Subgroups — C₂×C₃×#64155 #13179564

Order 1728.

2556 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×C₃³×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	C₃×#64155	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#3752	C₂	1	2	yes	maximal
5	C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3750	C₂	1	2	yes	maximal, complemented
7	C₂×#64155	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#946	—	3	4	no	maximal
9	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃³×Q₈	—	2	4	no	—
11	C₂×C₃³×Q₈	C₂²	1	4	yes	complemented
12	C₂²×C₃³×C₄	C₂²	1	2	yes	—
13	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
16	C₂×C₃×C₄×C₃⋊D₃	—	2	4	no	—
17	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	4	yes	—
18	C₃×#3752	C₂²	1	8	yes	—
19	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	4	yes	complemented
20	C₃×#3750	C₂²	1	8	yes	complemented
21	C₂²×C₃²×Q₈	—	2	4	no	—
22	C₂²×C₃²×Q₈	D₃	1	4	yes	complemented
23	C₂²×C₃²×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×C₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₃×C₄×D₃	—	3	4	no	—
26	#64155	C₂×C₃	1	8	yes	direct product factor
27	C₂×#3752	C₂×C₃	1	2	yes	—
28	C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×#3750	C₂×C₃	1	2	yes	complemented
30	C₃×#946	—	3	32	no	—
31	C₂×C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
32	C₂×C₃×C₄⋊Dic₃	—	3	4	no	—
33	C₂×C₃×Dic₃⋊C₄	—	3	8	no	—
34	C₂³×C₃³	C₂³	1	1	yes	characteristic
35	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
36	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
37	C₂²×C₃×C₃⋊D₃	Q₈	1	4	yes	complemented
38	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
39	C₃³×Q₈	—	2	8	no	—
40	C₂×C₃³×C₄	—	2	4	no	—
41	C₂×C₃³×C₄	D₄	1	4	yes	—
42	C₂×C₃³×C₄	C₂³	1	4	yes	—
43	C₂×C₃³×C₄	C₂³	1	2	yes	—
44	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
45	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
46	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
47	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
48	C₃×C₄×C₃⋊D₃	—	2	8	no	—
49	C₂×C₃×C₂²⋊Q₈	—	9	1	no	—
50	C₂×#946	—	3	4	no	—
51	C₂³×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
52	C₂³×C₃×D₃	—	3	4	no	—
53	C₂×C₃²×Q₈	—	2	32	no	—
54	C₂×C₃²×Q₈	—	2	16	no	—
55	C₂×C₃²×Q₈	—	2	16	no	—
56	C₂×C₃²×Q₈	—	2	4	no	—
57	C₂×C₃²×Q₈	C₂×D₃	1	16	yes	complemented
58	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
59	C₂²×C₃²×C₄	—	2	8	no	—
60	C₂²×C₃²×C₄	—	2	4	no	—
61	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
62	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
63	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
64	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
67	C₂×C₄×C₃⋊D₃	—	2	4	no	—
68	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	4	yes	—
69	C₂²×C₃×Dic₃	—	3	4	no	—
70	C₂²×C₃×Dic₃	—	3	8	no	—
71	C₂×C₃×C₄×D₃	—	3	16	no	—
72	C₂×C₃×C₄×D₃	—	6	16	no	—
73	#3752	C₂²×C₃	1	8	yes	—
74	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	4	yes	complemented
75	#3750	C₂²×C₃	1	8	yes	complemented
76	C₃×(C₂×D₃)⋊C₄	—	3	32	no	—
77	C₃×C₄⋊Dic₃	—	3	16	no	—
78	C₃×Dic₃⋊C₄	—	3	32	no	—
79	C₂²×C₃³	C₂×D₄	1	2	yes	—
80	C₂²×C₃³	C₂×Q₈	1	2	yes	—
81	C₂²×C₃³	#41	1	2	yes	—
82	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
83	C₂×C₃×C₃⋊D₃	—	2	8	no	—
84	C₂×C₃×C₃⋊D₃	—	2	2	no	—
85	C₂×C₃×C₃⋊D₃	—	2	2	no	—
86	C₂×C₃×C₃⋊D₃	C₂×Q₈	1	4	yes	complemented
87	C₃³×C₄	—	2	4	no	—
88	C₃³×C₄	C₂×D₄	1	4	yes	—
89	C₃×C₃⋊Dic₃	—	2	2	no	—
90	C₃×C₃⋊Dic₃	—	2	4	no	—
91	C₂²×C₃×Q₈	—	2	4	no	—
92	C₂²×C₃×Q₈	C₃×D₃	1	4	yes	complemented
93	C₂²×C₃×Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
94	C₂³×C₃×C₄	—	9	1	no	—
95	C₂²×C₄×D₃	—	3	4	no	—
96	C₃×C₂²⋊Q₈	—	9	8	no	—
97	C₂×C₃×C₄⋊C₄	—	9	2	no	—
98	C₂×C₃×C₄⋊C₄	—	9	1	no	—
99	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
100	#946	—	3	32	no	—
101	C₂×(C₂×D₃)⋊C₄	—	3	8	no	—
102	C₂×C₄⋊Dic₃	—	3	4	no	—
103	C₂×Dic₃⋊C₄	—	3	8	no	—
104	C₂³×C₃²	—	2	4	no	—
105	C₂³×C₃²	C₂²×D₃	1	4	yes	—
106	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
107	C₂²×C₃⋊D₃	—	2	2	no	—
108	C₂²×C₃⋊D₃	—	2	2	no	—
109	C₂²×C₃⋊D₃	C₃×Q₈	1	4	yes	complemented
110	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
111	C₂²×C₃×D₃	—	3	16	no	—
112	C₂²×C₃×D₃	—	3	8	no	—
113	C₂²×C₃×D₃	—	6	8	no	—
114	C₂²×C₃×D₃	—	6	8	no	—
115	C₃²×Q₈	—	2	64	no	—
116	C₃²×Q₈	—	2	32	no	—
117	C₃²×Q₈	—	2	8	no	—
118	C₂×C₃²×C₄	—	2	32	no	—
119	C₂×C₃²×C₄	—	2	16	no	—
120	C₂×C₃²×C₄	—	2	4	no	—
121	C₂×C₃²×C₄	—	2	16	no	—
122	C₂×C₃²×C₄	—	2	16	no	—
123	C₂×C₃²×C₄	—	2	8	no	—
124	C₂×C₃²×C₄	#67	1	16	yes	—
125	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
126	C₂×C₃²×C₄	C₂²×D₃	1	16	yes	—
127	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
128	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
129	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
130	C₂×C₃⋊Dic₃	—	2	2	no	—
131	C₂×C₃⋊Dic₃	—	2	4	no	—
132	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
133	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
134	C₄×C₃⋊D₃	—	2	8	no	—
135	C₂×C₃×Dic₃	—	3	8	no	—
136	C₂×C₃×Dic₃	—	3	16	no	—
137	C₂×C₃×Dic₃	—	6	16	no	—
138	C₂×C₃×Dic₃	—	6	8	no	—
139	C₃×C₄×D₃	—	6	32	no	—
140	C₂×C₂²⋊Q₈	—	9	1	no	Sylow
141	C₂×C₃³	C₂²⋊Q₈	1	4	yes	complemented
142	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₃³	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₃³	C₂×#41	1	1	yes	characteristic
145	C₃×C₃⋊D₃	—	2	4	no	—
146	C₂⁴×C₃	—	9	1	no	—
147	C₂³×D₃	—	3	4	no	—
148	C₂×C₃×Q₈	—	2	32	no	—
149	C₂×C₃×Q₈	—	2	16	no	—
150	C₂×C₃×Q₈	—	2	4	no	—
151	C₂×C₃×Q₈	—	2	16	no	—
152	C₂×C₃×Q₈	C₂×C₃×D₃	1	16	yes	complemented
153	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	4	yes	complemented
154	C₂²×C₃×C₄	—	2	8	no	—
155	C₂²×C₃×C₄	—	2	4	no	—
156	C₂²×C₃×C₄	—	9	2	no	—
157	C₂²×C₃×C₄	—	9	1	no	—
158	C₂²×C₃×C₄	—	9	4	no	—
159	C₂²×C₃×C₄	—	18	4	no	—
160	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
161	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
162	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
163	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
164	C₂²×Dic₃	—	3	4	no	—
165	C₂²×Dic₃	—	3	8	no	—
166	C₂×C₄×D₃	—	3	16	no	—
167	C₂×C₄×D₃	—	6	16	no	—
168	C₃×C₄⋊C₄	—	9	8	no	—
169	C₃×C₄⋊C₄	—	9	4	no	—
170	C₃×C₂²⋊C₄	—	9	8	no	—
171	(C₂×D₃)⋊C₄	—	3	32	no	—
172	C₄⋊Dic₃	—	3	16	no	—
173	Dic₃⋊C₄	—	3	32	no	—
174	C₂²×C₃²	—	2	4	no	—
175	C₂²×C₃²	—	2	8	no	—
176	C₂²×C₃²	—	2	8	no	—
177	C₂²×C₃²	—	2	8	no	—
178	C₂²×C₃²	D₃×Q₈	1	8	yes	—
179	C₂²×C₃²	#239	1	8	yes	—
180	C₂²×C₃²	C₂×#67	1	8	yes	—
181	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
182	C₂²×C₃²	C₂×C₃×Q₈	1	2	yes	—
183	C₂²×C₃²	C₃×#41	1	2	yes	—
184	C₂²×C₃²	C₂³×D₃	1	4	yes	—
185	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
186	C₂×C₃⋊D₃	—	2	8	no	—
187	C₂×C₃⋊D₃	—	2	2	no	—
188	C₂×C₃⋊D₃	—	2	2	no	—
189	C₂×C₃⋊D₃	C₂×C₃×Q₈	1	4	yes	complemented
190	C₂×C₃×D₃	—	3	16	no	—
191	C₂×C₃×D₃	—	6	32	no	—
192	C₂×C₃×D₃	—	6	8	no	—
193	C₂×C₃×D₃	—	6	8	no	—
194	C₃²×C₄	—	2	32	no	—
195	C₃²×C₄	—	2	16	no	—
196	C₃²×C₄	—	2	4	no	—
197	C₃²×C₄	—	2	16	no	—
198	C₃²×C₄	C₂×#67	1	16	yes	—
199	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
200	C₃⋊Dic₃	—	2	2	no	—
201	C₃⋊Dic₃	—	2	4	no	—
202	C₃×Dic₃	—	6	16	no	—
203	C₃×Dic₃	—	6	8	no	—
204	C₂²×Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
205	C₂³×C₄	—	9	1	no	—
206	C₂²⋊Q₈	—	9	8	no	—
207	C₂×C₄⋊C₄	—	9	2	no	—
208	C₂×C₄⋊C₄	—	9	1	no	—
209	C₂×C₂²⋊C₄	—	9	2	no	—
210	C₃³	C₂×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
211	C₂³×C₃	—	2	4	no	—
212	C₂³×C₃	—	9	2	no	—
213	C₂³×C₃	—	9	4	no	—
214	C₂³×C₃	—	18	2	no	—
215	C₂³×C₃	—	18	2	no	—
216	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
217	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
218	C₂²×D₃	—	3	8	no	—
219	C₂²×D₃	—	3	16	no	—
220	C₂²×D₃	—	6	8	no	—
221	C₂²×D₃	—	6	8	no	—
222	C₃×Q₈	—	2	64	no	—
223	C₃×Q₈	—	2	32	no	—
224	C₃×Q₈	—	2	8	no	—
225	C₂×C₃×C₄	—	2	32	no	—
226	C₂×C₃×C₄	—	2	16	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	16	no	—
229	C₂×C₃×C₄	—	2	16	no	—
230	C₂×C₃×C₄	—	2	8	no	—
231	C₂×C₃×C₄	—	9	4	no	—
232	C₂×C₃×C₄	—	9	2	no	—
233	C₂×C₃×C₄	—	18	4	no	—
234	C₂×C₃×C₄	—	18	2	no	—
235	C₂×C₃×C₄	—	18	8	no	—
236	C₂×C₃×C₄	C₃×#67	1	16	yes	—
237	C₂×C₃×C₄	#638	1	4	yes	—
238	C₂×C₃×C₄	C₂²×C₃×D₃	1	16	yes	—
239	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
240	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	4	yes	—
241	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
242	C₂×Dic₃	—	3	8	no	—
243	C₂×Dic₃	—	3	16	no	—
244	C₂×Dic₃	—	6	16	no	—
245	C₂×Dic₃	—	6	8	no	—
246	C₄×D₃	—	6	32	no	—
247	C₂×C₃²	—	2	16	no	—
248	C₂×C₃²	—	2	4	no	—
249	C₂×C₃²	—	2	4	no	—
250	C₂×C₃²	—	2	4	no	—
251	C₂×C₃²	#946	1	16	yes	complemented
252	C₂×C₃²	C₃×C₂²⋊Q₈	1	4	yes	complemented
253	C₂×C₃²	C₂×D₃×Q₈	1	4	yes	—
254	C₂×C₃²	C₂×#239	1	4	yes	—
255	C₂×C₃²	C₂²×#67	1	4	yes	—
256	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
257	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
258	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
259	C₃⋊D₃	—	2	4	no	—
260	C₃×D₃	—	6	16	no	—
261	C₂⁴	—	9	1	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
264	C₂²×C₄	—	9	2	no	—
265	C₂²×C₄	—	9	1	no	—
266	C₂²×C₄	—	9	4	no	—
267	C₂²×C₄	—	18	4	no	—
268	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
269	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
270	C₄⋊C₄	—	9	8	no	—
271	C₄⋊C₄	—	9	4	no	—
272	C₂²⋊C₄	—	9	8	no	—
273	C₂²×C₃	—	2	4	no	—
274	C₂²×C₃	—	2	8	no	—
275	C₂²×C₃	—	2	8	no	—
276	C₂²×C₃	—	2	8	no	—
277	C₂²×C₃	—	9	4	no	—
278	C₂²×C₃	—	18	2	no	—
279	C₂²×C₃	—	18	2	no	—
280	C₂²×C₃	—	18	8	no	—
281	C₂²×C₃	C₃×D₃×Q₈	1	8	yes	—
282	C₂²×C₃	C₃×#239	1	8	yes	—
283	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
284	C₂²×C₃	Q₈×C₃⋊D₃	1	2	yes	—
285	C₂²×C₃	#3832	1	2	yes	—
286	C₂²×C₃	C₂×#638	1	2	yes	—
287	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
288	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
289	C₂×D₃	—	3	16	no	—
290	C₂×D₃	—	6	32	no	—
291	C₂×D₃	—	6	8	no	—
292	C₂×D₃	—	6	8	no	—
293	C₃×C₄	—	2	32	no	—
294	C₃×C₄	—	2	16	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	2	16	no	—
297	C₃×C₄	—	18	4	no	—
298	C₃×C₄	—	18	2	no	—
299	C₃×C₄	C₂×C₃×#67	1	16	yes	—
300	C₃×C₄	C₂×#638	1	4	yes	—
301	Dic₃	—	6	16	no	—
302	Dic₃	—	6	8	no	—
303	C₃²	—	2	4	no	—
304	C₃²	C₂×#946	1	4	yes	complemented
305	C₃²	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic, complemented
306	C₂³	—	9	2	no	—
307	C₂³	—	9	4	no	—
308	C₂³	—	18	2	no	—
309	C₂³	—	18	2	no	—
310	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
311	Q₈	—	2	8	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	9	4	no	—
314	C₂×C₄	—	9	2	no	—
315	C₂×C₄	—	18	4	no	—
316	C₂×C₄	—	18	2	no	—
317	C₂×C₄	—	18	8	no	—
318	C₂×C₄	C₃×#638	1	4	yes	—
319	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	4	yes	—
320	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
321	C₂×C₃	—	2	4	no	—
322	C₂×C₃	—	2	4	no	—
323	C₂×C₃	—	2	16	no	—
324	C₂×C₃	—	2	4	no	—
325	C₂×C₃	—	18	4	no	—
326	C₂×C₃	C₃×#946	1	16	yes	complemented
327	C₂×C₃	#64155	1	4	yes	direct product factor
328	C₂×C₃	C₂×C₃×D₃×Q₈	1	4	yes	—
329	C₂×C₃	C₂×C₃×#239	1	4	yes	—
330	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
331	C₂×C₃	C₂×Q₈×C₃⋊D₃	1	1	yes	characteristic
332	C₂×C₃	C₂×#3832	1	1	yes	characteristic
333	C₂×C₃	C₂²×#638	1	1	yes	characteristic
334	D₃	—	6	16	no	—
335	C₂²	—	9	4	no	—
336	C₂²	—	18	2	no	—
337	C₂²	—	18	8	no	—
338	C₂²	—	18	2	no	—
339	C₂²	C₃×Q₈×C₃⋊D₃	1	2	yes	—
340	C₂²	C₃×#3832	1	2	yes	—
341	C₂²	C₂×C₃×#638	1	2	yes	—
342	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
343	C₄	—	2	4	no	—
344	C₄	—	18	4	no	—
345	C₄	—	18	2	no	—
346	C₄	C₂×C₃×#638	1	4	yes	—
347	C₃	—	2	4	no	—
348	C₃	C₂×C₃×#946	1	4	yes	complemented
349	C₃	C₂×#64155	1	1	yes	characteristic, direct product factor
350	C₂	—	18	4	no	—
351	C₂	C₃×#64155	1	4	yes	direct product factor
352	C₂	C₂×C₃×Q₈×C₃⋊D₃	1	1	yes	characteristic
353	C₂	C₂×C₃×#3832	1	1	yes	characteristic
354	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×Q₈	C₂
socle	C₂³×C₃³	C₂³
prime radical	C₂³×C₃×C₃⋊D₃	C₂²
hypercenter	C₂²×C₃×Q₈	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×C₂²⋊Q₈
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×Q₈	C₂	semidirect
3. C₃×#64155	C₂	direct (N × H)
5. C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	semidirect
6. C₂×C₃×#3750	C₂	semidirect
7. C₂×#64155	C₃	direct (N × H)
11. C₂×C₃³×Q₈	C₂²	semidirect
19. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
20. C₃×#3750	C₂²	semidirect
22. C₂²×C₃²×Q₈	D₃	semidirect
23. C₂²×C₃²×Q₈	C₂×C₃	semidirect
26. #64155	C₂×C₃	direct (N × H)
28. C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	semidirect
29. C₂×#3750	C₂×C₃	semidirect
37. C₂²×C₃×C₃⋊D₃	Q₈	semidirect
57. C₂×C₃²×Q₈	C₂×D₃	semidirect
58. C₂×C₃²×Q₈	C₂²×C₃	semidirect
74. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
75. #3750	C₂²×C₃	semidirect
86. C₂×C₃×C₃⋊D₃	C₂×Q₈	semidirect
92. C₂²×C₃×Q₈	C₃×D₃	semidirect
93. C₂²×C₃×Q₈	C₃⋊D₃	semidirect
109. C₂²×C₃⋊D₃	C₃×Q₈	semidirect
141. C₂×C₃³	C₂²⋊Q₈	semidirect
152. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
153. C₂×C₃×Q₈	C₂×C₃⋊D₃	semidirect
189. C₂×C₃⋊D₃	C₂×C₃×Q₈	semidirect
204. C₂²×Q₈	C₃×C₃⋊D₃	semidirect
210. C₃³	C₂×C₂²⋊Q₈	semidirect
251. C₂×C₃²	#946	semidirect
252. C₂×C₃²	C₃×C₂²⋊Q₈	semidirect
263. C₂×Q₈	C₂×C₃×C₃⋊D₃	semidirect
304. C₃²	C₂×#946	semidirect
305. C₃²	C₂×C₃×C₂²⋊Q₈	semidirect
326. C₂×C₃	C₃×#946	semidirect
327. C₂×C₃	#64155	direct (N × H)
348. C₃	C₂×C₃×#946	semidirect
349. C₃	C₂×#64155	direct (N × H)
351. C₂	C₃×#64155	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃³×Q₈	2
C₂²×C₃×C₄×C₃⋊D₃	2
C₃×#64155	2
C₂×C₃×#3752	2
C₂×C₃×C₄⋊(C₃⋊Dic₃)	2
C₂×C₃×#3750	2
C₂×#64155	3
C₂×C₃×#946	3

Subgroups — C2×C3×#64155 #13179564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64155 #13179564