₂³	C₂⁴×C₃	1	2	yes	—
286	C₂³	C₂⁴×C₃	1	4	yes	—
287	C₂³	C₂⁴×C₃	1	1	yes	characteristic
288	Q₈	—	2	2	no	—
289	Q₈	—	2	4	no	—
290	Q₈	—	2	8	no	—
291	Q₈	—	4	4	no	—
292	D₄	—	2	4	no	—
293	D₄	—	2	8	no	—
294	D₄	—	2	2	no	—
295	D₄	—	2	4	no	—
296	D₄	—	2	4	no	—
297	D₄	—	2	4	no	—
298	D₄	—	4	8	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	4	8	no	—
307	C₂×C₄	C₃×#41	1	4	yes	complemented
308	C₂×C₄	C₂⁴×C₃	1	2	yes	—
309	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
310	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
311	C₂×C₄	C₂⁴×C₃	1	2	yes	—
312	C₂×C₄	C₂⁴×C₃	1	4	yes	—
313	C₂×C₄	C₂⁴×C₃	1	2	yes	—
314	C₂×C₄	C₂⁴×C₃	1	8	yes	—
315	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
316	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
317	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
318	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
319	C₂×C₃	—	2	2	no	—
320	C₂×C₃	—	4	2	no	—
321	C₂×C₃	—	4	4	no	—
322	C₂×C₃	C₂²×#41	1	1	yes	characteristic
323	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	4	no	—
333	C₂²	C₂×C₃×#41	1	2	yes	—
334	C₂²	C₂⁵×C₃	1	1	yes	characteristic
335	C₄	—	2	4	no	—
336	C₄	—	2	2	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	8	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	1	no	—
342	C₄	C₂×C₃×#41	1	2	yes	—
343	C₄	C₂×C₃×#41	1	2	yes	—
344	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
345	C₄	C₃×2₋¹⁺⁴	1	2	yes	—
346	C₃	#3511	1	1	yes	characteristic, direct product factor, Sylow
347	C₂	—	2	2	no	—
348	C₂	—	4	2	no	—
349	C₂	—	4	4	no	—
350	C₂	C₂²×C₃×#41	1	1	yes	characteristic
351	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#556	C₂	semidirect
2. C₃×#555	C₂	semidirect
3. C₃×#554	C₂	semidirect
4. C₃×#553	C₂	semidirect
5. C₃×#548	C₂	semidirect
6. C₃×#547	C₂	semidirect
7. C₃×#542	C₂	semidirect
8. C₃×#537	C₂	semidirect
9. C₃×#533	C₂	semidirect
10. C₃×#532	C₂	semidirect
11. C₃×#532	C₂	semidirect
12. C₂×C₃×C₄⋊Q₈	C₂	semidirect
13. C₃×#520	C₂	semidirect
14. C₃×C₄×#41	C₂	semidirect
15. #3511	C₃	direct (N × H)
64. #556	C₂×C₃	semidirect
65. #555	C₂×C₃	semidirect
66. #554	C₂×C₃	semidirect
67. #553	C₂×C₃	semidirect
68. #548	C₂×C₃	semidirect
69. #547	C₂×C₃	semidirect
70. #542	C₂×C₃	semidirect
71. #537	C₂×C₃	semidirect
72. #533	C₂×C₃	semidirect
73. #532	C₂×C₃	semidirect
74. #532	C₂×C₃	semidirect
75. C₂×C₄⋊Q₈	C₂×C₃	semidirect
76. #520	C₂×C₃	semidirect
77. C₄×#41	C₂×C₃	semidirect
200. C₂×C₃×C₄	#41	semidirect
307. C₂×C₄	C₃×#41	semidirect
346. C₃	#3511	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#556	2
C₃×#555	2
C₃×#554	2
C₃×#553	2
C₃×#548	2
C₃×#547	2
C₃×#542	2
C₃×#537	2
C₃×#533	2
C₃×#532	2
C₂×C₃×C₄⋊Q₈	2
C₃×#520	2
C₃×C₄×#41	2
#3511	3

Subgroups — C3×#3511 #87395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3511 #87395